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AllQuestion and Answers: Page 1505

Question Number 50738 Answers: 0 Comments: 0

Question Number 50717 Answers: 2 Comments: 0

Question Number 50754 Answers: 3 Comments: 0

Question Number 50752 Answers: 0 Comments: 0

Question Number 50710 Answers: 2 Comments: 0

If x + y + z = 15 and xy + yz + zx = 85, find x^2 + y^2 + z^2

$$\mathrm{If}\:\:\mathrm{x}\:+\:\mathrm{y}\:+\:\mathrm{z}\:=\:\mathrm{15}\:\:\mathrm{and}\:\:\mathrm{xy}\:+\:\mathrm{yz}\:+\:\mathrm{zx}\:\:=\:\mathrm{85},\:\:\:\mathrm{find}\:\:\:\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2}} \:+\:\mathrm{z}^{\mathrm{2}} \\ $$

Question Number 50705 Answers: 1 Comments: 0

If cos 2y = tan^2 x, prove that cos2x=tan^2 y.

$$\mathrm{If}\:\mathrm{cos}\:\mathrm{2y}\:=\:\mathrm{tan}\:^{\mathrm{2}} \mathrm{x},\:\mathrm{prove}\:\mathrm{that}\:\mathrm{cos2x}=\mathrm{tan}\:^{\mathrm{2}} \mathrm{y}. \\ $$

Question Number 50701 Answers: 0 Comments: 0

how do we find the vertices and co vertices of an ellipse with the centre not at the origin ?

$${how}\:{do}\:{we}\:{find}\:{the}\:{vertices}\:{and}\:{co}\:{vertices}\:{of}\:{an}\:{ellipse}\:{with}\:{the}\:{centre}\:{not}\:{at}\:{the}\:{origin}\:? \\ $$

Question Number 50702 Answers: 0 Comments: 1

write the fourier series of f(x)=x 0≤x≤2

$${write}\:{the}\:{fourier}\:{series}\:{of}\: \\ $$$${f}\left({x}\right)={x}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{0}\leqslant{x}\leqslant\mathrm{2} \\ $$

Question Number 50698 Answers: 1 Comments: 0

Solve for x 4^(2x+1) ×5^(x−2) = 6^(1−x)

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{x} \\ $$$$ \\ $$$$\mathrm{4}^{\mathrm{2x}+\mathrm{1}} ×\mathrm{5}^{\mathrm{x}−\mathrm{2}} =\:\mathrm{6}^{\mathrm{1}−\mathrm{x}} \\ $$

Question Number 50689 Answers: 1 Comments: 0

If c is the line segement from (0, 0, 0) to (1, 2, 3) find ∫ x e^(yz) ds

$$\mathrm{If}\:\:\mathrm{c}\:\mathrm{is}\:\mathrm{the}\:\mathrm{line}\:\mathrm{segement}\:\mathrm{from}\:\:\left(\mathrm{0},\:\mathrm{0},\:\mathrm{0}\right)\:\mathrm{to}\:\left(\mathrm{1},\:\mathrm{2},\:\mathrm{3}\right) \\ $$$$\mathrm{find}\:\:\:\int\:\mathrm{x}\:\mathrm{e}^{\mathrm{yz}} \:\:\mathrm{ds} \\ $$

Question Number 50685 Answers: 1 Comments: 0

if : 3x+1=7 x=?

$$\boldsymbol{\mathrm{if}}\::\:\mathrm{3}\boldsymbol{\mathrm{x}}+\mathrm{1}=\mathrm{7} \\ $$$$\boldsymbol{\mathrm{x}}=? \\ $$

Question Number 50684 Answers: 1 Comments: 0

Question Number 50683 Answers: 0 Comments: 1

find f(λ) =∫_0 ^∞ ((arctan(λx))/(1+λx^2 ))dx with λ>0

$${find}\:{f}\left(\lambda\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{arctan}\left(\lambda{x}\right)}{\mathrm{1}+\lambda{x}^{\mathrm{2}} }{dx}\:\:{with}\:\lambda>\mathrm{0} \\ $$

Question Number 50676 Answers: 0 Comments: 3

Question Number 50674 Answers: 2 Comments: 3

Find the maximum area of a triangle inscribed in an ellipse with parameters a and b.

$${Find}\:{the}\:{maximum}\:{area}\:{of}\:{a}\:{triangle} \\ $$$${inscribed}\:{in}\:{an}\:{ellipse}\:{with}\:{parameters} \\ $$$${a}\:{and}\:{b}. \\ $$

Question Number 50659 Answers: 2 Comments: 4

∫_(0 ) ^( ∞) (dx/(4−x^2 )) = ?

$$\int_{\mathrm{0}\:} ^{\:\infty} \:\frac{{dx}}{\mathrm{4}−{x}^{\mathrm{2}} }\:=\:? \\ $$

Question Number 50640 Answers: 1 Comments: 2

Question Number 50638 Answers: 2 Comments: 1

Question Number 50633 Answers: 1 Comments: 1

please help integrate ((x+sin x)/(1+cos x))dx

$${please}\:{help}\:{integrate}\:\frac{{x}+\mathrm{sin}\:{x}}{\mathrm{1}+\mathrm{cos}\:{x}}{dx} \\ $$

Question Number 50630 Answers: 1 Comments: 0

Question Number 50625 Answers: 1 Comments: 2

2 opposite vertices of a square are (5,4) and (1,−6). Find coordinates of remaining two vertices ?

$$\mathrm{2}\:{opposite}\:{vertices}\:{of}\:{a}\:{square}\:{are}\: \\ $$$$\left(\mathrm{5},\mathrm{4}\right)\:{and}\:\left(\mathrm{1},−\mathrm{6}\right).\:{Find}\:{coordinates} \\ $$$${of}\:{remaining}\:{two}\:{vertices}\:? \\ $$

Question Number 50580 Answers: 2 Comments: 0

solve for: x,y,z . x^2 +y^2 =6 x^2 +z^2 =3 x(y−z)=2z

$$\boldsymbol{{solve}}\:\boldsymbol{{for}}:\:\:\boldsymbol{{x}},\boldsymbol{{y}},\boldsymbol{{z}}\:\:. \\ $$$$\:\:\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\boldsymbol{\mathrm{y}}^{\mathrm{2}} =\mathrm{6} \\ $$$$\:\:\:\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\boldsymbol{\mathrm{z}}^{\mathrm{2}} =\mathrm{3} \\ $$$$\:\:\:\:\boldsymbol{\mathrm{x}}\left(\boldsymbol{\mathrm{y}}−\boldsymbol{\mathrm{z}}\right)=\mathrm{2}\boldsymbol{\mathrm{z}} \\ $$

Question Number 50577 Answers: 1 Comments: 1

Question Number 50576 Answers: 0 Comments: 1

Question Number 50573 Answers: 0 Comments: 0

Question Number 50568 Answers: 1 Comments: 1

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