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Question Number 47727 Answers: 1 Comments: 0

Find the value of a for a : 4 : : 5 : 10

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:{a}\:\mathrm{for} \\ $$$$\:\:\:\:\:{a}\::\:\mathrm{4}\::\::\:\mathrm{5}\::\:\mathrm{10} \\ $$

Question Number 47725 Answers: 1 Comments: 2

Question Number 47713 Answers: 0 Comments: 4

Question Number 47712 Answers: 0 Comments: 0

show that ^(^2 C_2 ) C_n = (1/((1−n)!(n−1)(n−2)(n−3)...3(2)(1)))

$${show}\:{that}\: \\ $$$$\:\:^{\:^{\mathrm{2}} \:{C}_{\mathrm{2}} \:} {C}_{{n}} =\:\frac{\mathrm{1}}{\left(\mathrm{1}−{n}\right)!\left({n}−\mathrm{1}\right)\left({n}−\mathrm{2}\right)\left({n}−\mathrm{3}\right)...\mathrm{3}\left(\mathrm{2}\right)\left(\mathrm{1}\right)} \\ $$

Question Number 47720 Answers: 2 Comments: 0

find ∫ ln(1+x^3 )dx

$${find}\:\int\:{ln}\left(\mathrm{1}+{x}^{\mathrm{3}} \right){dx} \\ $$

Question Number 47740 Answers: 2 Comments: 0

∫(dx/(x(x+1)(x+2)(x+3)...(x+n)))

$$\int\frac{{dx}}{{x}\left({x}+\mathrm{1}\right)\left({x}+\mathrm{2}\right)\left({x}+\mathrm{3}\right)...\left({x}+{n}\right)} \\ $$

Question Number 47697 Answers: 1 Comments: 1

Question Number 47677 Answers: 0 Comments: 3

∫x^(x ) dx=

$$\int\mathrm{x}^{\mathrm{x}\:} \mathrm{dx}= \\ $$

Question Number 47675 Answers: 2 Comments: 0

A particle of mass 4kg was at rest a a point of position vector i +4j. A force F was applied to it and it moved at a velocity of (3i + 7j)ms^(−1) after a time of 5seconds. Find a) the magnitude of F b) The speed at which it moves,Hence, c) The distance it covered.

$${A}\:{particle}\:{of}\:{mass}\:\mathrm{4}{kg}\:{was}\:{at}\:{rest}\:{a}\:{a}\:{point}\:{of}\:{position}\:{vector} \\ $$$${i}\:+\mathrm{4}{j}.\:{A}\:{force}\:{F}\:{was}\:{applied}\:{to}\:{it}\:{and}\:{it}\:{moved}\:{at}\:{a}\:{velocity} \\ $$$${of}\:\left(\mathrm{3}{i}\:+\:\mathrm{7}{j}\right){ms}^{−\mathrm{1}} \:\:\:{after}\:{a}\:{time}\:{of}\:\:\mathrm{5}{seconds}.\:{Find}\: \\ $$$$\left.{a}\right)\:{the}\:{magnitude}\:{of}\:{F} \\ $$$$\left.{b}\right)\:{The}\:{speed}\:{at}\:{which}\:{it}\:{moves},{Hence}, \\ $$$$\left.{c}\right)\:{The}\:{distance}\:{it}\:{covered}. \\ $$$$ \\ $$$$ \\ $$

Question Number 47659 Answers: 2 Comments: 0

Question Number 47657 Answers: 1 Comments: 7

Question Number 47656 Answers: 1 Comments: 1

A square is divided into 9 identical smaller squares.Six identical balls are to be placed in these smaller squares such that each of the three rows gets at least one ball(one ball in one square only).In how many different ways can this be done? a)91 b)51 c)81 d)41

$${A}\:{square}\:{is}\:{divided}\:{into}\:\mathrm{9}\:{identical} \\ $$$${smaller}\:{squares}.{Six}\:{identical}\:{balls} \\ $$$${are}\:{to}\:{be}\:{placed}\:{in}\:{these}\:{smaller}\: \\ $$$${squares}\:{such}\:{that}\:{each}\:{of}\:{the}\:{three} \\ $$$${rows}\:{gets}\:{at}\:{least}\:{one}\:{ball}\left({one}\right. \\ $$$$\left.{ball}\:{in}\:{one}\:{square}\:{only}\right).{In}\:{how} \\ $$$${many}\:{different}\:{ways}\:{can}\:{this}\:{be} \\ $$$${done}? \\ $$$$\left.{a}\left.\right)\left.\mathrm{9}\left.\mathrm{1}\:{b}\right)\mathrm{51}\:{c}\right)\mathrm{81}\:{d}\right)\mathrm{41} \\ $$$$ \\ $$

Question Number 47651 Answers: 1 Comments: 1

calculate A_n =∫_0 ^1 sin([nx])e^(−2x) dx with n integr natural .

$${calculate}\:\:{A}_{{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} \:\:{sin}\left(\left[{nx}\right]\right){e}^{−\mathrm{2}{x}} {dx}\:{with}\:{n} \\ $$$${integr}\:{natural}\:. \\ $$

Question Number 47646 Answers: 1 Comments: 2

Question Number 47641 Answers: 0 Comments: 0

E=(E_1 ^2 +E_2 ^2 +2E_1 E_2 cos2θ)^(1/2) full explanation

$$\mathrm{E}=\left(\mathrm{E}_{\mathrm{1}} ^{\mathrm{2}} +\mathrm{E}_{\mathrm{2}} ^{\mathrm{2}} +\mathrm{2E}_{\mathrm{1}} \mathrm{E}_{\mathrm{2}} \mathrm{cos2}\theta\right)^{\mathrm{1}/\mathrm{2}} \\ $$$$\mathrm{full}\:\mathrm{explanation} \\ $$

Question Number 47638 Answers: 0 Comments: 3

∫_0 ^π (√((1+cos2x)/2)) dx

$$\int_{\mathrm{0}} ^{\pi} \sqrt{\frac{\mathrm{1}+{cos}\mathrm{2}{x}}{\mathrm{2}}}\:\:{dx} \\ $$

Question Number 47637 Answers: 1 Comments: 2

∫_0 ^1 sin([x]+[2x])dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} {sin}\left(\left[{x}\right]+\left[\mathrm{2}{x}\right]\right){dx} \\ $$

Question Number 47639 Answers: 1 Comments: 0

derivation or proof or full explanation of R=(R_1 ^2 +R_2 ^2 +2R_1 .R_2 cosθ)^(1/2)

$$\boldsymbol{\mathrm{derivation}}\:\boldsymbol{\mathrm{or}}\:\boldsymbol{\mathrm{proof}}\:\boldsymbol{\mathrm{or}}\:\boldsymbol{\mathrm{full}}\:\boldsymbol{\mathrm{explanation}} \\ $$$$\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{R}}=\left(\boldsymbol{\mathrm{R}}_{\mathrm{1}} ^{\mathrm{2}} +\boldsymbol{\mathrm{R}}_{\mathrm{2}} ^{\mathrm{2}} +\mathrm{2R}_{\mathrm{1}} .\mathrm{R}_{\mathrm{2}} \mathrm{cos}\theta\right)^{\mathrm{1}/\mathrm{2}} \\ $$

Question Number 47628 Answers: 1 Comments: 0

If the first term and n^(th) term of G.P., are a and b respectively, p is the product of n terms. Prove that p^2 = (ab)^n .

$$\mathrm{If}\:\mathrm{the}\:\mathrm{first}\:\mathrm{term}\:\mathrm{and}\:\mathrm{n}^{\mathrm{th}} \:\mathrm{term}\:\mathrm{of}\:\mathrm{G}.\mathrm{P}.,\:\:\mathrm{are}\:\mathrm{a}\:\mathrm{and}\:\mathrm{b}\:\mathrm{respectively},\: \\ $$$$\mathrm{p}\:\mathrm{is}\:\mathrm{the}\:\mathrm{product}\:\mathrm{of}\:\mathrm{n}\:\mathrm{terms}.\:\mathrm{Prove}\:\mathrm{that}\:\mathrm{p}^{\mathrm{2}} \:=\:\left(\mathrm{ab}\right)^{\mathrm{n}} . \\ $$$$ \\ $$$$ \\ $$

Question Number 47627 Answers: 0 Comments: 0

Could someone explain me how cellular automata theory can be used in the bioligical field in relation to the spread of disease and/or cancer cells ? Thank you very much !

$$\mathrm{Could}\:\mathrm{someone}\:\mathrm{explain}\:\mathrm{me}\:\mathrm{how}\:\mathrm{cellular} \\ $$$$\mathrm{automata}\:\mathrm{theory}\:\mathrm{can}\:\mathrm{be}\:\mathrm{used}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{bioligical}\:\mathrm{field}\:\mathrm{in}\:\mathrm{relation}\:\mathrm{to}\:\mathrm{the}\:\mathrm{spread} \\ $$$$\mathrm{of}\:\mathrm{disease}\:\mathrm{and}/\mathrm{or}\:\mathrm{cancer}\:\mathrm{cells}\:? \\ $$$${Thank}\:{you}\:{very}\:{much}\:! \\ $$

Question Number 47626 Answers: 0 Comments: 0

thanks sir

$$\mathrm{thanks}\:\mathrm{sir} \\ $$

Question Number 47624 Answers: 1 Comments: 0

Solve the d.e using method of variation of parameter. (d^2 y/dx^2 )+3(dy/dx)+2y=sin(e^x )

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{d}.\mathrm{e}\:\mathrm{using}\:\mathrm{method}\:\mathrm{of}\:\mathrm{variation} \\ $$$$\mathrm{of}\:\mathrm{parameter}. \\ $$$$ \\ $$$$\:\frac{\mathrm{d}^{\mathrm{2}} \mathrm{y}}{\mathrm{dx}^{\mathrm{2}} }+\mathrm{3}\frac{\mathrm{dy}}{\mathrm{dx}}+\mathrm{2y}=\mathrm{sin}\left(\mathrm{e}^{\mathrm{x}} \right) \\ $$

Question Number 47623 Answers: 0 Comments: 0

Solve the d.e using method of variation of parameter. (d^2 y/dx^2 )+3(dy/dx)+2y=sin(e^x )

Question Number 47613 Answers: 1 Comments: 0

1(8/9)=((2x−1)/5) sir plz help me

$$\mathrm{1}\frac{\mathrm{8}}{\mathrm{9}}=\frac{\mathrm{2x}−\mathrm{1}}{\mathrm{5}}\:\:\:\mathrm{sir}\:\mathrm{plz}\:\mathrm{help}\:\mathrm{me} \\ $$