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AllQuestion and Answers: Page 1180

Question Number 97752 Answers: 1 Comments: 4

Question Number 97751 Answers: 2 Comments: 3

(y^2 −xy)dx + 2xy dy = 0

$$\left(\mathrm{y}^{\mathrm{2}} −\mathrm{xy}\right)\mathrm{dx}\:+\:\mathrm{2xy}\:\mathrm{dy}\:=\:\mathrm{0}\: \\ $$

Question Number 97746 Answers: 1 Comments: 1

Determine all pairs (x,y) of integers satisfying 1+2^x +2^(2x+1) =y^2

$$\mathrm{Determine}\:\mathrm{all}\:\mathrm{pairs}\:\left(\mathrm{x},\mathrm{y}\right) \\ $$$$\mathrm{of}\:\mathrm{integers}\:\mathrm{satisfying}\:\mathrm{1}+\mathrm{2}^{\mathrm{x}} +\mathrm{2}^{\mathrm{2x}+\mathrm{1}} =\mathrm{y}^{\mathrm{2}} \: \\ $$

Question Number 97737 Answers: 2 Comments: 3

If ^((a^2 −a)) C_2 =^((a^2 −a)) C_4 , then a =

$$\mathrm{If}\:\:^{\left({a}^{\mathrm{2}} −{a}\right)} {C}_{\mathrm{2}} =\:^{\left({a}^{\mathrm{2}} −{a}\right)} {C}_{\mathrm{4}} \:,\:\mathrm{then}\:{a}\:= \\ $$

Question Number 97725 Answers: 0 Comments: 3

log _5 (4x)=log _(10) (x) find x ?

$$\mathrm{log}\:_{\mathrm{5}} \left(\mathrm{4x}\right)=\mathrm{log}\:_{\mathrm{10}} \left(\mathrm{x}\right) \\ $$$$\mathrm{find}\:\mathrm{x}\:? \\ $$

Question Number 97721 Answers: 1 Comments: 3

Question Number 97892 Answers: 1 Comments: 0

Question Number 97707 Answers: 3 Comments: 0

Question Number 97694 Answers: 1 Comments: 7

Question Number 97683 Answers: 3 Comments: 3

Evaluate ∫_0 ^1 (1/(√(16 + 9x^2 ))) dx

$$\:\mathrm{Evaluate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{1}}{\sqrt{\mathrm{16}\:+\:\mathrm{9}{x}^{\mathrm{2}} }}\:{dx} \\ $$

Question Number 97680 Answers: 0 Comments: 1

Question Number 97675 Answers: 1 Comments: 0

Question Number 97671 Answers: 0 Comments: 1

Question Number 97660 Answers: 2 Comments: 1

Question Number 97658 Answers: 0 Comments: 1

The value of cos ((2π)/7) +cos ((4π)/7)+cos ((6π)/7) is

$$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\mathrm{cos}\:\frac{\mathrm{2}\pi}{\mathrm{7}}\:+\mathrm{cos}\:\frac{\mathrm{4}\pi}{\mathrm{7}}+\mathrm{cos}\:\frac{\mathrm{6}\pi}{\mathrm{7}}\:\:\mathrm{is} \\ $$

Question Number 97657 Answers: 0 Comments: 1

If cos α+cos β = 0 = sin α+sin β, then cos 2α+cos 2β =

$$\mathrm{If}\:\:\mathrm{cos}\:\alpha+\mathrm{cos}\:\beta\:=\:\mathrm{0}\:=\:\mathrm{sin}\:\alpha+\mathrm{sin}\:\beta, \\ $$$$\mathrm{then}\:\:\mathrm{cos}\:\mathrm{2}\alpha+\mathrm{cos}\:\mathrm{2}\beta\:= \\ $$

Question Number 97656 Answers: 1 Comments: 1

Maximum value of 3 cos θ + 4 sin θ is

$$\mathrm{Maximum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{3}\:\mathrm{cos}\:\theta\:+\:\mathrm{4}\:\mathrm{sin}\:\theta\:\mathrm{is} \\ $$

Question Number 97649 Answers: 1 Comments: 3

Question Number 97648 Answers: 1 Comments: 1

Determine all function f:R/{0,1}→R satisfying the functional relation f(x) + f((1/(1−x))) = ((2(1−2x))/(x(1−x))) , x≠0, x≠1

$$\mathrm{Determine}\:\mathrm{all}\:\mathrm{function}\:\mathrm{f}:\mathrm{R}/\left\{\mathrm{0},\mathrm{1}\right\}\rightarrow\mathrm{R} \\ $$$$\mathrm{satisfying}\:\mathrm{the}\:\mathrm{functional}\:\mathrm{relation} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)\:+\:\mathrm{f}\left(\frac{\mathrm{1}}{\mathrm{1}−\mathrm{x}}\right)\:=\:\frac{\mathrm{2}\left(\mathrm{1}−\mathrm{2x}\right)}{\mathrm{x}\left(\mathrm{1}−\mathrm{x}\right)}\:,\:\mathrm{x}\neq\mathrm{0},\:\mathrm{x}\neq\mathrm{1} \\ $$

Question Number 97709 Answers: 0 Comments: 4

Question Number 97638 Answers: 0 Comments: 0

Question Number 97637 Answers: 0 Comments: 1

Given p,q∈R_+ ^∗ −{−1}/(1/p)+(1/q)=1 show that; ∀a,b ∈R ab≤(a^p /p)+(b^q /q)

$$\mathrm{Given}\:\mathrm{p},\mathrm{q}\in\mathbb{R}_{+} ^{\ast} −\left\{−\mathrm{1}\right\}/\frac{\mathrm{1}}{\mathrm{p}}+\frac{\mathrm{1}}{\mathrm{q}}=\mathrm{1}\:\mathrm{show}\:\mathrm{that}; \\ $$$$\forall\mathrm{a},\mathrm{b}\:\in\mathbb{R}\:\mathrm{ab}\leqslant\frac{\mathrm{a}^{\mathrm{p}} }{\mathrm{p}}+\frac{\mathrm{b}^{\mathrm{q}} }{\mathrm{q}} \\ $$

Question Number 97629 Answers: 1 Comments: 0

Question Number 97628 Answers: 1 Comments: 0

Question Number 97627 Answers: 2 Comments: 0

give ∫_0 ^∞ ((arctan(x))/((1+x^2 )^2 ))dx at form of serie

$$\mathrm{give}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{arctan}\left(\mathrm{x}\right)}{\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)^{\mathrm{2}} }\mathrm{dx}\:\mathrm{at}\:\mathrm{form}\:\mathrm{of}\:\mathrm{serie} \\ $$

Question Number 97626 Answers: 0 Comments: 2

solve y^(′′) −2y^′ +y =x^2 with y^′ (0) =y(0) =−1

$$\mathrm{solve}\:\mathrm{y}^{''} \:−\mathrm{2y}^{'} \:+\mathrm{y}\:\:=\mathrm{x}^{\mathrm{2}} \:\mathrm{with}\:\mathrm{y}^{'} \left(\mathrm{0}\right)\:=\mathrm{y}\left(\mathrm{0}\right)\:=−\mathrm{1} \\ $$

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