polarity of water

19. Light in Water Light traveling in water of refractive index 1.33 is incident on a plate of glass with index of refraction 1.53. At what angle of incidence is the reflected light fully polarized?20. Completely Polarized (a) At what angle of incidence will the light reflected from water be completely polarized? (b) Does this angle depend on the wavelength of the light?

number pattern

Proper Fractions:              Fractions having numerator less than the denominator are called proper fractions.                   Example: `3/7, 7/13.`Improper Fractions:             Fractions having numerator that are larger than or equal to their denominators are called improper fractions.                   Example: `12/5, 6/6, 21/11.` Mixed Fractions:             Numbers having a whole number part and a fractional part are called mixed numbers. We denote a mixed number in the form a `b/c` .                   Example: `2 5/2, 1 1/3` . Decimal Fractions:            Fractions having denominator as 10, 100 or 1000 or any other higher power of 10 are called decimal fractions.                   Example: `4/100` ,` 35/1000.` Simple Fractions:          Fractions having both the numerator and denominator as whole numbers are called simple fractions.                   Example: 4/5, 6/95. Like and Unlike Fractions:            Fractions having the same denominators are called like fractions, whereas fractions having different denominators are called unlike fractions.                Example: `4/9, 1/9` are all like fractions.                               `3/5, 4/7` are all unlike fractions.

pressure definition

Introduction to vapour pressure mixture:Consider a mixture of liquids like water and alcohol in a container which is closed.The vapor presure exertedby each component is partial vapor presure of that component.First we would consider water vapor presure.

general knowledge facts

The zoogeography or the knowledge of the distribution of animals on the earth has led to the division of the world into a number of distinct zoogeographical (biogeo-graphical also) realms (Fig. 42.1). Originally these were based on the mammalian faunas of the various parts of the world, but their validity is general.

writing chemical formulas

    We have to find the equation of the line using the following formula`(y-y1)/(y2-y1)`=`(x-x1)/(x2-x1)`    Here (x1,y1) and (x2,y2) are the given two points.  Substitute the given points in the above formula we have to get the equation of the line.Example:(1, 3) and (4, 8) write the equation of the line that passing through the given two points by Method - 1Solution:Here x1 = 1 and y1=3 and x2=4 and y2=8The formula for equation of the line is `(y-y1)/(y2-y1)`=`(x-x1)/(x2-x1)`Substitute the x1, y1, x2 and y2 values in the above equation we have to get, `(y-3)/(8-3)`=`(x-1)/(4-1)`Simplifying this we can get, 3y=5x+4This is the equation of the line that passes through the given two points.

binomial formula

Q. 6. Explain Stefan's law of thermal radiation. (1996,2000,01,04)Ans. Stefan's Law : This law states that the radiant energy '£' emitted from the unit area of surface of a perfect black-body in unit time is proportional to the 4th powerof the absolute temperature of the body. -i.e. Â£ oc T4 or £ = oT4 _Where c is a constant which is called Stefan's constant and its value is 5 • 67 x 10~8 j/m2-s-K4.Suppose that a black-body having absolute temperature T\ is surrounded by a black enclosure at absolute temperature Tz- The body will emit a7|4 joule energy per second per unit area of its surface. At the same time it will absorb <rlf joule energy per second per unit area from the surrounding atmosphere. Thus net energy emitted by unit area of the body in unit time will be£1-£2=o(rl4-T24)The rate of emission of radiant energy from the area A of a body with emissive power e, at the absolute temperature T is given byE = oT4eAQ. 7. Establish Newton's law of cooling from Stefan's law. (1996,2000,01,04)Ans. Newton's Law of Cooling : This law states that if the temperature difference between a body and its surrounding is small then rate of cooling of the body (or rate of loss of heat by the body) is proportional to the temperature difference between the body and surroundings.i.e. rate of loss of heat « temperature differenceDerivation of Newton's Law From Stefan's Law: Suppose that a body is placed in air for cooling. Let the absolute temperature of the body and that of surroundings be Ti and T. Let e be the emissive power of the body. Then according to Stefan's law the net rate of loss of heat by the body is given by.A£ = ae(Ti4-T4)Let Ti-T + t wheret = 7} -T > 0is smallthen AE = ce[(T + t)i-T4]= aeT4 jl + 4—.......j -1 (Using Binomial Expansion)t < T, hence ^ is very small, hence higher degrees of ^ are neglected.= 4oeT3fv Atmosphere is very big as compared to the body, hence its temperature remains almost constant.Hence, rate of heat loss oc t (temperature difference)Q. 8. Draw spectral distribution curves of black-body radiation and write the effect of rise in temperature on it. (1996,2001)Or Draw the curves between energy and wavelength at different temperatures of a black-body radiations and write the conclusions drawn from these curves. (2003)Ans. Spectral Distribution of Black-Body Radiation : A perfect black-body, when heated upto high temperature, emits radiation of all possible wavelengths, that is why it is called full radiator. In 1899, two scientists Lummer and Pringsheim studied the spectral energy distribution in black-body radiation at differenl temperatures. They heated the black-body at differenl temperatures and at each temperature they plotted the radiant energy, emitted at different wavelengths againsl wavelength. The general shape of these curves are shown in the fig. 13 -2.Following conclusions were drawn from these graphs:(i) At a given temperature, the radiant energy 'E\ emitted by the black-body at wavelength 'A.' first increases with the wavelength and attains a maxima at a certain wavelength and then goes on decreasing.(ii) At a given temperature, maximum energy is emitted at a certain wavelength which is denoted by Xm.(iii) As the temperature is increased, the energy 'Ex emitted at wavelength X is also increased for each wavelength.(iv) The product of absolute temperature T of black-body and wavelength X,„ at which maximum energy is emitted, is a constant.i.e. XmT = b (constant)This law is called Wein's displacement law and the constant 'b' is called Wein's constant.From this law we can observe that, at low temperatures the maximum energy is emitted at larger wavelengths, but as the temperature is increased more energy is emitted in shorter wavelengths and maximum energy peak is shifted towards shorter wavelengths (see graphs).(iv) The area under these curves increases with increasing temperature directly as the 4th power of the absolute temperature of the body. That means the total radiant energy (measured by the area under the curve) emitted by the body is directly proportional to 4th power of the absolute temperature.i.e. ExT4Thus Stefan's law is also verified by these curves.Q. 9. Explain Planck's hypothesis of radiation. Discuss its importance in modern physics. (1997,98,99)Or State Planck's hypothesis. (2004)Ans. Planck's Hypothesis: According to this hypothesis, emission or absorption of radiant energy is not continuous process but is takes place in the form of small packets of energy. Each such packet is called a photon or quanta. The energy associated with a photon of radiation having frequency v is hv. Here 'h' is a constant called Planck's constant. Thus we can conclude that energies emitted by a body can be hv, 2hv,3hv....(integer multiple of hv) but not in between.Classical mechanics and thermo-dynamics could not explain the spectral energy distribution in black-body radiation. Planck, used his hypothesis and derive a formula to explain the spectral energy distribution in black-body radiation and found it in close agreement with the results of Lummer and Pringsheim experiments. Further Einstein successfully explained photo-electric effect on the basis of Planck's hypothesis. In this way Planck's hypothesis gained recogni tion.Q. 10. Find the expression for kinetic mass and momentum of photon using Planck's hypothesis. (1999,2004)Ans. Momentum of Photon: According to Planck's hypothesis, the rest mass mo of photon is zero and each photon travels with the speed of light c.If v is the frequency of photon, then its energy will be E = hv. Further if m is the kinetic mass of photon then by mass energy relation, we haveE = mc2.2 ' hv h f v 1)E = hv = mc => m = = — '•' ~ = -c2 cX V c X):. Kinetic mass of photon m = ~= —v c2cXIf p is the linear momentum of photon, thenp = kinetic mass x velocityor p=mc or p = (v velocity = c)h hvor p = — = —c/v c (â– -• X = c/v)Momentum p = — = —y X c

in situ conservation

In situ conservation is the most appropriate method to maintain species of wild animals and plants in their natural habiats. This approach in-cludes protection of total ecosystems through a network of protected areasThe common natural habitats (protectedareas) that have been set for in situ conservation ofwild animals and plants include —1. National parks2. Wildlife sanctuaries3. Biosphere reserves4. Several wetlands, tnangrooves and coralreefs.5. Sacred grooves and Lakes.In situ conservation ilso includes the intro-duction of plants and ani mal species back intoagricultural, horticultural and animal husbandrypractices so that they are cultivated/reproduced fortheir reuse by the farmers/animal husbandrypeople. Farmers and horticulturists have beentraditionally maintaining large genetic diversity ofcrop plants/flowers by savir g seeds for next plant-ing season by a wide variety of indegenously developed practices. For example, tubers,rhizomes, bulbs and seeds of large variety of plant species ai e stored by the far ners/horticulturists fortheir cultivation in the next sieason. Similarly, native species of cattle, which are better adapted to dis-eases, drought and other adverse conditions, arebeing maintained by animal husbandry people.

heat of neutralization

The heat of neutralization of all strong acids and bases are the same in dilute solution. It can be explained easily on the basis of this theory. According to this theory, the strong acids and bases are completely ionised in solution. They combine to form a highly ionised salt and feebly ionised water and since in all cases water is formed, the heat produced should be same. Heat of neutralization is, in fact, the heat of formation of water from H+ and OH" ions, which is always the same irrespective of the nature of acids and bases.H+ + CI" + Na+ + OH" Na+ + CF + H20 + 13-7k calsor H+ + OH"—»H20 + 13-7 k cals

matrix division

A AEROBIC RESPIRATION oxidation of food in the presence of oxygen ANAEROBIC RESPIRATION oxidation of food in the absence of oxygep ANTIBIOTIC medicine that kills disease-causing bacteria ANUS opening at one end of the digestive tract through which undigested food leaves the body ATP (adenosine triphosphate) small molecule in a cell which can store, transfer or release energy AUTOTROPHS organisms that make their own food AXON long fibre thai extends from the cell body of a neuronB  BALL AN D SOCKET JOINT joint in which end of one bone is rounded, which fits into the hollow part of the other bone BERI BERI condition caused due to deficiency of vitamin B BOWMAN'S CAPSULE cup-shaped structure at one end of a nephron BRONCHUS {plural bronchi) thin pipe that branches off from the trachea to enter a lung C CAMBIUM lateral meristematic tissue that produces new xylem and phloem cells in a stem CARNIVORES animals that eat other animalsCELL BODY central part of a neuron CELL WALL structure in plant cell Outside the cell membrane CENTRIOLE organelle in animal cells which helps in cell division CHLOROPLASTplastid containing chlorophyll CHROMOPLAST plastid containing coloured pigments CHROMOSOME small, thread-like structure in the nucleus of a cell CISTERNAE flattened sac-like vesicles of endoplasmic reticulum and golgi bodiesCONNECTIVE TISSUE tissue that joins and supports different body parts CRISTAE folds of the inner membrane of mitochondrion CUTANEOUS RESPIRATION exchange of gases through the skin of animals CYTOPLASM jelly-like'substance that fills most of the cell D  DENDRITE short branched extension of a neuronDERMIS inner thick layer of the skin DIGESTION process of converting complex food into a simple, absorbable form E ENDOPLASMIC RETICULUM network of membranes in the cytoplasm EPIDERMIS outer layer of the skin EPITHELIAL TISSUE layer of cells that covers the external surface of the body and also forms the lining of the internal organs EXTEN50R muscle that contracts to straighten a part of the body F FLEXOR muscle that contracts and causes a part of the body to bend towards the bodyGGEOTROPiSM movement of plant parts in response to force of gravity GLAND organ that produces secretions GLIDING JOINT joint that allows sliding movement between two bonesH HAEMOGLOBIN red oxygen-carrying pigment in RBCs HERBIVORES animals that feed or plantsIHETEROTROPHS organisms that obtain food directly or indirectly from plantsINTERNAL RESPIRATION using oxygen to break down food and release energy in the bodyJJOINT place where two or more bones meet together in the skeletonkKIDNEY organ that filters wastes from the bloodL LACUNA tiny fluid-filled spaces in cartilagenous connective tissue LIGAMENT strong band of connective tissue that hold two or more bones at jointsLIVER organ that produces bile which helps in digestion LOCOMOTION movement of the entire body of the animal from one place to another LYMPH colourless fluid connective tissue; it surrounds cells of the bodyM MATRIX ground substance of connective tissue in which cells are presentMERISTEMATIC TISSUE plant tissue made up of cells that divide continuously MICROORGANISMS living organisms that can be seen only through a microscope MITOCHONDRION {plural mitochondria} rod-like organelle which helps get energy from food MUSCULAR SYSTEM system consisting of the muscles in the body MUSCULAR TISSUE animal tissue that forms the muscles in the body NNASTIC MOVEMENTS non-directional plant movements that occur in response to environmental stimuli NERVE bundle of nerve cells that carry messages throughout the body NEURON specialized cell that makes up the brain, spinal cord and nerves O OESOPHAGUS tube that leads from the mouth to stomach ORGAN part of an organism made up of one or more .types of tissues, which performs a specific function ORGAN SYSTEM group of organs that work togetherORGANELLE small structure found in the cytoplasm of a cellP PALISADE TISSUE parenchyma tissue in leaves containing chloroplastsPARENCHYMA plant tissue composed of simple cells with thin wailsPERMANENT TISSUE plant tissue made up of ceils that cannot dividePLASMA liquid part of blood in which the blood cells floatPROTOZOA group consisting of only single-celled animalsRRED BLOOD CELL cell that transports oxygenRESPIRATION process of taking in oxygen and using it,to release energy from foodRESPONSE reaction of an organism to a stimulus S SCAVENGERS animals that consume dead animals and dispose them SCLERENCHYMA hard and strong supporting tissue made up of dead and thick-walled cells SIEVE CELL elongated cell of phloem having minute pores SPECIES a group of living organisms which can breed among themselves SPIRILLA spiral-shaped bacteriaTTENDON connective tissue that joins skeletal muscles to bones TISSUE cells that have similar structure and perform similar functions TRACHEA tube passing through the neck that divides into two bronchi TRACHEID tube-like dead cell in xylem TRANSPIRATION loss of water from leaves through the stomataV VACUOLE sac-like organelle which stores food, water or wastesVASCULAR BUNDLE xylem and phloem tissues present togetherVASCULAR TISSUE permanent tissue in plants made up of xylem and phloemVERTEBRA smalt bone of a vertebral columnVESICLE small, round membranous structure in a cellVESSEL non-living part of xylem that, has tube-like ceils joined end to endW WARM BLOODED ANIMAL animal ' that has a constant body temperatureWHITE BLOOD CELL cell in blood that, fights disease-causing microorganisms xXYLEM complex vascular tissue that transports water and mineral salts

aldol condensation

(i) With hydroxylamine : Aldehydes and ketones react with hydroxylamine to give corresponding oximes containing (> C = N - OH) group. The reaction is carried in the presence of a base like NaOH.(a) Acetaldehyde with hydroxylamine gives acetaldoxime. h hI ________ICH3 - C = Jo + _H2]nOH ) CH3 - cf NOH + HzO *acetaldehyde acetaldoximeCH3 CH3 ....CH3 - c =€f +~H21NOH ) CH3 - c = NOH + H20i____.Z'i ; - acetone acetoxime (ii) With hydrazine : Aldehydes and ketones react with hydrazine to give corresponding hydrazones. h h 1 r-___„ * IH3C-C = jO + H2|- N-NH2-> H3C-C =N-NH2 + H2O acetaldehyde acetaldehyde hydrazone ch3 ch3 I .1 h3c - c =jo_ + JH2_j- n - nh2—> h3c - c = n - nh2 + h2oacetone acetone hydrazone(iii) With phenylhydrazine : Aldehydes and ketones react with phenylhydrazine to give the corresponding phenylhydrazone.(a) Acetaldehyde with phenylhydrazine gives acetaldehyde phenylhydrazone.H HI Ich3 - c = jo + H2j nnhc6h5 -4 ch3 - c = nnhc6h5 + h2oacetaldehyde acetaldehyde phenylhydrazone(b) Acetone with phenylhydrazine gives acetone phenylhydrazone.CH3 CH3I ICH3- C=iO + H^N -NH-CgHs —» CH3-C = N-NH_C6H5 +H20acetone acetone phenylhydrazone(iv) Aldol condensation : Aldehydes or ketones containing active a-hydrogen atom, i.e. hydrogen on the carbon atom adjacent to carbonyl group (a-carbon atom) give P-hydroxy aldehyde, i.e. aldol or p-hydroxy ketone respectively on warming with dilute solution of sodium hydroxide (10%) or sodium carbonate. This reaction is known as aldol condensation. Formaldehyde and benzaldehyde do not give this reaction as they have no a-hydrogen atom. Aldol contains an aldehydic group (-cho) and also alcoholic group (-oh). (Aid for aldehyde group and -ol for alcohol, hence the name aid + ol = aldol.)(a) This is an addition reaction. This addition takes place in such a way that a-carbon atom of one aldehyde molecule is attached to the carbonyl carbon of the second molecule and a-hydrogen of one aldehyde is attached to carbonyl oxygen of the other to give P-hydroxy aldehvde.Aldol loses one water molecule on heating with an acid to form unsaturated aldehyde.When aldol condensation takes place between two molecules of different aldehydes, then it is known as cross aldol condensation. h h I „ Na2C03 I „ch3ch2c =o+hch2c = o-> ch3ch2-cp-ch2-c = o| solution ( |h oh hpropionaldehyde acetaldehyde propionaldol(b) Certain ketones like acetone in presence of barium hydroxide or sodium hydroxide give diacetone alcohol (p-hydroxy ketone). CH3 H O CH3 H O I I II Ba(OH)2 J J II CH3 -C + H-c«-c-CH3---^ cha-pc-aC -C-CH3Oh oh hacetone acetone diacetone alcohol(4-hydroxy, 4 -methyl, pentan-2-one)

modern periodic table

Learn table of Pythagorean related trigonometric identities:cos2θ + sin2θ = 1sin θ = ± `sqrt(1 - cos^2 theta)`cos θ = ± `sqrt(1 - sin^2 theta)`sin θ = `1/(csc theta)`cos θ = `1/(sec theta)` tan θ = `1/(cot theta)`csc   θ = `1/(sin theta)` sec   θ = `1/(cos theta)`  cot   θ = `1/(tan theta)`1 + tan2θ = sec2θ1 + cot2θ = csc2θsin θ = ± `(tan theta)/(sqrt(1 + tan^2theta))`cos θ = ± `1/(sqrt(1 + tan^2theta))`tan θ = Â± `sqrt(sec^2 theta - 1)`csc θ = ± `(sqrt(1 + tan^2theta))/(tan theta)`    sec θ = ± `(sqrt(1 + tan^2theta))`cot θ =  ± `1/(sqrt(sec^2 theta - 1))`Learn table of symmetry related trigonometric identities:sin (-θ) = - sin θ       cos (-θ) = + cos θ      tan (-θ) = - tan θ   csc (-θ) = - csc θ  sec (-θ) = + sec θ      cot (-θ) = - cot θ     sin (∏ - θ) = + sin θcos (∏ - θ) = - cos θtan (∏ - θ) = - tan θcsc (∏ - θ) = + csc θsec (∏ - θ) = - sec θcot (∏ - θ) = - cot sin (`pi/2` - θ) = + cos θcos (`pi/2` - θ) = + sin θtan (`pi/2` - θ) = + cot θcsc (`pi/2` - θ) = + sec θsec (`pi/2` - θ) = + csc θcot (`pi/2` - θ) = + tan θLearn table of shifts and periodicity related trigonometric identities:sin (θ + `pi/2` ) = + cos θ cos (θ + `pi/2` ) = - sin θ tan (θ + `pi/2` ) = - cot θ   csc (θ + `pi/2` ) = + sec θsec (θ + `pi/2` ) = - csc θ     cot (θ + `pi/2` ) = - tan θ    sin (θ + ∏) = - sin θcos (θ + ∏) = - cos θtan (θ + ∏) = + tan θcsc (θ + ∏) = - csc θsec (θ + ∏) = - sec θcot (θ + ∏) = + cot θsin (θ + 2∏) = + cos θcos (θ + 2∏) = + sin θtan (θ + 2∏) = + cot θcsc (θ + 2∏) = + sec θsec (θ + 2∏) = + csc θcot (θ + 2∏) = + tan θ

process mapping examples

1)What is the addition of the following array in math.     Solution     The given array is as follows,             Now we can add the numbers .       This is the addition process.2)What is the difference of the following Array?   Solution     The given array is as follows,              Now subtract the second group from the first group.       This is the process of the subtraction.3) Multiply the following array.     Solution     Here we can multiply the first row of the first group into all columns of the second group.     So the multiplication is as follows,   This is the multiplication process.

math test generator

 Example 1- Study online exponential generating functionDraw the graph for given exponential function `f(x)=(50/25)+e^x`Solution:      We have to find the corresponding value of f(x) by substituting the value of x. After find out the f(x)-value for all x-value make them into table format as represented below.`f(x)=(50/25)+e^x``f(0)= (50/25)+e^0=3``f(1)= (50/25)+e^1=3.718``f(2)= (50/25)+e^2=9.38``f(3)= (50/25)+e^3=22.08`x0123f(x)34.7189.38922.08       When plotting the graph we have to assume scale as per our x and f(x) value. After find out the x-value and y-value ie f(x) we have to mark the points on a graph sheet then we have to join the points as coordinate respectively.Scale:In x-axis 1 unit=1 cmIn y-axis 1 unit=5 cmGraph for the given function is given below

equation for photosynthesis

Before 1930, it was considered by physiologists that one molecule each of CO2 and H2O form a molecule of formaldehyde (HCHO), of which 6 mols are polymerized to one molecule of glucose (a hexose sugar).LightCO2 + H2O -> HCHO + 02Chlorophyll (Formaldehyde) Polymerization6CH20 (or 6HCHO)-> C6Hi206(Formaldehyde) (Hexose sugar)However formaldehyde is a toxic substance which may kill the plants. Hence, formaldehyde hypothesis could not be accepted.On the basis of discovery of Nicolas de Saussure (1804) that "The amount of O2 released fromplants is equal to the amount of CO2 absorbed by plants", it was considered that O2 released inphotosynthesis comes from CO2, but later on it was proved wrong.In 1930, C.B. van Niel proved that, sulphur bacteria use H2S (in place of water) and CO2 tosynthesize carbohydrates as follows :6CO2 + 12H2S-> C6H1206 + 6H20 + 12SThis led van Niei to the postulation that in green plants, water (H2O) is utilized in place of H2Sand O2 is evolved in place of sulphur (S).6C02 + 12H20-> C6H1206 + 6H20 + 602This was confirmed by Ruben and Kamen in 1941 using chlorella a green alga. He used water(H20), having heavy isotope of oxygen (O18), oxygen of 18 atomic weight (normal oxygen is of 1618atomic weight) and found that oxygen released in the process of photosynthesis was of O 0 type (i.e., heavy oxygen). On the contrary when CO28 was used, the released oxygen was of normal type, i.e., O26. From this it can be concluded that, oxygen released by green plants comes from splitting of water (oxidation of water).Furthermore because 6 molecules of oxygen can be produced by 12 molecules of water only, the summary equation of photosynthesis is written as follows :Oxygenic and Anoxygenic Photosynthesis(i) Oxygenic photosynthesis (with evolution of O2) is found in eukaryotes and cyanobacteria. Water acts as H-donar to produce NADP.2H thus photolysis of water is essentialLightC02 + H2O-> Sugar + OxygenChlorophyll(ii) Anoxygenic photosynthesis (without the evolution of O2) is found in photosynthetic bacteria. H2S acts as H-donar and no photolysis of water is needed.LightCO2 + H2S-> Sugar + Sulphur or other oxidised compounds orChlorophyll some other inorganic compoundsAnoxygenic photosynthesizing forms are strictly anaerobic and thus O2 acts as a poison for them.

alternating current generator

An AC circuit consists of combinations of circuit elements like resistors, inductors and capacitors fed by an AC generator which provides sinusoidal voltage. To analyse an AC circuit is to find the current through the given circuit and the phase difference between the current and the applied voltage.

grade 12 math

Olfactory I: This sensory cranial nerve located in olfactory bulb of brain and has olfactory receptors for sense of smell.Optic Nerve II: This sensory cranial nerve leads from eyes to thalamus. It is responsible for sense of sight of retina.Oculomotor Nerve III: This motor nerve arise from midbrain and leads to eye muscles (including eyelids and lens) and pupil. This nerve is associated with eye movement and pupil constriction.Trochlear Nerve IV: This motor nerve arises from midbrain and leads to eye muscles. It works with oculomotor nerve to produce the eye movements.Trigeminal Nerve V: This cranial nerve, located in pons, has both sensory and motor nerve fibers. It leads to most of the face (including eyes and mouth) and carry somatosensory information to face, head and chewing muscles of jaws.Abducens Nerve VI: Another mixed cranial nerve, located in pons. This is associated with eye movement.Facial VII: This is mixed cranial nerve, located in pons. Facial nerve splits into several branches that control the muscles used for facial expressions (smiling, frowning etc).  It also stimulates salivary glands to produce saliva.A branch of facial nerve carries taste sensation from the front 2/3 part of the tongue. The facial nerve comes out just below the ear and passes through the salivary gland. Part of facial nerves carries sensation from the outside of the ear.Vestibulocochlear VIII: This sensory cranial nerve leads from inner ear to pons and is associated with sense of hearing and balance.Glossopharyngeal IX: This is a mixed cranial nerve, located in medulla oblongata. This is sensory to posterior of throat (pharynx) and is associated with taste sensation from rest 1/3 part of tongue. This is also associated with gag reflexes.Vagus X: This is a sensory cranial nerve that leads from many visceral organs to medulla oblongata. It carries somatosensory information from organs of thoracic, abdominal cavity including heart and from that of gastrointestinal tract.Spinal Accessory Nerve XI: This motor nerve arises from medulla oblongata and leads to muscles of neck, back and larynx. It controls the head movement.Hypoglossal Nerve XII: This motor nerve arises from medulla oblongata and controls the muscles of tongue.

algebra factoring

Sec. 19-2 â–¡ Thermometers and Temperature Scales1. Fahrenheit and Celsius At what temperature is the Fahrenheit scale reading equal to (a) twice that of the Celsius and (b) half that of the Celsius?2. Oyntyakon (a) In 1964, the temperature in the Siberian village of Oymyakon reached — 71°C. What temperature is this on the Fahrenheit scale? (b) The highest officially recorded temperature in the continental United States was 134°F in Death Valley, California. What is this temperature/on the Celsius scale?Sec. 19-4 â–¡ Heating, Cooling, and Temperature3. Hot and Cold It is an everyday observation that hot and cold objects cool down or warm up to the temperature of their surroundings. If the temperature difference AT between an object and its surroundings (AT = Tobj - Tsur) is not too great, the rate of cooling or warming of the object is proportional, approximately, to this temperature difference; that is,where A is a constant. (The minus sign appears because AT decreases with time if AT is positive and increases if AT is negative.) This is known as Newton's law of cooling, (a) On what factors does A depend? What are its dimensions? (b) If at some instant f, = 0 the temperature difference is Ar1; show that it isat a later time t2.4. House Heater The heater of a house breaks down one day when the outside temperature is 7.0°C. As a result, the inside temperature drops from 22°C to 18°C in 1.0 h. The owner fixes the heater and adds insulation to the house. Now she finds that, on a similar day, the house takes twice as long to drop from 22°C to 18°C when the heater is not operating. What is the ratio of the new value of constant A in Newton's law of cooling (see Problem 3) to the previous value?Sec. 19-5 â–¡ Thermal Energy Transfer to Solids and Liquids5. A Certain Substance A certain substance has a mass per mole of 50 g/mol. When 314 J of thermal energy is transferred to a 30.0 g sample, the sample's temperature rises from 25.0°C to 45.0°C. What are (a) the specific heat and (b) the molar specific heat of this substance? (c) How many moles are present?6. Diet Doctor A certain diet doctor encourages people to diet by drinking ice water. His theory is that the body must burn off enough fat to raise the temperature of the water from 0.00°C to the body temperature of 37.0°C. How many liters of ice water would have to be consumed to burn off 454 g (about 1 lb) of fat, assuming that this much fat burning requires 3500 Cal be transferred to the ice water? Why is it not advisable to follow this diet? (One liter = 103 cm3. The density of water is 1.00 g/cm3.)7. Minimum Energy Calculate the minimum amount of energy, in joules required to completely melt 130 g of silver initially at 15.0°C.8. How Much Unfrozen How much water remains unfrozen after 50.2 kJ of thermal energy is transferred from 260 g of liquid water initially at its freezing point?9. Energetic Athlete An energetic athlete can use up all the energy from a diet of 4000 food calories/day where a food calorie = 1000 cal. If he were to use up this energy at a steady rate, how would his rate of energy use compare with the power of a 100 W bulb? (The power of 100 W is the rate at which the bulb converts electrical energy to thermal energy and the energy of visible light.)10. Four Lightbulbs A room is lighted by four 100 W incandescent lightbulbs. (The power of 100 W is the rate at which a bulb converts electrical energy tff thermal energy and the energy of visible light.) Assuming that 90% of the energy is converted to thermal energy, how much thermal energy is transferred to the room in 1.00 h?11. Drilling a Hole A power of 0.400 hp is required for 2.00 min to drill a hole in a 1.60 lb copper block, (a) If the full power is the rate at which thermal energy is generated, how much is generated in Btu?_(b) What is the rise in temperature of the copper if the copper absorbs 75.0%-of this energy? (Use the energy conversion 1 ft- lb = 1.285 X lO^Btu.)12. How Much Butter How man^ grams of butter, which has a usable energy content of 6.0 Cal/g (= 6000 cal/g), would be equivalent to the change in gravitational potential energy of a 73.0 kg man who ascends from sea level to the top of Mt. Everest, at elevation 8.84 km? Assume that the average value of g is 9.80 m/s2.13. Immersion Heater A small electric immersion heater is used to heat 100 g of water for a cup of instant coffee. The heater is labeled "200 watts," so it converts electrical energy to thermal energy that is transferred to the water at this rate. Calculate the time required to bring the water from 23°C to 100°C ignoring any thermal energy that transfers out of the cup.14. T\ib of Water One way to keep the contents of a garage from becoming too cold on a night when a severe subfreezing temperature is forecast is to put a tub of water in the garage. If the mass of the water is 125 kg and its initial temperature is 20°C, (a) how much thermal energy must the water transfer to its surroundings in order to freeze completely and (b) what is the lowest possible temperature of the water and its surroundings until that happens?15. A Chef A chef, on finding his stove out of order, decides to boil the water for his wife's coffee by shaking it in a thermos flask. Suppose that he uses tap water at 15°C and that the water falls 30 cm each shake, the chef making 30 shakes each minute. Neglecting any transfer of thermal energy out of the flask, how long must he shake the flask for the water to reach 100°C?16. Copper Bowl A 150 g copper bowl contains 220 g of water, both at 20.0°C. A very hot 300 g copper cylinder is dropped into the water, causing the water to boil, with 5.00 g being converted to steam. The final temperature of the system is 100°C. Neglect energy transfers with the environment, (a) How much energy (in calories) is transferred to the water? (b) How much to the bowl? (d) What is the original temperature of the cylinder?17. Ethyl Alcohol Ethyl alcohol has a boiling point of 78°C, a freezing point of -114°C, a heat of vaporization of 879 kJ/kg, a heat of fusion of 109 kJ/kg, and a specific heat of 2.43 kJ/kg • C°. How much thermal energy must be transferred out of 0.510 kg of ethyl alcohol that is initially a gas at 78°C so that it becomes a solid at -114°C?18. Metric-Nonmetric Nonmetric version: How long does a 2.0 x 105 Btu/h water heater take to raise the temperature of 40 gal of water from 70°F to 100°F? Metric version: How long does a 59 kW water heater take to raise the temperature of 150 L of water from 21°C to 38°C?19. Buick A 1500 kg Buick moving at 90 km/h brakes to a stop, at a uniform rate and without skidding, over a distance of 80 m. At what average rate is mechanical energy transformed into thermal energy in the brake system?20. Solar Water Heater In a solar water heater, radiant energy from the Sun is transferred to water that circulates through tubes in a rooftop collector. The solar radiation enters the collector through a transparent cover and warms the water in the tubes; this water is pumped into a holding tank. Assume that the efficiency of the overall system is 20% (that is, 80% of the incident solar energy is lost from the system). What collector area is necessary to raise the temperature of 200 L of water in the tank from 20°C to 40°C in 1.0 h when the intensity of incident sunlight is 700 W/m2?21. Steam What mass of steam at 100°C must be mixed with 150 g of ice at its melting point, in a thermally insulated container, to produce liquid water at 50°C?22. Iced Tea A person makes a quantity of iced tea by mixing 500 g of hot tea (essentially water) with an equal mass of ice at its melting point. If the initial hot tea is at a temperature of (a) 90°C and (b) 70°C, what are the temperature and mass of the remaining ice when the tea and ice reach a common temperature? Neglect energy transfers with the environment.23. Ice Cubes (a) Two 50 g ice cubes are dropped into 200 g of water in a thermally insulated container. If the water is initially at 25°C, and the ice comes directly from a freezer at -15°C, what is the final temperature of the drink when the drink reaches thermal equilibrium? (b) What is the final temperature if only one ice cube is used?24. Thermos of Coffee An insulated Thermos contains 130 cm3 of hot coffee, at a temperature of 80.0°C. You put in a 12.0 g ice cube at its melting point to cool the coffee. By how many degrees has your coffee cooled once the ice has melted? Treat the coffee as though it were pure water and neglect energy transfers with the environment.Sec. 19-8 â–  Some Special Cases of the First Law of Thermodynamics25. Gas Expands A sample of gas expands from 1.0 m3 to 4.0 m3 while its pressure decreases from 40 Pa to 10 Pa. How much work is done by the gas if its pressure changes with volume via each of the three paths shown in the P-V diagram in Fig. 19-30?26. Work Done Consider that 200 J of work is done on a system and 70.0 cal of thermal energy is transferred out of the system. In the sense of the first law of thermodynamics, what are the values (including algebraic signs) of (a) W, (b) Q, and (c) A£""?27. Closed Chamber Gas within a closed chamber undergoes the cycle shown in the P-V diagram of Fig. 19-31. Calculate the net thermal energy added to the system during one complete cycle.28. Thermodynamic A thermodynamic system is taken from an initial state A to another state B and back again to A, via state C, as shown by path ABCA in the P-V diagram of Fig. 19-31a. (a) Complete the table in Fig. 19-32b by filling in either + or - for the sign of each thermodynamic quantity associated with each step of the cycle, (b) Calculate the numerical value of the work done by the system for the complete cycle ABCA.29. From i to / When a system is taken from state i to state / along path iaf in Fig. 19-33. Q = 50 cal and W = 20 cal. Along path ibf, Q = 36 cal. (a) What is W along path ibfl (b) If W = -13 cal for the return path fi, what is Q for this path? (c) Take Efl = 10 cal. What is E'fl (d) If Ef' = 22 cal, what are the values of Q for path ib and path bp.30. Gas Within Gas within a chamber passes through the cycle shown in Fig. 19-34. Determine the thermal energy transferred by the system during process CA if the thermal energy added Qab>Sec. 19-9 â–¡ More on Temperature Measurement

alveolar gas equation

The state of a given mass of gas is determined by three parameters namely, pressure, volume and temperature. When a gas is heated both its pressure and volume undergo a change. Thus a gas has two different coefficients of expansion.Volume coefficient" the coefficient of expansion of a gas at constant pressure.Pressure coefficient" coefficient of expansion of a gas at constant volume.The volume coefficient of a gas is defined as the ratio of increase in volume of a given mass of gas per degree rise of temperature to its volume at 0°C when pressure is kept constant. It is denoted by a. If VQ and V be the volumes of a given mass of gas at 0°C and t°C respectively and at the same pressure thenIf Vj and V2 be the volumes of a given mass of gas at C and t2 C respectively pressure remaining constant then using equation (2) it can be proved thatThe pressure coefficient of a gas is defined as the ratio of increase in pressure of a given mass of gas per degree rise of temperature to its pressure at 0°C when volume is kept constant. It is denoted by (3.

force acts

Now let us move from forces' in solids to forces in liquids. If a solid is placed into a liquid the solid will push the liquid out of its path with the result that the liquid will push back on the solid. This is an example of Newton's Third law of motion which states 'action and reaction are equal and opposite'. The upward force exerted by liquids on objects placed in the liquid is known as the upthrust. Upthrust acts on a body in a liquid even if the body is resting on some support such as the bottom of a vessel, provided the space between the body and the support is not evacuated. A marble dropped into water in a beaker will sink to the bottom of the beaker as in Fig. 3.13(a). The forces acting on the marble are its weight W, the upthrust U of the water and the reaction R of the base of the beaker; W = R + U. A marble resting in a hole in the container will not have an upthrust acting on it. This time the downward forces on the marble are its weight W and the weight w of the liquid above it pressing the marble into the hole. The total reaction on the edges of the hole R2 = W + w, which is much greater than the reaction R in the beaker where R = W — U.

hybridized

3. Simple interaction (9:3:3:1 ratio)Bateson and Punnett gave classical example in fowl to show two genes influencing the same character. There are four types of combs recognised among fowls—pea, rose, walnut and single. These are caused by two allelomorphic pairs of genes symbolised by PPrr (pea), ppRR (rose). A cross between the two produces a new comb form in Fj generation called walnut (RrPp). The F[ generation on selfing produced F2 generation as follows—9 walnut, 3 pea, 3 rose and 1 single. Thus when dominant gene P is present alone (without other dominant gene R) the comb is pea type. When R is present alone, the comb is green or red or rose. But when both P and R are present there is an interaction and the comb becomes walnut. When no dominant gene is present, the comb is of double recessive, i.e., single type (Fig. 65.4).A Summary Chart of Common Types of Interaction of Genes Observeds.No.FactorsExamplesF2Phenotypic ratioP,Parent-1P2Parent-2FiIndividualF2 Population (Genotype and Phenotype)1.Simple interactionComb colour in fowl9:3:3:1RRpp Rose combrrPP Pea combR-P-Walnut combR-P-Walnut (9)R-pp Rose (3)rrP-Pea(3)rrpp Single (1)2.Epistasis(dominantepistasis)Body colour in dogsaaBB BlackAAbb WhiteA-B-White| A-B-| (9) WhiteA-MT~j (3) White 1aaB-(3) Blackaabb (1) BrownSeed coat colour in Cajanus cajan12:3:1BBrr Black seededbbRR Red seededB-R-Black seededir B-R-1 (9) Black L_____B-rr 1 (3) Black 1bbR-(3) Redbbrr (1) White3.Supplementary factors (Recessive epistasis)Flower colour in Antirrhinum9:3:4AAbb IvoryaaBB WhiteA-B-MagentaA-B- (9) MagentaA-bb (3) Ivory, aaB-1 (3) Whiteaabb (1) White jSkin colour in riceAAbb Black skinaaBB Albino skinA-B-Agauti colourA-B-(9) AgautiA-bb (3) BlackaaB1-" I (3) Albinoaabb j (1) Albino JAComplementary factors. IV V W V r 111colour of paddyAAbb GrayaaBB GrayA-B-RedA D ri u(9) Redi "/^bb1 (3) Gray1aaB-(3) Grayaabb ! (1) Gray JFlower colour in Lathyrus odoratus9 : 7CCpp White flowersccPP White flowersC-P-Red flowersC-P-(9) Redr c-pp1 (3) WhiteccP-(3) Whiteccpp J (1) White j5.Inhibitory factorsPigmentation in leaves of paddy13 : 3Ilpp Green pig.iiPP Purple pig.I-P-Green pig.I-P-(9) GreenI-pp (3) GreeniiP-(3) Purpleiipp (1) Green6.Duplicate factorsFruit shape of Capsella15 : 1AABB Triangularaabb Top shapedA-B-Triangular shapeA-B- (9) TriangularA-bb (3) TriangularaaB- (3) Triangularaabb (1) Top shapedAwned character in paddy grainsA1A1a2a2 Awneda j A2A2 AwnedA, - A2 AwnedA, - A2 (9) AwnedA j a2a2 (3) Awneda,a| A2-(3) Awneda^ aja2a2 (1) Awnless7.Polymorphism additive effectPericarp colour in wheat9:6:1Light redLight redR, - R2-Deep redR, - R2 (9) Deep redR, - r2r2 (3) Light redr,r,R2- (3) Light redrlrlr2r2 (1) WhiteC j C j . Deep redC|C|C2C2ColourlessC,-C2-Deep redC,-C2 Deep redC j c2c2 Light redLight redc1c,c2c2 White4. Complementary factors (9 : 7 ratio)Sometimes a trait is produced by the interaction of two or more genes situated on separate chromosomes which complement one another. In some varieties of sweet pea the following interaction of two pairs of genes has been noted, (Fig. 65.5) ccR-, C-rr and ccrr- white colour C-R-Red colour. It was observed by Bateson and Punnett in Lathyrus odoratus.Here gene C and R are complementory to each other and necessary for the production of colour in flower. When they are together (C - R -), red colour in petals develop.

inorganic chemistry notes

inevitably, adv. unavoidably ease, v. relieve from pain or anxietycaption, n. wording appended, to an illustrationbiochemist, n. a person who makes a study of the chemistry of living organismsingredient, n. component part in a mixturecrystalline, adj. having the structure and form of a crystalcomputation, n. calculation enormous, adj. great ego, n. selfstrike a balance, find or take an intermediate position; compromisemacro-molecule, n. any very large molecule, such as proteinmonomer, n. a compound whose molecules can join together to form a polymerinalienable rights, rights that cannot be transferred to anotherorganelle, a structural and functional unit in a cell orunicellular organism ribosome, n. any of numerous minute particles in the cytoplasm of cells that contain RNA and protein and are the site of protein synthesistrillion, (US) a thousand billions (written as 1,000,000,000,000) penultimate, adj. next to the last dry ice, n. solid carbon dioxide used as a refrigerant fraud, n. a deceptive personout on a limb, in a risky, vulnerable, or questionable positionincubator, n. a device for the artificial development of micro-organismscell culture, the development of cells or micro-organisms in artificial mediacrassest, adj. coarsestmaterial, adj. composed of mattermagnitude, n. size or extentminiaturization, n. reductioa of the size ofAlfred North Whitehead (1861-1947) English mathematician and philosopherThe following chemicals are named in the passage:hemoglobin NADP trypsininsulin acetate kinase alkaline phosphatasehyaluronic acid bilirubin human DNAUNA collagen human albuminbradykinin prolactin proteinamino acid ribonucleas ribosome follicle-stimulating hormone

surface area and volume formulas

Example 1:Find the surface of the sphere, whose radius is 6 cm.Solution:Formula for finding the surface area of sphere is given as,Surface area of sphere     = 4 âˆ r2                                     = 4*3.14*62                                     = 12.56*36                                     = 452.16 cm2.Example 2:Find the area of sphere ball whose diameter is 8 cm.Solution: Formula for finding the surface area of sphere is given as,Surface area of sphere = 4 âˆ r2Radius  = Diameter/2            = 8/2            = 4 cmArea     = 4*3.14*42            = 12.56*16            = 200.96 cm2. Example 3:Find the volume of the sphere, whose radius is 3 cm.Solution:Formula for finding the volume of sphere is given as,Volume of sphere = (4∏r3)/3                             = 4*3.14*33 / 3                             = 12.56*27 / 3                             = 12.56*9                             = 113.04 cm3.

human heart diagram

Supply of oxygenated blood to the upper part of the body:Subclavian arteries that arise from the aorta carries blood to the arms and the carotid artery carries blood to the head.Supply of oxygenated blood to the lower part of the body:The hepatic artery that arise from the blood vessel aorta carries blood to liver, the mesenteric artery carries blood to the small intestine, the renal artery carries blood to kidneys, and the iliac artery carries blood to legs.Supply of oxygenated blood is shown in red color in the below systemic circulation diagram

problem solving in mathematics

Problem 1: Subtract 56 from 78.Answer: 22Problem 2: Multiply 2 and 15.Answer: 30

isosceles triangle definition

Simplify the following isosceles triangle tutor. Problem: Find the perimeter of isosceles triangle whose side 14cm, and base 10cm.Solution:The given problem is to find the perimeter of isosceles triangle whose side are 14cm, and base 10cm.Step 1: The perimeter of isosceles triangle is 2a+bStep 2: The given side a=14cm, and base b =10cm. Step 3:  substitute the value in the formula= 2(14)+10 = 28+10Step 4: The perimeter of isosceles triangles is 38cm.

pituitary gland function

Digestive organsFunctions of digestive systemMouthKeeps food between teeth; Foods uniformly chewed during mastication.TeethSolid foods reduced to smaller particles for swallowing.TongueFood maneuvered for mastication.Salivary GlandsSecrete saliva; lining of mouth and pharynx lubricated; Salivary amylase splits starch into smaller fragments.PharynxMoves bolus of food from pharynx into esophagus; closes air passage ways.EsophagusPermits entry of bolus from pharynx into esophagus; pushes bolus down esophagus; permits entry of bolus into stomach; lubricates esophagus for smooth passage of bolus.StomachMaceration of food; Mixes it with gastric juice; reduce food to chime; Kills many microbes in food; Activates Pepsin.PancreasContains enzymes that digest carbohydrates, proteins, triglycerides and nucleic acids.LiverProduces bile; Emulsification and absorption of lipids in small intestine.Gall BladderStores and concentrates bile and releases it into small intestine.Small IntestineMixes chyme with digestive juices; Completes the digestion of carbohydrates, proteins, lipids and nucleic acids; Absorption of 90 % of nutrients and water.Large IntestineDrives the contents of colon into rectum; Absorption of some water, ions and vitamins; defecation.

reactive metals

Reaction with oxygenSulphur's most prominent chemical property is that it burns. When it does so, it gives off a pale blue flame and sulphur dioxide (SO 2 ) gas. Sulphur dioxide has a very obvious strong, choking odor.When heated in air or oxygen, sulphur first melts and then burns with a blue flame to form sulphur dioxide and some traces of sulphur trioxide.Reaction with nonmetalswith hydrogen gas:The compound formed in this reaction is hydrogen sulphide (H 2 S). Hydrogen sulphide has one of the best known odors of all compounds. It smells like rotten eggs. Hydrogen sulphide is added to natural gas (methane) used in homes for cooking and heating. Methane is odorless. So the unique smell of hydrogen sulphide makes it easy to know when there is a methane leak.When hydrogen is passed through boiling sulphur, both hydrogen and sulphur combine to form hydrogen sulphideWith CarbonVapors of sulphur is passed over white-hot charcoal. They combine to form carbon disulphideWith chlorineWhen chlorine is bubbled through boiling sulphur, it forms sulphur monochloride Reaction with acidsSulphur does not react with hydrochloric acid. Dilute sulphuric acid and dilute nitric acid also do not affect sulphur.Reaction with hot concentrated Sulphuric acidWith hot concentrated sulphuric acid d is added to sulphur it oxidises to sulphur dioxide. During the reaction sulphuric acid undergoes thermal decomposition and in the process water, sulphur dioxide and nascent oxygen are formed.Nascent oxygen reacts with sulphur to form additional sulphur dioxide.ORReaction with hot concentrated nitric acidHot concentrated nitric acid oxidises sulphur to sulphuric acid.Sulphur is further oxidised by the nascent oxygen to sulphur trioxide.Sulphur trioxide then combines with water to form sulphuric acid.ORReaction with metalsWith most of the metals the reaction of sulphur is highly exothermic. Sulphur combines with metals under varying conditions of temperature to form the respective sulphides.With mercurySulphur is very reactive with mercury and can combine even at the temperature of liquid air (-200oC). Usually both are rubbed together to make them combine. With sodiumThe reaction of sulphur with sodium is as follows: With IronIron and sulphur combine on heating to form iron (II) sulphide, evolving a large quantity of heat energy. With CopperOn heating to about 400oC, copper combines with sulphur to form cuprous sulphide. If the temperature is above 400oC, then cupric sulphide is formed.With zincThe reaction of sulphur with zinc is as follows:Reaction with oxidizing agentsWhen sulphur is mixed with potassium nitrate, potassium chlorate etc., it forms an explosive mixture. When struck or heated or ignited, the mixture explodes e.g. gun powder.

latent heat of ice

Put equal quantities of crushed ice into two identical filter funnels P and Q (see Fig. 14.5). If the ice has been taken out. of a freezer, it must be left until it attains a temperature of 0 °C and starts to melt. Place an immersion heater connected to an ammeter, voltmeter and rheostat in P, making sure that it is completely covered with ice. At the same time as you switch on the immersion heater, place dry empty beakers of known mass under P and Q. Note the readings of the ammeter and voltmeter, and if necessary adjust the rheostat to keep them constant throughout the experiment. After several minutes, when a reasonable amount of water is in the beaker under P, note the time, remove the beakers and switch off the heater. Find the masses of the beakers and their content.

define mass communication

An artificial satellite revolving in a circular orbit round the earth in the equatorial plane, in the same sense as that of the rotation of the earth and with the same period of revolution as the period of rotation of the earth (i.e. 24 hours or 86400 seconds), is called a communication satellite (Fig. 2.6). Such a satellite always appears stationary from the surface of the earth and hence it is also called a geostationary satellite or a geosynchronous satellite.In order to launch a communication satellite in its orbit, it is first raised to a certain height above the equator and then projected with a certain velocity in the same direction as that of the sense of rotation of the earth. The height and the velocity of the satellite are determined as follows.(1) If r is the radius of the orbit of the satellite, the period (T) of the satellite is given byT = 2n J-; \GMT2 GM' r3 = —...(2.37)AnNow, M = mass of the earth = 5.98 x 1024 kg and G = constant of gravitation = 6.67 x 10"11 Nm2/kg2. For the communication satellite, 7=24 hours = 86400 s. Substituting these values in the above equation, we get(86400J2 x6.67xl0~n x5.98 x 1024^ = 4 x (3.14 J2= 7.55 x 1022r = (7.55 x 1022)1/3 = 4.227 x 107 m = 42.27 x 106 mIf h is the height of the satellite above the surface of the earth and R is the radius of the earth,r = R + hh = r-RNow R = 6400 km = 6.4 x 106 mh =r-R = 42.27 x 106 - 6.4xl06 = 35.87 x 106 m= 35870 km(2) The velocity of projection ( vc) of the satellite is given byIGM lGM~ 16.67 xlO"11 x 5.98 x 1024~ vc= ]lR + h=i= V 4.227 xlO7= 3.072 x 103 m/s = 3.072 km/s The above consideration shows that the height of the communication satellite above the surface of the earth is about 36000 km and its speed is about 3.1 km/s.

organelle functions

Cell Wall           This is the layer that surrounds the plant cell which is made  up of  fibres of cellulose , hemi cellulose,   pectin and proteins.  This outer protective layer is very thick and rigid that provide  strength to the plant body.Cell Membrane             This is the thin layer inner to the cell wall.   It is made up of lipids and proteins that surrounds the cytoplasm  and is semi permeable .Cytoplasm           The plant cell anatomy reveals the appearance of cytoplasm.  It is fluid in which cell organelles like endoplasmic reticulam, golgi apparatus, mitochondria, plastids etc... are distributed  and also acting as the site for various cellular activities.Endoplasmic reticulam:  It is a network of tiny tubular structures  scattered in the cytoplasm acting as a channel for transporting materials.There are two types of endoplasmic reticulam- ribosome bearing -Rough Endoplasmic Reticulam (RER)   and without  ribosome-Smooth Endoplasmic Reticulam(SER).Golgi apparatus-It is  flattened ,disc-shaped sac or cisternae arranged parallel to each other.Its function is packaging and delivery of materials  inside or out side the cells.Lysosomes-They are membrane bound vescicular structures  containing highly active hydrolytic enzymes capable of digesting  carbohydrates,proteins,lipids and  nucleic acids.But found rarely in plant cells..Vacuoles-These are membrane bound organelles containing  water,sap, excretory products and other  useful substances needed  for the cellular activities. Its outer  membrane is called tonoplast.In young plant cells small vacuoles are  present  while the  older plant cells are identified with a big vacuole.Mitochondria-Cylindrical or sausage shaped organelles act as sites for cellular respiration.It is with a  double membrane and the  outer membrane is the smooth  limiting membrane  and inner membrane  form infoldings  called  cristae  in to the  matrix  to increase the surface area for respiration. Here energy is produced in the form of ATP molecules  and stored . Hence they are called  ' power houses' of he cell.It contains a circular DNA  in its matrix.PLASTIDS-Three types of plastids present-chloroplast,chromoplast and leucoplast.Chloroplasts  contain chlorophyll pigments that trap light  energy for photosynthesis. Chromoplasts  are  the plastids   that give colour to the  flowers and other parts.Leucoplasts are the colourless plastids present   in roots.Plastids are also double membraned structures contain the matrix called  stroma in which flattened  membranous  sacs   called thylakoids ,arranged  as stalks called grana.This also contains circular DNA.Ribosomes-Granular structures composed of   RNA and act as sites  for protein synthesis.Cytoskeleton-Plant cell anatomy  shows some proteinaceous filamentous net work in the cytoplasm which provides mechanical support and maintain the shape of the cell.Nucleus--In the study of plant cell anatomy the important  structure locating as the centre for controlling  cellular activities is the nucleus. The nuclear membrane is  double  layered   that  covers  the nucleoplasm which contains  chromatin fibres (chromosomes) and nucleolus.  Chromosomes  are the structures  made up of  DNA  -- the heriditary units.

is one a prime number

            A prime number is a natural number; it means which number is divisible by 1 and itself only. Based on some criteria prime numbers are classified as followings:Twin prime numbers: A pair of prime numbers is given in brackets.Cousin prime numbers: Which prime numbers of a pair differ by digit four is known as cousin prime numbers.Balanced prime numbers: It has a balanced distance to its previous and next prime number.Palindromic prime numbers: the reverse of the prime number is same as the original prime number.Reversible prime numbers: the reversal of one prime number gives another prime number.Permutable prime numbers:  This prime number’s permutation should give a prime.Pythagorean prime numbers: Which number’s square is equal to the sum of square of any two prime numbers. Centered square prime numberMersenne prime numbers

electrical conductivity of metals

The response of a metal to electromagnetic radiation is determined by the frequency dependent conductivity. This in turn depends on the available mechanisms for energy absorption by the conduction electrons at the given frequency. The electronic excitation spectrum in the superconducting state is characterised by an energy gap 2Eg. So we expect the AC conductivity to differ substantially from its normal state form at frequencies small compared with 2Eg Ifi, and to be essentially the same in the superconducting and normal states at frequencies large compared with 2Eg / h. The value of 2Eg /h, is typically in the range between microwave and infrared frequencies. In the superconducting state, an AC behaviour is observed which is indistinguishable from that in the normal state at optical frequencies. Deviations from normal state behaviour first appear in the infrared. At microwave frequencies AC behaviour fully displaying the lack of electronic absorption characteristic of an energy gap becomes completely developed.

define desert

Some common phenomena and applications related to refraction are as follows:Lens: Refraction is at the core of the functioning of a lens. A lens uses refraction for image formation which is used for several purposes such as magnification. Our eye is also a lens where what we see is projected on our retina. Here also refraction is used to form the image on the retina. Uses of a lens in our daily life are galore like magnifying glasses, eye glasses, contact lenses.Prism: A prism uses refraction to form a spectrum of colors from an incident beam of light.A prism can be used to break light up into its constituent spectral colours (the colors of the rainbow). Prisms can also be used to reflect light, or to split light into components with different polarizations.Mirage: A mirage is a naturally occurring optical phenomenon in which light rays are bent to produce a displaced image of distant objects or the sky. Some common examples are water bodies in a desert and wet roads on a hot sunny day.

decimal to fraction calculator

Example 5${\displaystyle \int7x^{4/3}dx=7\int x^{4/3}dx=7\frac{x^{4/3+1}}{\frac{4}{3}+1}=3x^{7/3}+\mathrm{c}}$, where $c$ is an arbitrary constant of integration. Example 6${\displaystyle \int\{3x^{2}+1+\frac{1}{x^{2}}\}dx=\int3x^{2}dx+\int1dx+\int\frac{1}{x^{2}}dx}$   $=3\cdot\frac{x^{3}}{3}+c_{1}+x+c_{2}+\frac{x^{-2+1}}{-2+1}+c_{3}=x^{3}\prime+x-\frac{1}{x}+c,$ where $c(=c_{1}+c_{2}+c_{3})$ is an arbitrary constant of integration. Note. There is no need to introduce an arbitrary constant after calculating each integral (as is done in the above example). By combining all arbitrary constants, we get a single arbitrary constant denoted by $c$ which is added to the final answer. Example 7${\displaystyle \int(2\cos2x+\frac{3}{x}-9e^{x})dx=2\int\cos2xdx+3\int\frac{1}{x}dx-9\int e^{x}dx}$ $=2{\displaystyle \frac{\sin2x}{2}+3\log|x|-9e^{x}+c=\sin2x+3\log|x|-9e^{x}+c}$, where $c$ is an arbitrary constant of integration. Example 8${\displaystyle \int\frac{(2x-3)^{3}}{x^{2}}dx=\int\frac{8x^{3}-36x^{2}+54x-27}{x^{2}}dx}$ $=8{\displaystyle \int xdx,-36\int dx+54\int\frac{1}{x}dx-27\int\frac{1}{x^{2}}dx}$  $=4x^{2}-36x+54{\displaystyle \log|x|+\frac{27}{x}+c}$, where $\mathrm{c}$ is an arbitrary constant of integration. Example 9$\int \left (3\sec 3x\tan 3x-8e^{8x}+20\sec ^2 20x+\frac {5}{\sqrt {1-x^2}} \right )dx$  $=3\cdot\frac{\sec3x}{3}-8\cdot\frac{e^{8x}}{8}+20\cdot\frac{\tan20x}{20}+5\sin^{-1}x+c$  $=\sec3x-e^{8x}+\tan20x+5\sin^{-1}x+c,$ where $c$ is an arbitrary constant of integration. Example 10 Find $y$ when $dy/dx=x^{\dot{2}}$. $dy=x^{2}dx$ and hence${\displaystyle \int dy=\int x^{2}dx}$, or,   $y={\displaystyle \frac]{3}x^{3}+c}$.

natural log rules

The base a can be changed to e.Therefore,         ex = m,Then x is the logarithm of m to the base e and it is written as,                           logem  or ln m, this is called the natural logarithms.                           Where e = 2.71828182846 (base of natural logarithm).that is ,      if logem = x    then ex = m.

formula for fahrenheit to celsius

Answer key 1: The area of the square is 289 sq cm.Answer key 2: The temperature 35 degrees Celsius to degrees Fahrenheit is 95 degrees Fahrenheit.Answer key 3: The new two angles are 40 degree.

finding the inverse of a function

Find the value of parameter $\alpha$ for which the funciion $f(x)=1+\alpha x,\alpha\neq0$ is the inverse of itself. SOLUTION Clearly, $f(x)$ is a bijection from R to itself. Now,  $fof^{-1}(x)=x$ $\Rightarrow f(f^{-1}(x))=x$  $\Rightarrow1+\alpha f^{-1}(x)=x$ $\Rightarrow f^{-1}(x)=\frac{x-1}{\alpha}$ It is given that  $f(x)=f^{-1}(x)$ for all$x\in R$   $\Rightarrow1+{\displaystyle \alpha x=\frac{x-1}{\alpha}}for\: all\: x\in R$   $\Rightarrow{\displaystyle \alpha x+1=(\frac{1}{\alpha})x+\left(\frac{-1}{\alpha}\right)}for\: all\: x\in R$   $\Rightarrow{\displaystyle \alpha=\frac{1}{\alpha}}and1=-{\displaystyle \frac{1}{\alpha}}$   $\Rightarrow\alpha^{2}=1\mathrm{and}\alpha=-1$   $\Rightarrow\alpha=-1.$

1984 chapter summaries

Force is equal to the rate of change of momentum. An unbalanced force F causes a mass m to accelerate with acceleration a given by F = ma. The impulse p of a force F acting for a time t is Ft and is equal to the change in momentum. The change in momentum is calculated from the difference between the final momentum and the initial momentum. Momentum is always conserved in collisions but kinetic energy is not necessarily conserved.The following worked examples will illustrate some of these points.ExampleA car of mass 1200 kg is brought to rest from a speed of 20 m s"1 by a constant braking force 3000 N. Calculate the retardation and the time the car takes to come to rest.F= -3000 N m= 1200 kg a = ?ExampleAn ice hockey puck of mass 0.1 kg travelling at 20 ms"1 is struck by a stick so as to return it along its original path at 10 ms"1. Calculate the impulse of the force applied by the hockey stick.Let p be the impulse produced by the Force F applied by the stick for the time t.m = 0.1 kg u = +20 m s 1 i/=-10ms_1 F=1 t = ?P = Ft = mv — mu= 0.1 x(-10) -0.1 x (+20) = - 1 -2 = -3NsThe impulse applied by the stick is -3 N s. The minus sign indicates that the direction of the impulse is in the opposite direction to the original direction of motion of the puck.ExampleA rifle pellet of mass 5 g is fired horizontally into a block of wood fixed to a model truck which runs freely on a straight track. The mass of the truck and the block is 495 g and these move with a velocity of 0.8 m s"1 when the pellet embeds itself into the wood. Calculate the initial velocity of the pellet.m = 0.005 kg u = l M = 0.495 kg v= 0.8 ms"1mu = (m + M\v 0.005 x u = (0.005 + 0.495) x 0.8_ 0.5 x 0.8 u 0.005u- 80 ms"1The initial velocity of the pellet is 80 m s-1.ExampleA bullet of mass 0.01 kg travelling horizontally at 100 ms"1 penetrates a fixed block of wood and comes to rest in 0.02 s. Calculate (a) the distance of penetration x of the bullet into the wood and (b) the average retarding force exerted by the wood on the bullet.(a)u= 100ms"1 f=0ms_1 a = ? /=0.02s v=u +at 0 = 100 + a x 0.02 0.02a = -100 a = -100/0.02 a = -5000 ms"2v2 = u2 + 2 ax 0= 1002-2x5000* 10 000 x = 10 000 *=lmThe bullet penetrates 1 m into the block (note the deep penetration).(b)F=? m = 0.01 kg a = -5000 ms"2 F= maF= 0.01 x (-5000) F= -50 NThe average retarding force exerted by the wood is -50 N.

i need help with math

Pick out the Adjective Phrases, in the followingsentences:— < Â« *1. A man in great difficulties came to me for help.2. He is a person of very considerable renown.3. Wild beasts in small cages are a sorry sight.4. A man without an enemy is a man with few friends.5. He tells a tale with the ring of truth in it.6. A friend in need is a friend indeed.7. A stitch in time saves nine.8. A bird in the hand is worth two in the bush.9. Gardens with cooj shady trees surround the village.10. Only a man with plenty of money buys a car of such beauty and power.11. In a low voice he told the tale of his cruel wrongs.12. Po you know the story of the noble Padmini ?« Â»13. He was a lad of great promise,14. He bore a banner with a strange device.15. The police arrested a man of one of the criminal tribes.

math pictures

Introduction to pictures of scatter plots:            Let us see about pictures of scatter plots. Scatter plots are also known as scatter graph. It is a mathematical stature used by Cartesian coordinates to display the variables of the group of data. In scatter plots are using when a variable survive that is under the control of the trial. The variable is either self-governing or dependent variable.

exponential notation

It is easier to understand exponents through tables. Here is the table for exponents from -3 to 6 for base 10.Remember 100  is always 1.  ExponentialNotation (Powers of 10)Exponential Form (Power)Expanded FormStandard Name10610x10x10x10x10x10100000010510x10x10x10x1010000010410x10x10x101000010310x10x10100010210x1010010110101001110-11/100.110-21/10 x 1/100.0110-31/10 x 1/10 x 1/10  0.001 

band name list

The midbrain bears two imperfectly divided optic lobes. A membrane, choroid plexus lies between the optic lobes. It is fused with the plexus over the fourth ventricle, the cavity of the medulla oblongata. Mesencephalon is concerned with sight.RhombencephalonIt is divisible into an anterior meten-cephalon (cerebellum) and a posterior my-elencephalon (medulla oblongata). The cerebellum is small and occurs as a transverse band roofing over the anterior end of the fourth ventricle. The medulla oblongata is largest and highly developed. It controls the powerful sucking structures through trigeminal nerve.Cavities of the brainThe cavities of the brain are ventricles and that of the spinal cord is central canal (p. 114).Spinal cordThe spinal cord is tubular, of fairly uniform diameter throughout its length, tapering gradually towards the posterior, and encloses the central canal. It is flattened, convex dorsally and concave ventrally. Grey matter is in the form of a longitudinal band surrounded by white matter, the two not sharply differentiated

global change biology

Major issues of global environmental change are global warming and ozone depletion. The need of the hour is to stabilise the atmospheric concentrations of green house gases. It can be achieved only when all the countries join hand in lowering the global emission of green house gases from their present levels.1. Montreal Protocol. On 16th September, 1987, twenty seven industrialized countries signed an agreement to limit the production and use of ozone-depleting substances (ODS) e.g. chlorofluorocarbons, phasing out of ODS, and also to help the developing countries to implement use of alternatives to CFCs. In May, 1989 Montreal Protocol was ratified by 82 nations at Helsinki (Helsinki Declaration). 175 countries have signed this protocol till date.2. Earth Summit. United Nations Conference on Environment and Development was held in Rio-de-Janerio, Brazil in 1992. It is popularly known as Earth Summit. In this conference, recommendations of CCC (Convention on Climate Change) were signed by 154 nations. A general agreement was reached to maintain emissions of green house gases at 1990 level.3. Kyoto Protocol. A follow up international conference was held in December, 1997 in Kyoto, Japan. In this conference, an agreement was signed by different countries to mitigate global environmental change by taking appropriate measures to reduce emissions of green house gases at a level 5% below the 1990 level by 2008 A.D. to 2012 A.D.

u substitution integration

1. Indefinite integrations:          An indefinite integration is the family of functions that have a given function as a common derivative. The indefinite integral of f(x) is written ∫ f(x) dx.2. Definite integrations:                If F(x) is the integral of function f(x) over the interval [a, b] ,i.e., ∫ f(x) dx = F(x) then the definite integral of function  f(x) over the interval [a, b] is denoted by `int_a^bf(x)dx` and is defined as `int_a^bf(x)dx`  = F(b) – F(a).                   Where 'a' is called the lower limit and b is called the upper limit of integration and the interval [a, b] is called of integration.Methods of integration:                        It is not possible to integrate each integral with help of the following methods but a large number of varieties of the problems can be solved by these methods so, we have the following methods of integration:                        1. Integration by substitution                        2. Integration by parts.                        3. Partial fractions

body surface area calculator

The behaviour of liquid surfaces and the phenomenon of surface tension can be explained by considering the forces of attraction between the molecules of a liquid.Intermolecular forces of attraction are of two types : (i) Attraction between two molecules of the same substance is called cohesion and the force of attraction is called the cohesive force, (ii) Attraction between two molecules of different substances is called adhesion and the corresponding force of attraction is called the adhesive force.These intermolecular forces, both cohesive and adhesive, are short range forces, i.e. they are effective over a very short distance, beyond which they are negligible. The maximum distance between two molecules upto which the intermolecular forces are effective is called the range of molecular attraction (R). An imaginary sphere drawn round a molecule as centre, with a radius equal to the range of molecular attraction, is called the sphere of influence of that molecule. The molecule is attracted only by the other molecules inside this sphere since the forces exerted by molecules outside the sphere are negligible.Three molecules. A, B and C of a liquid, with their spheres of influence, are shown in Fig. 6.3. The molecule A is well within the liquid, molecule B is just inside the liquid surface and molecule C is on the liquid surface.The sphere of influence of the molecule A is completely inside the liquid, so that the other liquid molecules are symmetrically distributed around the molecule A. The molecule is therefore attracted equally in all directions, so that the resultant intermolecular force acting on this molecule is zero.The molecule B is just inside the liquid surface. Its distance from the liquid surface is less than the range of molecular attraction. Therefore a part of its sphere of influence lies outside the liquid surface. This part contains molecules of air, but their number is very small and the forces of attraction exerted by them on molecule B are negligible compared to those exerted by the liquid molecules, inside the sphere of influence. It is clear from the consideration of symmetry, that a resultant downward force acts on the molecule B, trying to pull it inside the liquid.For the molecule C, which is on the liquid surface, half of the sphere of influence lies outside the liquid. This half contains air molecules whose number is extremely small compared to the number of liquid molecules in the lower half of the sphere. Therefore the molecule C experiences maximum downward force, trying to pull it into the liquid.Thus all molecules in a layer of thickness R, below the free surface of the liquid, experience an inward pull. The pull is greater if the molecule is nearer to the surface and it is maximum for a molecule on the surface.In order to increase the surface area, molecules from inside the liquid must be brought to the surface. For this purpose, work must be performed against the in ward pull exerted by the liquid. This work is stored in the surface in the form of potential energy. Thus potential energy of the liquid increases due to increase in its surface area. Conversely, the potential energy of a liquid decreases with decrease in its surface area. Now the natural tendency of a body is to attain the condition of minimum potential energy. Therefore the free surface of a liquid has a tendency to contract and minimise its area, so that the potential energy of the liquid is minimum. This tendency to minimise the surface area gives rise to the phenomenon of surface tension. In order to minimise the surface area, the forces due to surface tension always act tangentially to the liquid surface.The free surface of a liquid is ordinarily plane and horizontal. Sometimes, however, we find the liquid surface to be concave or convex. For example, the surface of water in a capillary tube is concave, while the surface of mercury in a capillary tube is convex. We shall consider the explanation of curved surfaces in Art. 6.4

Math Answers for Number Theory

Number Theory - Its a study of numerical of math such as Rational and Irrational Numbers, Natural Numbers, Whole numbers, significant Figures, Prime Numbers, Fractions etc.
And the basic of number theory lies in understanding natural numbers, whole numbers, fractions and rational-irrational numbers. They are defined as follows.

* Natural numbers - The countable numbers are called Natural Numbers.
* Whole numbers - The set of whole numbers is the set of natural numbers along with zero. so
W = the set of whole numbers = 0, 1, 2, 3, ............
* Fractions - Fraction is an equal part of one whole object.
* Rational numbers - The rational numbers can be expressed as terminating or recurring decimals.
* Irrational numbers - Numbers which are not rational are called irrational numbers.

So math answers for number theory is as follows...

Natural numbers :
Therefore 1 is the smallest or least of all natural numbers.

The highest natural number cannot be said because Natural numbers are infinite.

The set of Natural numbers is a subset of Rational numbers

Whole numbers :
Properties of Whole numbers

It is advisable to use a number line inorder to understand the properties of whole numbers.

1. Number 3 < 5 and the number 3 is to the left of the number 5. Hence of an two numbers on a number line, the smaller number is to the left of the greater number.So too,of any two numbers on a number line the number to the left of the other number, is the smaller of the two.

2 . There is no whole number to the left of zero on the number line.So zero is the smaller number than each of the numbers to its right on the number line.That means 0 is the smallest or least of the whole numbers.

3. A whole number which is greater than a given whole number by 1 is said to be a successive whole number. 1 is the successive whole number to 0.Every whole number has one successor.

4. There is no whole number left to zero.hence 0 is not a successive whole number of any whole.

Fractions :
A part of a whole when it is divided into equal parts is a fraction.
Set of Fraction is a subset of the set of Rational Numbers
Eg : The whole Pizza is divided into 5 equal parts,then one part of it is expressed as 1/5

Rational numbers :
The rational numbers can be expressed as terminating or recurring decimals. Decimal fraction has denominator as 10 or a power of 10. A recurring decimal is denoted by placing dots or a bar over recurring digits.

Irrational numbers :
Numbers which are not rational are called irrational numbers. When expressed as decimals, they are non-terminating and non-recurring. We can obtain infinite number of irrationals between two irrational numbers.

How to Solve Percentage Problem

In mathematics, a percentage is a method of representing numbers as a fraction of 100 (percent meaning "per hundred"). percentage is represented as percent sign, "%".
percentage is represented as percent sign, "%".

How to solve percentage problems:
Some Rules:

1)When we compare two quantities of the same kind by division, we have a ratio of those two quantities.
2) The ratio should be in the lowest form.
3) The order in the ratio is very important. It cannot be interchanged.
4) Ratio has no unit.
5) Two or more ratios can be compared
6) Proportion is an equality of two ratios.

A Percentage problem :
The speed of a car is 60km per hour. If it is increased by 10% find the new speed of the car.

Solution:

Speed of car = 60km

Increased percentage =10 % of 60km

= (10 / 100) × (60) =6km

New speed =60 + 6 = 66km