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Question Number 142556 Answers: 1 Comments: 0

{ ((x^2 +y^2 =2yz+2−z^2 )),((z=4022−x−y)) :} x,y,z∈Z^+ . then z=

$$\begin{cases}{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{2}{yz}+\mathrm{2}−{z}^{\mathrm{2}} }\\{{z}=\mathrm{4022}−{x}−{y}}\end{cases} \\ $$$$\:{x},{y},{z}\in\mathbb{Z}^{+} \:.\:{then}\:{z}= \\ $$

Question Number 142553 Answers: 2 Comments: 0

Evaluate : ∫_0 ^1 ((log(x)log((x/(1−x))))/( (√(x/(1−x))))) dx

$$ \\ $$$$\:\:\:\:{Evaluate}\::\: \\ $$$$\:\:\:\:\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{log}\left({x}\right){log}\left(\frac{{x}}{\mathrm{1}−{x}}\right)}{\:\sqrt{\frac{{x}}{\mathrm{1}−{x}}}}\:{dx} \\ $$

Question Number 142548 Answers: 0 Comments: 1

Question Number 142546 Answers: 0 Comments: 1

i need help

$${i}\:{need}\:{help} \\ $$

Question Number 142545 Answers: 1 Comments: 0

nice .....integral Ω:=∫_(−∞) ^( +∞) (dx/((x^2 +π^2 )cosh(x))) =? .....

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:{nice}\:.....{integral} \\ $$$$\:\:\:\:\:\Omega:=\int_{−\infty} ^{\:\:+\infty} \frac{{dx}}{\left({x}^{\mathrm{2}} +\pi^{\mathrm{2}} \right){cosh}\left({x}\right)}\:=? \\ $$$$..... \\ $$

Question Number 142538 Answers: 1 Comments: 0

2x^7 +x^(28) =3x^(21) find x

$$\mathrm{2}\boldsymbol{{x}}^{\mathrm{7}} +\boldsymbol{{x}}^{\mathrm{28}} =\mathrm{3}\boldsymbol{{x}}^{\mathrm{21}} \\ $$$$\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{x}} \\ $$

Question Number 142537 Answers: 0 Comments: 0

Given: z_1 =e^(i(π/3)) (z+3)−3 and z_2 =e^(−i((2π)/3)) (z−3)+3. Show that ((z_2 −z)/(z_1 −z))=i(√3)((z−3)/(z+3))

$$\mathrm{Given}: \\ $$$$\mathrm{z}_{\mathrm{1}} =\mathrm{e}^{\mathrm{i}\frac{\pi}{\mathrm{3}}} \left(\mathrm{z}+\mathrm{3}\right)−\mathrm{3}\:\mathrm{and}\:\mathrm{z}_{\mathrm{2}} =\mathrm{e}^{−\mathrm{i}\frac{\mathrm{2}\pi}{\mathrm{3}}} \left(\mathrm{z}−\mathrm{3}\right)+\mathrm{3}. \\ $$$$\mathrm{Show}\:\mathrm{that}\: \\ $$$$\frac{\mathrm{z}_{\mathrm{2}} −\mathrm{z}}{\mathrm{z}_{\mathrm{1}} −\mathrm{z}}=\mathrm{i}\sqrt{\mathrm{3}}\frac{\mathrm{z}−\mathrm{3}}{\mathrm{z}+\mathrm{3}} \\ $$

Question Number 142534 Answers: 0 Comments: 0

Question Number 142531 Answers: 0 Comments: 0

if 𝛗 (q):= ∫_1 ^( ∞) (1/( (√x) (q+x)^x ))dx then :: lim _(q→1) 𝛗(q):=?

$$\: \\ $$$$\:\:{if}\:\:\:\:\boldsymbol{\phi}\:\left({q}\right):=\:\int_{\mathrm{1}} ^{\:\infty} \frac{\mathrm{1}}{\:\sqrt{{x}}\:\left({q}+{x}\right)^{{x}} }{dx} \\ $$$$\:\:\:\:{then}\:::\:\:{lim}\:_{{q}\rightarrow\mathrm{1}} \boldsymbol{\phi}\left({q}\right):=? \\ $$$$\:\:\:\:\:\: \\ $$

Question Number 142528 Answers: 1 Comments: 0

∫_1 ^( ∞) (dx/(e^x −2^x ))

$$\int_{\mathrm{1}} ^{\:\infty} \:\frac{{dx}}{{e}^{{x}} −\mathrm{2}^{{x}} } \\ $$

Question Number 142516 Answers: 0 Comments: 0

∫(dx/((−lnx)^(1/x) ))

$$\int\frac{{dx}}{\left(−{lnx}\right)^{\frac{\mathrm{1}}{{x}}} }\:\: \\ $$

Question Number 142514 Answers: 5 Comments: 0

..... number theory..... Solve in Z : (1/x)+(1/y)+(1/(xy)) =(1/4) ....? .........

$$\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:.....\:{number}\:\:{theory}..... \\ $$$$\:\:\:\:\:\:\:{Solve}\:{in}\:\mathbb{Z}\:: \\ $$$$\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{1}}{{x}}+\frac{\mathrm{1}}{{y}}+\frac{\mathrm{1}}{{xy}}\:=\frac{\mathrm{1}}{\mathrm{4}}\:....? \\ $$$$\:\:\:\:\:......... \\ $$

Question Number 142518 Answers: 0 Comments: 0

Question Number 142510 Answers: 0 Comments: 1

Question Number 142505 Answers: 0 Comments: 0

Question Number 142504 Answers: 1 Comments: 0

Question Number 142503 Answers: 1 Comments: 0

Question Number 142502 Answers: 0 Comments: 0

(dy/dx) y= 3a^x −cot 2x

$$\frac{{dy}}{{dx}}\: \\ $$$${y}=\:\mathrm{3}{a}^{{x}} −\mathrm{cot}\:\mathrm{2}{x} \\ $$

Question Number 142499 Answers: 2 Comments: 1

Question Number 142492 Answers: 1 Comments: 0

Prove that Σ_(n = 0) ^∞ (n/(3n^2 + 2)) diverges.

$$\mathrm{Prove}\:\mathrm{that}\:\underset{{n}\:=\:\mathrm{0}} {\overset{\infty} {\sum}}\frac{{n}}{\mathrm{3}{n}^{\mathrm{2}} \:+\:\mathrm{2}}\:\mathrm{diverges}. \\ $$

Question Number 142489 Answers: 0 Comments: 3

In a certain urn there are 3 blue, 2red and 5 yellow marbles. Calculate probability that atmost 2 marbles will be red if 3 marbles are drawn without replacement

$$\mathrm{In}\:\:\mathrm{a}\:\mathrm{certain}\:\mathrm{urn}\:\mathrm{there}\:\mathrm{are}\:\mathrm{3}\:\mathrm{blue}, \\ $$$$\mathrm{2red}\:\mathrm{and}\:\mathrm{5}\:\mathrm{yellow}\:\mathrm{marbles}. \\ $$$$\mathrm{Calculate}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{atmost} \\ $$$$\mathrm{2}\:\mathrm{marbles}\:\mathrm{will}\:\mathrm{be}\:\mathrm{red}\:\mathrm{if}\:\mathrm{3}\:\mathrm{marbles} \\ $$$$\:\mathrm{are}\:\mathrm{drawn}\:\mathrm{without}\:\mathrm{replacement} \\ $$

Question Number 142488 Answers: 2 Comments: 0

∫_0 ^1 (t^(k−1) /(1+t^2 ))dt

$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{t}^{{k}−\mathrm{1}} }{\mathrm{1}+{t}^{\mathrm{2}} }{dt} \\ $$

Question Number 142477 Answers: 0 Comments: 0

Question Number 142475 Answers: 2 Comments: 0

Question Number 142469 Answers: 1 Comments: 0

...... Calculus ..... Evaluate: ∫_0 ^( 1) (((log((1/x)))/(1−x)))^3 dx=??

$$\:\:\:\:\:\:\:\:\:\:\:\:......\:\:{Calculus}\:..... \\ $$$$\:\:\:\:{Evaluate}:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \left(\frac{{log}\left(\frac{\mathrm{1}}{{x}}\right)}{\mathrm{1}−{x}}\right)^{\mathrm{3}} {dx}=?? \\ $$

Question Number 142467 Answers: 0 Comments: 2

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