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Question Number 40569    Answers: 0   Comments: 0

Question Number 40551    Answers: 1   Comments: 5

Question Number 40550    Answers: 1   Comments: 0

if three numbers are drawn at random successively without replacement from a set S={1,2,......10}then probability that the minimum of the choosen number is 3 or their maximum is 7 Answer=((11)/(40))

$$\mathrm{if}\:\mathrm{three}\:\mathrm{numbers}\:\mathrm{are}\:\mathrm{drawn}\:\mathrm{at}\:\mathrm{random} \\ $$$$\mathrm{successively}\:\mathrm{without}\:\mathrm{replacement}\:\mathrm{from} \\ $$$$\mathrm{a}\:\mathrm{set}\:\mathrm{S}=\left\{\mathrm{1},\mathrm{2},......\mathrm{10}\right\}\mathrm{then}\:\mathrm{probability}\:\mathrm{that} \\ $$$$\mathrm{the}\:\mathrm{minimum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{choosen}\:\mathrm{number}\:\mathrm{is} \\ $$$$\mathrm{3}\:\mathrm{or}\:\mathrm{their}\:\mathrm{maximum}\:\mathrm{is}\:\mathrm{7}\:\:\:\:\:\:\:\: \\ $$$$\:\mathrm{Answer}=\frac{\mathrm{11}}{\mathrm{40}} \\ $$

Question Number 40523    Answers: 1   Comments: 1

If (1+ax+bx^2 )(1−2x)^(18) can be expanded using binomial theorem in ascending power of x.Determine the value of a and b,if the coefficient of x^3 and x^(4 ) are both zero.

$${If}\:\left(\mathrm{1}+{ax}+{bx}^{\mathrm{2}} \right)\left(\mathrm{1}−\mathrm{2}{x}\right)^{\mathrm{18}} \:\:{can}\:{be}\:{expanded}\:{using} \\ $$$${binomial}\:{theorem}\:{in}\:{ascending}\:{power}\:{of}\:{x}.{Determine} \\ $$$${the}\:{value}\:{of}\:\:\:{a}\:{and}\:{b},{if}\:{the}\:{coefficient}\:{of}\:{x}^{\mathrm{3}} \:\:{and}\:{x}^{\mathrm{4}\:} \:\:{are}\:{both}\:{zero}. \\ $$

Question Number 40544    Answers: 1   Comments: 0

solve for x 3^((2x−1)) −4(3^x )+1=0

$$\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{for}}\:\boldsymbol{{x}} \\ $$$$\mathrm{3}^{\left(\mathrm{2}\boldsymbol{{x}}−\mathrm{1}\right)} −\mathrm{4}\left(\mathrm{3}^{\boldsymbol{{x}}} \right)+\mathrm{1}=\mathrm{0} \\ $$

Question Number 40519    Answers: 1   Comments: 1

Question Number 40499    Answers: 1   Comments: 0

A particle of mass 2×10^(−27) kg moves according to the following y=5cos(((πt)/3)+(π/4)) find the maximum kinetic energy

$${A}\:{particle}\:{of}\:{mass}\:\mathrm{2}×\mathrm{10}^{−\mathrm{27}} {kg}\:{moves} \\ $$$${according}\:{to}\:{the}\:{following} \\ $$$${y}=\mathrm{5}{cos}\left(\frac{\pi{t}}{\mathrm{3}}+\frac{\pi}{\mathrm{4}}\right) \\ $$$${find}\:{the}\:{maximum}\:{kinetic}\:{energy} \\ $$

Question Number 40498    Answers: 1   Comments: 0

A gas at 17° has the ratio of its initial to final volume as 25 with initial pressure of 2×10^5 Nm^(−2) .Calculate the final pressure and temperature after compression.(γ=1.5)

$${A}\:{gas}\:{at}\:\mathrm{17}°\:{has}\:{the}\:{ratio}\:{of}\:{its}\:{initial} \\ $$$${to}\:{final}\:{volume}\:{as}\:\mathrm{25}\:{with}\:{initial} \\ $$$${pressure}\:{of}\:\mathrm{2}×\mathrm{10}^{\mathrm{5}} {Nm}^{−\mathrm{2}} .{Calculate} \\ $$$${the}\:{final}\:{pressure}\:{and}\:{temperature} \\ $$$${after}\:{compression}.\left(\gamma=\mathrm{1}.\mathrm{5}\right) \\ $$

Question Number 40497    Answers: 0   Comments: 1

please i want to have applications of limits in maths and other sciences

$${please}\:{i}\:{want}\:{to}\:{have}\:{applications}\:{of}\: \\ $$$${limits}\:{in}\:{maths}\:{and}\:{other}\:{sciences}\: \\ $$$$ \\ $$

Question Number 40505    Answers: 1   Comments: 0

calcilate ∫_(π/6) ^(π/4) ((sin(x))/(cos(x) +cos(2x)))dx

$${calcilate}\:\int_{\frac{\pi}{\mathrm{6}}} ^{\frac{\pi}{\mathrm{4}}} \:\:\:\frac{{sin}\left({x}\right)}{{cos}\left({x}\right)\:+{cos}\left(\mathrm{2}{x}\right)}{dx} \\ $$

Question Number 40504    Answers: 1   Comments: 0

let u_n =Σ_(k=1) ^n (1/(n^2 +k)) find lim_(n→+∞) n{1−n u_n } .

$${let}\:{u}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:\:\frac{\mathrm{1}}{{n}^{\mathrm{2}} +{k}} \\ $$$${find}\:{lim}_{{n}\rightarrow+\infty} {n}\left\{\mathrm{1}−{n}\:{u}_{{n}} \right\}\:. \\ $$

Question Number 40510    Answers: 1   Comments: 0

Given that ax+b is a factor of x^2 +2x^2 −1 and −a is a root of x^2 +2x −1=0 show that the value of b is −1 or 3+2(√(2 .))

$${Given}\:{that}\:{ax}+{b}\:{is}\:{a}\:{factor}\:{of}\:{x}^{\mathrm{2}} \\ $$$$+\mathrm{2}{x}^{\mathrm{2}} −\mathrm{1}\:{and}\:−{a}\:{is}\:{a}\:{root}\:{of}\:{x}^{\mathrm{2}} +\mathrm{2}{x} \\ $$$$−\mathrm{1}=\mathrm{0}\:{show}\:{that}\:{the}\:{value}\:{of}\:{b}\:{is} \\ $$$$−\mathrm{1}\:{or}\:\mathrm{3}+\mathrm{2}\sqrt{\mathrm{2}\:.} \\ $$

Question Number 40489    Answers: 2   Comments: 3

Question Number 40479    Answers: 1   Comments: 0

Question Number 40474    Answers: 2   Comments: 0

When x^7 −97x^6 −199x^5 +99x^4 − 2x+190 is divided by x−99 find the remainder.

$${When}\:{x}^{\mathrm{7}} −\mathrm{97}{x}^{\mathrm{6}} −\mathrm{199}{x}^{\mathrm{5}} +\mathrm{99}{x}^{\mathrm{4}} − \\ $$$$\mathrm{2}{x}+\mathrm{190}\:{is}\:{divided}\:{by}\:{x}−\mathrm{99}\:{find}\: \\ $$$${the}\:{remainder}. \\ $$

Question Number 40469    Answers: 0   Comments: 4

Question Number 40457    Answers: 1   Comments: 0

Question Number 40442    Answers: 2   Comments: 0

Solve : y^4 dx + 2xy^3 dy = ((ydx− xdy)/(x^3 y^3 )).

$$\mathrm{Solve}\:: \\ $$$$\mathrm{y}^{\mathrm{4}} \mathrm{d}{x}\:+\:\mathrm{2}{x}\mathrm{y}^{\mathrm{3}} \mathrm{dy}\:=\:\frac{\mathrm{yd}{x}−\:{x}\mathrm{dy}}{{x}^{\mathrm{3}} \mathrm{y}^{\mathrm{3}} }. \\ $$

Question Number 40434    Answers: 0   Comments: 3

prove that ln(x) is irrational for x natural

$${prove}\:{that}\:\mathrm{ln}\left({x}\right)\:{is}\:{irrational}\:{for}\:{x}\:{natural} \\ $$

Question Number 40426    Answers: 0   Comments: 0

Question Number 40422    Answers: 1   Comments: 1

Solve: ydx − xdy +log xdx =0

$$\mathrm{Solve}: \\ $$$$\mathrm{yd}{x}\:−\:{xdy}\:+\mathrm{log}\:{xdx}\:=\mathrm{0} \\ $$

Question Number 40418    Answers: 2   Comments: 1

Question Number 40417    Answers: 0   Comments: 0

Question Number 40407    Answers: 1   Comments: 0

let f(x)= x^3 −x−1 1) prove that ∃ α ∈ ]1,2[ /f(α)=0 2) use the newton method with x_0 =(3/2) to find a better value for α (take onlly 5 terms)

$${let}\:{f}\left({x}\right)=\:{x}^{\mathrm{3}} −{x}−\mathrm{1} \\ $$$$\left.\mathrm{1}\left.\right)\:{prove}\:{that}\:\exists\:\alpha\:\in\:\right]\mathrm{1},\mathrm{2}\left[\:/{f}\left(\alpha\right)=\mathrm{0}\right. \\ $$$$\left.\mathrm{2}\right)\:{use}\:{the}\:{newton}\:{method}\:\:{with}\:{x}_{\mathrm{0}} =\frac{\mathrm{3}}{\mathrm{2}} \\ $$$${to}\:{find}\:{a}\:{better}\:{value}\:{for}\:\alpha\:\left({take}\:{onlly}\:\mathrm{5}\:{terms}\right) \\ $$

Question Number 40406    Answers: 1   Comments: 0

Question Number 40399    Answers: 3   Comments: 0

Solve : (2(√(xy)) −x)dy + ydx = 0.

$$\mathrm{Solve}\:: \\ $$$$\left(\mathrm{2}\sqrt{{xy}}\:−{x}\right){dy}\:+\:{ydx}\:=\:\mathrm{0}. \\ $$

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