Question and Answers Forum

A panel of 3 women and 4 men is to be formed from 8 women and 7 men.Find the number of ways which the panel can be formed if it must contain at least 2 women.

$${A}\:{panel}\:{of}\:\mathrm{3}\:{women}\:{and}\:\mathrm{4}\:{men}\:{is} \\ $$$${to}\:{be}\:{formed}\:{from}\:\mathrm{8}\:{women}\:{and} \\ $$$$\mathrm{7}\:{men}.{Find}\:{the}\:{number}\:{of}\:{ways} \\ $$$${which}\:{the}\:{panel}\:{can}\:{be}\:{formed}\:{if} \\ $$$${it}\:{must}\:{contain}\:{at}\:{least}\:\mathrm{2}\:{women}. \\ $$

Question Number 35639 Answers: 0 Comments: 1

Three boys,two girls and a puppy sit at a round table.In how many ways can they be arranged if the puppy is to be seated i)between the two girls ii)between any two boys

$${Three}\:{boys},{two}\:{girls}\:{and}\:{a}\:{puppy} \\ $$$${sit}\:{at}\:{a}\:{round}\:{table}.{In}\:{how}\:{many} \\ $$$${ways}\:{can}\:{they}\:{be}\:{arranged}\:{if}\:{the} \\ $$$${puppy}\:{is}\:{to}\:{be}\:{seated} \\ $$$$\left.{i}\right){between}\:{the}\:{two}\:{girls} \\ $$$$\left.{ii}\right){between}\:{any}\:{two}\:{boys} \\ $$

Question Number 35635 Answers: 1 Comments: 1

Question Number 35992 Answers: 0 Comments: 1

let f(x)= ((sin(2x))/x) χ_(]−a,a[) (x) with a>0 calculate the fourier trsnsform of f .

$${let}\:{f}\left({x}\right)=\:\frac{{sin}\left(\mathrm{2}{x}\right)}{{x}}\:\chi_{\left.\right]−{a},{a}\left[\right.} \left({x}\right)\:\:{with}\:{a}>\mathrm{0} \\ $$$${calculate}\:{the}\:{fourier}\:{trsnsform}\:{of}\:{f}\:. \\ $$

Question Number 35632 Answers: 0 Comments: 2

let ϕ(x)= (1/(√(a^2 −x^2 ))) if ∣x∣<a and ϕ(x)=0 if ∣x∣≥a find the fourier transform of ϕ .

$${let}\:\varphi\left({x}\right)=\:\frac{\mathrm{1}}{\sqrt{{a}^{\mathrm{2}} −{x}^{\mathrm{2}} }}\:\:{if}\:\mid{x}\mid<{a}\:\:{and}\:\varphi\left({x}\right)=\mathrm{0}\:{if}\:\mid{x}\mid\geqslant{a} \\ $$$${find}\:{the}\:{fourier}\:{transform}\:{of}\:\varphi\:. \\ $$

Question Number 35631 Answers: 0 Comments: 0

let U_n = ∫_0 ^∞ e^(−(t/n)) arctan(t)dt find a equivalent of U_n (n→+∞)

$${let}\:{U}_{{n}} =\:\int_{\mathrm{0}} ^{\infty} \:\:\:{e}^{−\frac{{t}}{{n}}} \:\:{arctan}\left({t}\right){dt} \\ $$$${find}\:{a}\:{equivalent}\:{of}\:{U}_{{n}} \:\:\left({n}\rightarrow+\infty\right) \\ $$

Question Number 35630 Answers: 0 Comments: 5

1) find the value of f(x)=∫_0 ^∞ ((1−cos(xt))/t^2 ) e^(−t) dt 2) calculate ∫_0 ^∞ ((1−cos(t))/t^2 ) e^(−t) dt .

$$\left.\mathrm{1}\right)\:{find}\:{the}\:{value}\:{of}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{1}−{cos}\left({xt}\right)}{{t}^{\mathrm{2}} }\:{e}^{−{t}} {dt} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{\mathrm{1}−{cos}\left({t}\right)}{{t}^{\mathrm{2}} }\:{e}^{−{t}} \:{dt}\:. \\ $$

Question Number 35629 Answers: 0 Comments: 0

let f(x,y) = ∫_x ^y ((ln(t)ln(1−t))/t)dt with 0<x<y<1 give f(x,y) at form of serie .

$${let}\:\:{f}\left({x},{y}\right)\:=\:\int_{{x}} ^{{y}} \:\:\frac{{ln}\left({t}\right){ln}\left(\mathrm{1}−{t}\right)}{{t}}{dt}\:\:{with}\:\mathrm{0}<{x}<{y}<\mathrm{1} \\ $$$${give}\:{f}\left({x},{y}\right)\:{at}\:{form}\:{of}\:{serie}\:. \\ $$

Question Number 35628 Answers: 0 Comments: 1

find the value of I =∫_0 ^1 ((ln(t)ln(1−t))/t)dt

$${find}\:{the}\:{value}\:{of}\:\:{I}\:\:=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{ln}\left({t}\right){ln}\left(\mathrm{1}−{t}\right)}{{t}}{dt} \\ $$

Question Number 35627 Answers: 0 Comments: 0

study the convergence of I =∫_0 ^∞ (dx/((1+x^2 ∣sinx∣)^(3/2) ))

$${study}\:{the}\:{convergence}\:{of}\: \\ $$$${I}\:\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\:\:\:\frac{{dx}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \mid{sinx}\mid\right)^{\frac{\mathrm{3}}{\mathrm{2}}} } \\ $$

Question Number 35626 Answers: 0 Comments: 0

1) study the diagonalisstion of the matrice A = (((1+a^2 a 0)),((a 1+a^2 a)) ) ( 0 a 1+a^2 ) 2) calculate A^n

$$\left.\mathrm{1}\right)\:{study}\:{the}\:{diagonalisstion}\:{of}\:{the}\:{matrice} \\ $$$${A}\:=\begin{pmatrix}{\mathrm{1}+{a}^{\mathrm{2}} \:\:\:\:\:{a}\:\:\:\:\:\:\:\mathrm{0}}\\{{a}\:\:\:\:\:\:\:\:\:\mathrm{1}+{a}^{\mathrm{2}} \:\:\:\:\:{a}}\end{pmatrix} \\ $$$$\:\:\:\:\:\:\:\:\:\:\left(\:\mathrm{0}\:\:\:\:\:\:\:\:\:\:{a}\:\:\:\:\mathrm{1}+{a}^{\mathrm{2}} \:\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{A}^{{n}} \\ $$

Question Number 35625 Answers: 0 Comments: 0

find lim_(ξ→0) ∫_0 ^(π/2) (dx/(√( sin^2 x +ξ cos^2 x)))

$${find}\:{lim}_{\xi\rightarrow\mathrm{0}} \:\:\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\:\:\:\frac{{dx}}{\sqrt{\:{sin}^{\mathrm{2}} {x}\:+\xi\:{cos}^{\mathrm{2}} {x}}} \\ $$

Question Number 35624 Answers: 0 Comments: 0

let R_n = Σ_(k=n+1) ^∞ (1/(k!)) find a equivalent of R_n when n→+∞

$${let}\:{R}_{{n}} \:=\:\sum_{{k}={n}+\mathrm{1}} ^{\infty} \:\:\frac{\mathrm{1}}{{k}!} \\ $$$${find}\:{a}\:{equivalent}\:{of}\:{R}_{{n}} \:\:{when}\:{n}\rightarrow+\infty \\ $$

Question Number 35623 Answers: 0 Comments: 0

solve the differencial system {_(y^′ = y +2z +t^2 ) ^(x^′ = y +t^2 ) {z^′ =2x−2y

$${solve}\:{the}\:{differencial}\:{system} \\ $$$$\left\{_{{y}^{'} =\:{y}\:+\mathrm{2}{z}\:+{t}^{\mathrm{2}} } ^{{x}^{'} \:\:=\:{y}\:+{t}^{\mathrm{2}} } \right. \\ $$$$\left\{{z}^{'} \:=\mathrm{2}{x}−\mathrm{2}{y}\right. \\ $$

Question Number 35622 Answers: 0 Comments: 0

find all matrices M ∈M_3 (R) / M^2 =M

$${find}\:{all}\:{matrices}\:{M}\:\in{M}_{\mathrm{3}} \left({R}\right)\:\:/\:\:{M}^{\mathrm{2}} \:={M} \\ $$

Question Number 35621 Answers: 0 Comments: 2

calculate S(x) = Σ_(n=0) ^∞ (x^(3n) /(3n+1)) after finding the radius of convergence . 2) find the value of Σ_(n=0) ^∞ (1/((3n+1)8^n ))

$${calculate}\:\:\:{S}\left({x}\right)\:=\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\:\:\frac{{x}^{\mathrm{3}{n}} }{\mathrm{3}{n}+\mathrm{1}}\:\:{after}\:{finding} \\ $$$${the}\:{radius}\:{of}\:{convergence}\:. \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\:\:\:\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\:\:\frac{\mathrm{1}}{\left(\mathrm{3}{n}+\mathrm{1}\right)\mathrm{8}^{{n}} } \\ $$

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