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Question Number 219562 Answers: 1 Comments: 0

prove that exists X ∈ M_(2,3) (R) Y ∈ M_(3,2) (R) such that X∙Y = ((1,1),(1,1) ) Y∙X = ((2,6,6),(3,9,9),((-3),(-9),(-9)) )

$$\mathrm{prove}\:\mathrm{that}\:\mathrm{exists}\:\:\:\mathrm{X}\:\in\:\mathrm{M}_{\mathrm{2},\mathrm{3}} \:\left(\mathbb{R}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{Y}\:\in\:\mathrm{M}_{\mathrm{3},\mathrm{2}} \:\left(\mathbb{R}\right) \\ $$$$\mathrm{such}\:\mathrm{that}\:\:\:\mathrm{X}\centerdot\mathrm{Y}\:=\:\begin{pmatrix}{\mathrm{1}}&{\mathrm{1}}\\{\mathrm{1}}&{\mathrm{1}}\end{pmatrix}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{Y}\centerdot\mathrm{X}\:=\:\begin{pmatrix}{\mathrm{2}}&{\mathrm{6}}&{\mathrm{6}}\\{\mathrm{3}}&{\mathrm{9}}&{\mathrm{9}}\\{-\mathrm{3}}&{-\mathrm{9}}&{-\mathrm{9}}\end{pmatrix}\: \\ $$

Question Number 219561 Answers: 0 Comments: 3

let be the sequence (x_n )n ≥ 1 defined by x_1 = 1 x_(n+2) = 3x_(n+1) − x_n ∀n ∈ N find L =lim_(n→∞) ((Σ_(k=0) ^0 (x_(2k+1) /(x_k + x_(k+1) ))))^(1/n) = ?

$$\mathrm{let}\:\mathrm{be}\:\mathrm{the}\:\mathrm{sequence}\:\:\:\left(\mathrm{x}_{\boldsymbol{\mathrm{n}}} \right)\mathrm{n}\:\geqslant\:\mathrm{1} \\ $$$$\mathrm{defined}\:\mathrm{by}\:\:\:\mathrm{x}_{\mathrm{1}} =\:\mathrm{1} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{x}_{\boldsymbol{\mathrm{n}}+\mathrm{2}} \:=\:\mathrm{3x}_{\boldsymbol{\mathrm{n}}+\mathrm{1}} −\:\mathrm{x}_{\boldsymbol{\mathrm{n}}} \\ $$$$\forall\mathrm{n}\:\in\:\mathbb{N} \\ $$$$\mathrm{find}\:\:\:\boldsymbol{\mathrm{L}}\:=\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\mathrm{lim}}\:\sqrt[{\boldsymbol{\mathrm{n}}}]{\underset{\boldsymbol{\mathrm{k}}=\mathrm{0}} {\overset{\mathrm{0}} {\sum}}\:\:\frac{\mathrm{x}_{\mathrm{2}\boldsymbol{\mathrm{k}}+\mathrm{1}} }{\mathrm{x}_{\boldsymbol{\mathrm{k}}} \:+\:\mathrm{x}_{\boldsymbol{\mathrm{k}}+\mathrm{1}} }}\:=\:? \\ $$

Question Number 219560 Answers: 0 Comments: 0

Suppose that an urn contains 100,000 marbles and 120 are red . If a random sample of 1000 is drawn, what are the probabilities that 0,1,2,3 and 4 respectively will be red. What is the mean and variance?

Question Number 219556 Answers: 0 Comments: 0

Question Number 219555 Answers: 0 Comments: 0

p= number of responses/total number of responded

$${p}=\:{number}\:{of}\:{responses}/{total}\:{number}\:{of}\:{responded} \\ $$

Question Number 219554 Answers: 1 Comments: 0

I_n =∫_0 ^( 1) ∫_0 ^1 ...∫_0 ^( 1) (((x_1 x_2 ...x_n )^a )/((1−x_1 x_2 ...x_n )))ln(x_(1 ) )ln(x_2 )...ln(x_(n ) )dx_1 dx_2 ...dx_(n )

$$ \\ $$$$\:{I}_{{n}} =\int_{\mathrm{0}} ^{\:\mathrm{1}} \int_{\mathrm{0}} ^{\mathrm{1}} ...\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\left({x}_{\mathrm{1}} {x}_{\mathrm{2}} ...{x}_{{n}} \right)^{{a}} }{\left(\mathrm{1}−{x}_{\mathrm{1}} {x}_{\mathrm{2}} ...{x}_{{n}} \right)}{ln}\left({x}_{\mathrm{1}\:} \right){ln}\left({x}_{\mathrm{2}} \right)...{ln}\left({x}_{{n}\:} \right){dx}_{\mathrm{1}} {dx}_{\mathrm{2}} ...{dx}_{{n}\:} \:\:\:\:\: \\ $$$$ \\ $$

Question Number 219553 Answers: 0 Comments: 0

I_n = ∫_0 ^( 1) ∫_0 ^( 1) ....∫_0 ^( 1) ((ln(1+x_1 x_2 ....x_n ))/((1−x_1 )(1−x_2 )....(1−x_(n ) ))) dx_1 dx_2 ....dx_n

$$ \\ $$$$\:{I}_{{n}} =\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \int_{\mathrm{0}} ^{\:\mathrm{1}} ....\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\frac{{ln}\left(\mathrm{1}+{x}_{\mathrm{1}} {x}_{\mathrm{2}} \:....{x}_{{n}} \right)}{\left(\mathrm{1}−{x}_{\mathrm{1}} \right)\left(\mathrm{1}−{x}_{\mathrm{2}} \right)....\left(\mathrm{1}−{x}_{{n}\:} \right)}\:{dx}_{\mathrm{1}} {dx}_{\mathrm{2}} \:....{dx}_{{n}} \:\:\:\:\:\:\:\: \\ $$$$ \\ $$

Question Number 219552 Answers: 2 Comments: 0

Question Number 219550 Answers: 4 Comments: 0

Question Number 219549 Answers: 6 Comments: 0

Question Number 219548 Answers: 0 Comments: 0

Question Number 219540 Answers: 2 Comments: 0

Question Number 219529 Answers: 1 Comments: 1

∫_( 0) ^( 1) ((1+x−x^2 +x^3 −x^4 −x^5 )/(1−x^7 )) dx

$$ \\ $$$$\:\:\:\:\int_{\:\mathrm{0}} ^{\:\mathrm{1}} \:\:\:\:\frac{\mathrm{1}+{x}−{x}^{\mathrm{2}} +{x}^{\mathrm{3}} −{x}^{\mathrm{4}} −{x}^{\mathrm{5}} }{\mathrm{1}−{x}^{\mathrm{7}} }\:\:\:{dx} \\ $$$$ \\ $$

Question Number 219527 Answers: 2 Comments: 2

Question Number 219522 Answers: 0 Comments: 0

∫^( ∞) _( 0) ((10x^(17) e^(2x) (e^(2x) −1)+x^(17) e^x (e^(4x) −1))/((e^x −1)^6 )) dx

$$ \\ $$$$\:\:\:\underset{\:\mathrm{0}} {\int}^{\:\infty} \:\frac{\mathrm{10}{x}^{\mathrm{17}} {e}^{\mathrm{2}{x}} \left({e}^{\mathrm{2}{x}} −\mathrm{1}\right)+{x}^{\mathrm{17}} {e}^{{x}} \left({e}^{\mathrm{4}{x}} −\mathrm{1}\right)}{\left({e}^{{x}} −\mathrm{1}\right)^{\mathrm{6}} }\:{dx}\:\:\: \\ $$$$ \\ $$

Question Number 219521 Answers: 0 Comments: 1

Question Number 219520 Answers: 1 Comments: 0

find the laplace transform of f(t)=∫_0 ^t ((sint)/t)dt

$$\boldsymbol{{find}}\:\boldsymbol{{the}}\:\boldsymbol{{laplace}}\:\boldsymbol{{transform}}\:\boldsymbol{{of}} \\ $$$$\boldsymbol{{f}}\left(\boldsymbol{{t}}\right)=\int_{\mathrm{0}} ^{\boldsymbol{{t}}} \frac{\boldsymbol{{sint}}}{\boldsymbol{{t}}}\boldsymbol{{dt}} \\ $$

Question Number 219519 Answers: 1 Comments: 0

find the laplace transform of ∫_0 ^∞ te^(−2t) sintdt

$$\boldsymbol{{find}}\:\boldsymbol{{the}}\:\boldsymbol{{laplace}}\:\boldsymbol{{transform}}\:\boldsymbol{{of}} \\ $$$$\int_{\mathrm{0}} ^{\infty} \boldsymbol{{te}}^{−\mathrm{2}\boldsymbol{{t}}} \boldsymbol{{sintdt}} \\ $$

Question Number 219515 Answers: 2 Comments: 0

Find: 𝛀 = ∫_0 ^( 1) x^x^2 dx = ?

$$\mathrm{Find}:\:\:\:\boldsymbol{\Omega}\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\mathrm{x}^{\boldsymbol{\mathrm{x}}^{\mathrm{2}} } \:\mathrm{dx}\:=\:?\: \\ $$

Question Number 219503 Answers: 1 Comments: 0

Question Number 219506 Answers: 2 Comments: 0

Q. Integrate ((x^2 +x+1)/(2x^2 −x−3)).

$${Q}.\:{Integrate}\:\frac{{x}^{\mathrm{2}} +{x}+\mathrm{1}}{\mathrm{2}{x}^{\mathrm{2}} −{x}−\mathrm{3}}. \\ $$$$ \\ $$

Question Number 219496 Answers: 0 Comments: 0

p(t)=−(1/(iπ))∫_(−∞i+𝛄) ^( ∞i+𝛄) ((e^(st) (ln(s)+𝛄_0 ))/s) ds q(t)=(1/(iπ))∫_(−∞i+𝛄) ^( ∞i+𝛄) {−(π/(2s))L_0 (s)+(π/(2s))iY_0 (−is)}e^(st) ds g(s)=∫_0 ^( ∞) J_ν (t)J_ν (st)dt h(s)=∫_0 ^( ∞) cos(t)J_ν (st)dt e^t is exponential function ln(t) is natural logarithm cos(t) is cosine function J_ν (t) is Bessel function of the First kind Y_ν (t) is Bessel function of the Second kind L_ν (t) is modified StruveH function 𝛄_0 is Euler-mascheroni Const.(0.5772156649015.....) π is pi (3.141592653589793238.........) i is (√(−1)) ∞ is infinity

$${p}\left({t}\right)=−\frac{\mathrm{1}}{\boldsymbol{{i}}\pi}\int_{−\infty\boldsymbol{{i}}+\boldsymbol{\gamma}} ^{\:\infty\boldsymbol{{i}}+\boldsymbol{\gamma}} \:\:\frac{{e}^{{st}} \left(\mathrm{ln}\left({s}\right)+\boldsymbol{\gamma}_{\mathrm{0}} \right)}{{s}}\:\mathrm{d}{s} \\ $$$${q}\left({t}\right)=\frac{\mathrm{1}}{\boldsymbol{{i}}\pi}\int_{−\infty\boldsymbol{{i}}+\boldsymbol{\gamma}} ^{\:\:\infty\boldsymbol{{i}}+\boldsymbol{\gamma}} \:\left\{−\frac{\pi}{\mathrm{2}{s}}\boldsymbol{\mathrm{L}}_{\mathrm{0}} \left({s}\right)+\frac{\pi}{\mathrm{2}{s}}\boldsymbol{{i}}{Y}_{\mathrm{0}} \left(−\boldsymbol{{i}}{s}\right)\right\}{e}^{{st}} \:\mathrm{d}{s} \\ $$$$\mathrm{g}\left({s}\right)=\int_{\mathrm{0}} ^{\:\infty} \:\:{J}_{\nu} \left({t}\right){J}_{\nu} \left({st}\right)\mathrm{d}{t} \\ $$$${h}\left({s}\right)=\int_{\mathrm{0}} ^{\:\infty} \:\mathrm{cos}\left({t}\right){J}_{\nu} \left({st}\right)\mathrm{d}{t} \\ $$$${e}^{{t}} \:\mathrm{is}\:\mathrm{exponential}\:\mathrm{function} \\ $$$$\mathrm{ln}\left({t}\right)\:\mathrm{is}\:\mathrm{natural}\:\mathrm{logarithm} \\ $$$$\mathrm{cos}\left({t}\right)\:\mathrm{is}\:\mathrm{cosine}\:\mathrm{function}\: \\ $$$${J}_{\nu} \left({t}\right)\:\mathrm{is}\:\mathrm{Bessel}\:\mathrm{function}\:\mathrm{of}\:\mathrm{the}\:\mathrm{First}\:\mathrm{kind} \\ $$$${Y}_{\nu} \left({t}\right)\:\mathrm{is}\:\mathrm{Bessel}\:\mathrm{function}\:\mathrm{of}\:\mathrm{the}\:\mathrm{Second}\:\mathrm{kind} \\ $$$$\boldsymbol{\mathrm{L}}_{\nu} \left({t}\right)\:\mathrm{is}\:\mathrm{modified}\:\mathrm{StruveH}\:\mathrm{function} \\ $$$$\boldsymbol{\gamma}_{\mathrm{0}} \:\mathrm{is}\:\mathrm{Euler}-\mathrm{mascheroni}\:\mathrm{Const}.\left(\mathrm{0}.\mathrm{5772156649015}.....\right) \\ $$$$\pi\:\mathrm{is}\:\mathrm{pi}\:\left(\mathrm{3}.\mathrm{141592653589793238}.........\right) \\ $$$$\boldsymbol{{i}}\:\mathrm{is}\:\sqrt{−\mathrm{1}}\: \\ $$$$\infty\:\mathrm{is}\:\mathrm{infinity}\: \\ $$

Question Number 219509 Answers: 2 Comments: 0

I = ∫^( 16) _( 1) (((x +(√x))^(1/4) )/x^(3/4) ) dx

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:{I}\:=\:\underset{\:\mathrm{1}} {\int}^{\:\mathrm{16}} \:\frac{\left({x}\:+\sqrt{{x}}\right)^{\frac{\mathrm{1}}{\mathrm{4}}} }{{x}^{\frac{\mathrm{3}}{\mathrm{4}}} }\:{dx} \\ $$$$ \\ $$

Question Number 219492 Answers: 3 Comments: 0

a + b = 1 a^2 + b^2 = 2 Find: a^(11) + b^(11) = ?

$$\mathrm{a}\:+\:\mathrm{b}\:=\:\mathrm{1} \\ $$$$\mathrm{a}^{\mathrm{2}} \:+\:\mathrm{b}^{\mathrm{2}} \:=\:\mathrm{2} \\ $$$$\mathrm{Find}:\:\:\:\mathrm{a}^{\mathrm{11}} \:+\:\mathrm{b}^{\mathrm{11}} \:=\:? \\ $$

Question Number 219491 Answers: 1 Comments: 0

if x′′−2x′+10x=e^(2t) , at t=0,x=0 and x′=1 find x(t) using laplace transform

$$\boldsymbol{{if}}\:\boldsymbol{{x}}''−\mathrm{2}\boldsymbol{{x}}'+\mathrm{10}\boldsymbol{{x}}=\boldsymbol{{e}}^{\mathrm{2}\boldsymbol{{t}}} ,\:\boldsymbol{{at}}\:\boldsymbol{{t}}=\mathrm{0},\boldsymbol{{x}}=\mathrm{0}\:\boldsymbol{{and}}\:\boldsymbol{{x}}'=\mathrm{1} \\ $$$$\boldsymbol{{find}}\:\boldsymbol{{x}}\left(\boldsymbol{{t}}\right)\:\boldsymbol{{using}}\:\boldsymbol{{laplace}}\:\boldsymbol{{transform}} \\ $$

Question Number 219488 Answers: 1 Comments: 0

solve the initial value problem y′−2e^(−t^2 ) +2ty=0 y(0)=1

$$\boldsymbol{{solve}}\:\boldsymbol{{the}}\:\boldsymbol{{initial}}\:\boldsymbol{{value}}\:\boldsymbol{{problem}}\: \\ $$$$\boldsymbol{{y}}'−\mathrm{2}\boldsymbol{{e}}^{−\boldsymbol{{t}}^{\mathrm{2}} } +\mathrm{2}\boldsymbol{{ty}}=\mathrm{0}\:\:\boldsymbol{{y}}\left(\mathrm{0}\right)=\mathrm{1} \\ $$

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