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AllQuestion and Answers: Page 102

Question Number 210667 Answers: 3 Comments: 0

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given that the roots of the equation 3x^2 −(4+2k)x+2k=0 are α and β find the value of k for which β=3α

$${given}\:{that}\:{the}\:{roots} \\ $$$$\:{of}\:{the}\:{equation} \\ $$$$\mathrm{3}{x}^{\mathrm{2}} −\left(\mathrm{4}+\mathrm{2}{k}\right){x}+\mathrm{2}{k}=\mathrm{0} \\ $$$${are}\:\alpha\:{and}\:\beta \\ $$$${find}\:{the}\:{value}\:{of}\:{k} \\ $$$${for}\:{which}\:\beta=\mathrm{3}\alpha \\ $$

Question Number 210630 Answers: 1 Comments: 0

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Find the value of : Ω = ∫_0 ^( 1) ∫_0 ^( (√(1−x^2 ))) ∫_(√( x^( 2) +y^( 2) )) ^( (√(2−x^2 −y^2 ))) xy dz dy dx =?

$$ \\ $$$$\:\: \\ $$$$\:\:\:\:\:\:\:\:\:{Find}\:\:{the}\:\:{value}\:{of}\:: \\ $$$$ \\ $$$$\:\:\:\:\:\Omega\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \int_{\mathrm{0}} ^{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }} \:\int_{\sqrt{\:{x}^{\:\mathrm{2}} \:+{y}^{\:\mathrm{2}} }} ^{\:\sqrt{\mathrm{2}−{x}^{\mathrm{2}} \:−{y}^{\mathrm{2}} }} \:{xy}\:{dz}\:{dy}\:{dx}\:=?\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\: \\ $$

Question Number 210593 Answers: 1 Comments: 0

∫ ((sin x cos x)/( ((cos 2x))^(1/3) + (√(cos 2x)))) dx =? ∫ (dx/(sec x ((sin x))^(1/2) + cos x ((cosec^5 x))^(1/3) )) =?

$$\:\:\int\:\frac{\mathrm{sin}\:\mathrm{x}\:\mathrm{cos}\:\mathrm{x}}{\:\sqrt[{\mathrm{3}}]{\mathrm{cos}\:\mathrm{2x}}\:+\:\sqrt{\mathrm{cos}\:\mathrm{2x}}}\:\mathrm{dx}\:=? \\ $$$$\:\:\int\:\frac{\mathrm{dx}}{\mathrm{sec}\:\mathrm{x}\:\sqrt[{\mathrm{2}}]{\mathrm{sin}\:\mathrm{x}}\:+\:\mathrm{cos}\:\mathrm{x}\:\sqrt[{\mathrm{3}}]{\mathrm{cosec}\:^{\mathrm{5}} \mathrm{x}}}\:=? \\ $$

Question Number 210591 Answers: 3 Comments: 0

If a + b = 1 a^2 + b^2 = 2 then, a^(11) + b^(11) = ??

$$\mathrm{If} \\ $$$$\:\:\:\:\mathrm{a}\:\:+\:\:\mathrm{b}\:\:=\:\:\mathrm{1} \\ $$$$\:\:\:\mathrm{a}^{\mathrm{2}} \:\:+\:\:\mathrm{b}^{\mathrm{2}} \:\:=\:\:\mathrm{2} \\ $$$$\mathrm{then},\:\:\:\:\:\mathrm{a}^{\mathrm{11}} \:\:+\:\:\mathrm{b}^{\mathrm{11}} \:\:=\:\:?? \\ $$

Question Number 210590 Answers: 0 Comments: 0

Question Number 210587 Answers: 0 Comments: 3

f(x)= (√( 13 −12(√x) )) + (√(25 −24(√(1−x)) )) find : Min ( f )=?

$$ \\ $$$$\:\:\:\:\:{f}\left({x}\right)=\:\sqrt{\:\mathrm{13}\:−\mathrm{12}\sqrt{{x}}\:\:}\:+\:\sqrt{\mathrm{25}\:−\mathrm{24}\sqrt{\mathrm{1}−{x}}\:} \\ $$$$ \\ $$$$\:\:\:\:\:\:{find}\::\:\:\:\:\mathrm{M}{in}\:\left(\:{f}\:\right)=? \\ $$$$ \\ $$$$ \\ $$

Question Number 210581 Answers: 1 Comments: 0

{ ((x^2 +3x−(√(x^2 +3x−1 = 7)))),((2(√2) sin y = x)) :} x=? and y=?

$$\:\:\begin{cases}{{x}^{\mathrm{2}} +\mathrm{3}{x}−\sqrt{{x}^{\mathrm{2}} +\mathrm{3}{x}−\mathrm{1}\:=\:\mathrm{7}}}\\{\mathrm{2}\sqrt{\mathrm{2}}\:\mathrm{sin}\:{y}\:=\:{x}}\end{cases} \\ $$$$\:\:\:{x}=?\:\:\:\:{and}\:\:\:\:{y}=? \\ $$

Question Number 210579 Answers: 0 Comments: 4

Please... Can anyone help me.. Find the value(s) of x, if (x−2)^((x^2 −2x+4)) =3

$${Please}...\:{Can}\:{anyone}\:{help}\:{me}.. \\ $$$$ \\ $$$$\:{Find}\:{the}\:{value}\left({s}\right)\:{of}\:{x},\:{if} \\ $$$$\:\:\:\left({x}−\mathrm{2}\right)^{\left({x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{4}\right)} =\mathrm{3} \\ $$$$ \\ $$

Question Number 210574 Answers: 3 Comments: 0

if the roots of the equation x^2 +(k+1)x+k=0 are α and β, find the value of the real constant k for which α=2β

$${if}\:{the}\:{roots}\:{of}\:{the}\:{equation}\: \\ $$$${x}^{\mathrm{2}} +\left({k}+\mathrm{1}\right){x}+{k}=\mathrm{0} \\ $$$${are}\:\alpha\:{and}\:\beta, \\ $$$$\:{find}\:{the}\:{value}\:{of}\:{the} \\ $$$$\:{real}\:{constant}\:{k}\:{for} \\ $$$${which}\:\alpha=\mathrm{2}\beta \\ $$

Question Number 210573 Answers: 1 Comments: 0

Question Number 210572 Answers: 1 Comments: 0

Question Number 210571 Answers: 1 Comments: 0

If x,y,z∈R^+ and x^2 +y^2 +z^2 =3 Prove that (1/(4−x)) + (1/(4−y)) + (1/(4−z)) ≤ 1

$$\mathrm{If}\:\:\mathrm{x},\mathrm{y},\mathrm{z}\in\mathrm{R}^{+} \:\:\mathrm{and}\:\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{z}^{\mathrm{2}} =\mathrm{3} \\ $$$$\mathrm{Prove}\:\mathrm{that} \\ $$$$\frac{\mathrm{1}}{\mathrm{4}−\mathrm{x}}\:\:+\:\:\frac{\mathrm{1}}{\mathrm{4}−\mathrm{y}}\:\:+\:\:\frac{\mathrm{1}}{\mathrm{4}−\mathrm{z}}\:\:\leqslant\:\:\mathrm{1} \\ $$

Question Number 210566 Answers: 1 Comments: 0

Prove that: if (x∈]−(π/2),(π/2)[ y =∫^( x) _( 0) (dt/(cos(t))) ) ⇒ (y∈IR x =∫^( y) _( 0) (dt/(cosh(t))) )

$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\mathrm{if}\:\left(\mathrm{x}\in\right]−\frac{\pi}{\mathrm{2}},\frac{\pi}{\mathrm{2}}\left[\:\:\mathrm{y}\:=\underset{\:\mathrm{0}} {\int}^{\:\mathrm{x}} \frac{\mathrm{dt}}{\mathrm{cos}\left(\mathrm{t}\right)}\:\right)\:\Rightarrow\:\:\left(\mathrm{y}\in\mathrm{IR}\:\:\:\mathrm{x}\:=\underset{\:\mathrm{0}} {\int}^{\:\mathrm{y}} \frac{\mathrm{dt}}{\mathrm{cosh}\left(\mathrm{t}\right)}\:\right) \\ $$

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