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Question Number 142252 Answers: 1 Comments: 0

Question Number 141814 Answers: 1 Comments: 2

please help me finding the roots of x^5 +5x^4 +20x^3 +60x^2 +120x+120=0?

$${please}\:{help}\:{me}\:{finding}\:{the}\:{roots}\:{of}\:\: \\ $$$${x}^{\mathrm{5}} +\mathrm{5}{x}^{\mathrm{4}} +\mathrm{20}{x}^{\mathrm{3}} +\mathrm{60}{x}^{\mathrm{2}} +\mathrm{120}{x}+\mathrm{120}=\mathrm{0}? \\ $$

Question Number 141812 Answers: 1 Comments: 2

Question Number 141811 Answers: 1 Comments: 0

Θ:=(Σ_(n=1) ^∞ (n^4 /(2^n . n!)))^(1/2) =?

$$\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\Theta:=\left(\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{{n}^{\mathrm{4}} }{\mathrm{2}^{{n}} \:.\:{n}!}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} =? \\ $$

Question Number 141805 Answers: 2 Comments: 0

∫(dx/(1−tanx))

$$\int\frac{{dx}}{\mathrm{1}−{tanx}} \\ $$

Question Number 141797 Answers: 0 Comments: 0

Question Number 143584 Answers: 1 Comments: 0

{ ((x^2 −xy+y^2 =7)),(((x+3)(y−2)=(√(xy+3))+(√(xy−2)))) :} Find x,y

$$\begin{cases}{{x}^{\mathrm{2}} −{xy}+{y}^{\mathrm{2}} =\mathrm{7}}\\{\left({x}+\mathrm{3}\right)\left({y}−\mathrm{2}\right)=\sqrt{{xy}+\mathrm{3}}+\sqrt{{xy}−\mathrm{2}}}\end{cases} \\ $$$${Find}\:{x},{y} \\ $$

Question Number 143586 Answers: 1 Comments: 1

Question Number 141791 Answers: 4 Comments: 0

Calculate Σ_(n=1) ^(+∞) (n^2 /3^n )

$$\mathrm{Calculate} \\ $$$$\:\underset{\mathrm{n}=\mathrm{1}} {\overset{+\infty} {\sum}}\:\frac{\mathrm{n}^{\mathrm{2}} }{\mathrm{3}^{\mathrm{n}} } \\ $$

Question Number 141786 Answers: 1 Comments: 0

If y=1−cos2t and x=(√(1+t^2 )) .Show that (dy/dx)=((2(√(1+t^2 )) sin2t)/t) Help please.

$$\boldsymbol{\mathrm{If}}\:\:\boldsymbol{\mathrm{y}}=\mathrm{1}−\boldsymbol{\mathrm{cos}}\mathrm{2}\boldsymbol{\mathrm{t}}\:\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{x}}=\sqrt{\mathrm{1}+\boldsymbol{\mathrm{t}}^{\mathrm{2}} }\:.\boldsymbol{\mathrm{Show}}\:\boldsymbol{\mathrm{that}} \\ $$$$\frac{\boldsymbol{\mathrm{dy}}}{\boldsymbol{\mathrm{dx}}}=\frac{\mathrm{2}\sqrt{\mathrm{1}+\boldsymbol{\mathrm{t}}^{\mathrm{2}} }\:\boldsymbol{\mathrm{sin}}\mathrm{2}\boldsymbol{\mathrm{t}}}{\boldsymbol{\mathrm{t}}} \\ $$$$\boldsymbol{\mathrm{Help}}\:\boldsymbol{\mathrm{please}}. \\ $$

Question Number 141785 Answers: 1 Comments: 0

If x=asin2t+bcos2t,prove that (dx/dt)=2(√(a^2 +b^2 −x^2 )) Solution....

$$\boldsymbol{\mathrm{If}}\:\:\boldsymbol{\mathrm{x}}=\boldsymbol{\mathrm{asin}}\mathrm{2}\boldsymbol{\mathrm{t}}+\boldsymbol{\mathrm{bcos}}\mathrm{2}\boldsymbol{\mathrm{t}},\boldsymbol{\mathrm{prove}}\:\boldsymbol{\mathrm{that}}\: \\ $$$$\frac{\boldsymbol{\mathrm{dx}}}{\boldsymbol{\mathrm{dt}}}=\mathrm{2}\sqrt{\boldsymbol{\mathrm{a}}^{\mathrm{2}} +\boldsymbol{\mathrm{b}}^{\mathrm{2}} −\boldsymbol{\mathrm{x}}^{\mathrm{2}} } \\ $$$$\boldsymbol{\mathrm{Solution}}.... \\ $$

Question Number 141783 Answers: 0 Comments: 0

Question Number 141775 Answers: 1 Comments: 0

find ∫_0 ^∞ (e^(−x^2 ) /((x^2 +3)^2 ))dx

$$\mathrm{find}\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{e}^{−\mathrm{x}^{\mathrm{2}} } }{\left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{3}\right)^{\mathrm{2}} }\mathrm{dx} \\ $$

Question Number 141774 Answers: 2 Comments: 0

calculate ∫_0 ^∞ (e^(−x^2 ) /(1+x^2 ))dx

$$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{e}^{−\mathrm{x}^{\mathrm{2}} } }{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\mathrm{dx} \\ $$

Question Number 141769 Answers: 1 Comments: 0

If y=2sinx+tanx, prove that (d^2 y/dx^2 )=2sinx(sec^3 x−1) Any detailed solution please.

Question Number 141768 Answers: 0 Comments: 0

Let a,b,x,y > 0 and (a+x)(b+y) = (a+b)^2 . Prove that ((a−y)/x)+((b−x)/y) ≤ ((b−x)/a)+((a−y)/b)

$$\mathrm{Let}\:{a},{b},{x},{y}\:>\:\mathrm{0}\:\mathrm{and}\:\left({a}+{x}\right)\left({b}+{y}\right)\:=\:\left({a}+{b}\right)^{\mathrm{2}} \:.\:\:\:\:\:\:\:\: \\ $$$$\mathrm{Prove}\:\mathrm{that} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{{a}−{y}}{{x}}+\frac{{b}−{x}}{{y}}\:\leqslant\:\frac{{b}−{x}}{{a}}+\frac{{a}−{y}}{{b}}\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$ \\ $$

Question Number 141759 Answers: 0 Comments: 0

Question Number 141757 Answers: 0 Comments: 1

Γ(n+(1/2))=(((√π)∙Γ(2n+1))/(2^(2n) Γ(n+1)))

$$\Gamma\left(\mathrm{n}+\frac{\mathrm{1}}{\mathrm{2}}\right)=\frac{\sqrt{\pi}\centerdot\Gamma\left(\mathrm{2n}+\mathrm{1}\right)}{\mathrm{2}^{\mathrm{2n}} \Gamma\left(\mathrm{n}+\mathrm{1}\right)} \\ $$

Question Number 141755 Answers: 0 Comments: 0

Question Number 141752 Answers: 1 Comments: 0

Question Number 141750 Answers: 1 Comments: 0

Question Number 141749 Answers: 1 Comments: 0

{ ((x^2 −y+(√(y^2 +5))=xy−(√(x−1)))),((y^2 +(√(xy+2))=2(x+y))) :} Find x,y

$$\begin{cases}{\mathrm{x}^{\mathrm{2}} −\mathrm{y}+\sqrt{\mathrm{y}^{\mathrm{2}} +\mathrm{5}}=\mathrm{xy}−\sqrt{\mathrm{x}−\mathrm{1}}}\\{\mathrm{y}^{\mathrm{2}} +\sqrt{\mathrm{xy}+\mathrm{2}}=\mathrm{2}\left(\mathrm{x}+\mathrm{y}\right)}\end{cases} \\ $$$$\mathrm{Find}\:\mathrm{x},\mathrm{y} \\ $$

Question Number 141777 Answers: 0 Comments: 1

A pack of 52 cards distributed equally to 4 people so as 4 cards each from same suit( of any 3 suit=4×3=12) and last card from 4th remaining suit . Number of such distributions is?

$${A}\:{pack}\:{of}\:\mathrm{52}\:{cards}\:{distributed}\:{equally}\:{to} \\ $$$$\mathrm{4}\:{people}\:{so}\:{as}\:\mathrm{4}\:{cards}\:{each}\:{from}\: \\ $$$${same}\:{suit}\left(\:{of}\:{any}\:\mathrm{3}\:{suit}=\mathrm{4}×\mathrm{3}=\mathrm{12}\right) \\ $$$${and}\:{last}\:{card}\:{from}\:\mathrm{4}{th}\:{remaining} \\ $$$${suit}\:.\:{Number}\:{of}\:{such} \\ $$$${distributions}\:{is}? \\ $$$$ \\ $$$$ \\ $$

Question Number 141733 Answers: 0 Comments: 0

Question Number 141730 Answers: 0 Comments: 2

x^2 +y^2 +xy=9 y^2 +z^2 +yz=16 x^2 +z^2 +xz=25 xy+yz+xz=?

$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{xy}=\mathrm{9} \\ $$$${y}^{\mathrm{2}} +{z}^{\mathrm{2}} +{yz}=\mathrm{16} \\ $$$${x}^{\mathrm{2}} +{z}^{\mathrm{2}} +{xz}=\mathrm{25} \\ $$$${xy}+{yz}+{xz}=? \\ $$

Question Number 141753 Answers: 2 Comments: 1

∫(dx/(sinx+cosx))

$$\int\frac{{dx}}{{sinx}+{cosx}} \\ $$

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