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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

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

Question Number 47621 Answers: 1 Comments: 1

Find locus of point P from which tangents PA & PB to circles x^2 +y^2 =a^2 and x^2 +y^2 =b^2 respectively are perpendicular.

$${Find}\:{locus}\:{of}\:{point}\:{P}\:{from}\:{which} \\ $$$${tangents}\:{PA}\:\&\:{PB}\:{to}\:{circles}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} ={a}^{\mathrm{2}} \\ $$$${and}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} ={b}^{\mathrm{2}} \:{respectively}\:{are}\:{perpendicular}. \\ $$

Question Number 47607 Answers: 1 Comments: 1

∫_a ^b ((∣x∣)/x)dx

$$\int_{{a}} ^{{b}} \frac{\mid{x}\mid}{{x}}{dx} \\ $$

Question Number 47801 Answers: 1 Comments: 0

An object starts from rest and moves with a velocity of (3i+4j)ms^(−1) . It covers a distance of 400km.Find a) its acceleration b) the time taken to cover the distance 400km.

$${An}\:{object}\:{starts}\:{from}\:{rest}\:{and}\:{moves}\:{with}\:{a}\:{velocity}\:{of}\: \\ $$$$\left(\mathrm{3}{i}+\mathrm{4}{j}\right){ms}^{−\mathrm{1}} .\:{It}\:{covers}\:{a}\:{distance}\:{of}\:\mathrm{400}{km}.{Find}\: \\ $$$$\left.{a}\right)\:{its}\:{acceleration} \\ $$$$\left.{b}\right)\:{the}\:{time}\:{taken}\:{to}\:{cover}\:{the}\:{distance}\:\mathrm{400}{km}. \\ $$

Question Number 47595 Answers: 0 Comments: 3

Question Number 47593 Answers: 0 Comments: 0

Which of the following statements are/is true?

$$\mathrm{Which}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following}\:\mathrm{statements}\: \\ $$$$\mathrm{are}/\mathrm{is}\:\mathrm{true}? \\ $$

Question Number 47590 Answers: 1 Comments: 1

f(x)=e^x g(x)=x^2 (f+g)(x)=? (f×x)(x)=? (f/g)(x)=?

$$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{e}^{\mathrm{x}} \: \\ $$$$\mathrm{g}\left(\mathrm{x}\right)=\mathrm{x}^{\mathrm{2}} \\ $$$$\left(\mathrm{f}+\mathrm{g}\right)\left(\mathrm{x}\right)=? \\ $$$$\left(\mathrm{f}×\mathrm{x}\right)\left(\mathrm{x}\right)=? \\ $$$$\left(\mathrm{f}/\mathrm{g}\right)\left(\mathrm{x}\right)=? \\ $$

Question Number 47586 Answers: 1 Comments: 0

Given the function f(θ)= cos2θ − sinθ. (for 0°≤θ≤π) plot the graph for intervals of (π/6). hence find the value of cos2θ=sinθ.

$${Given}\:{the}\:{function}\:{f}\left(\theta\right)=\:{cos}\mathrm{2}\theta\:−\:{sin}\theta.\:\left({for}\:\mathrm{0}°\leqslant\theta\leqslant\pi\right) \\ $$$${plot}\:{the}\:{graph}\:{for}\:\:{intervals}\:{of}\:\frac{\pi}{\mathrm{6}}. \\ $$$${hence}\:{find}\:{the}\:{value}\:{of}\:{cos}\mathrm{2}\theta={sin}\theta. \\ $$

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