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Question Number 41096 Answers: 0 Comments: 1

Question Number 41095 Answers: 1 Comments: 0

For all real values of x solve the inequality ∣((1−x^3 )/(x^6 −2x^3 +5))∣≤(1/4)

$${For}\:{all}\:{real}\:{values}\:{of}\:{x}\:{solve}\:{the} \\ $$$${inequality} \\ $$$$\:\mid\frac{\mathrm{1}−{x}^{\mathrm{3}} }{{x}^{\mathrm{6}} −\mathrm{2}{x}^{\mathrm{3}} +\mathrm{5}}\mid\leqslant\frac{\mathrm{1}}{\mathrm{4}} \\ $$

Question Number 41086 Answers: 1 Comments: 0

A woman is four times older than her daughter. Six years ago the product of their ages is 136. How old is the woman?

$$\mathrm{A}\:\mathrm{woman}\:\mathrm{is}\:\mathrm{four}\:\mathrm{times}\:\mathrm{older}\:\mathrm{than}\: \\ $$$$\mathrm{her}\:\mathrm{daughter}.\:\mathrm{Six}\:\mathrm{years}\:\mathrm{ago}\:\mathrm{the} \\ $$$$\mathrm{product}\:\mathrm{of}\:\mathrm{their}\:\mathrm{ages}\:\mathrm{is}\:\mathrm{136}. \\ $$$$\mathrm{How}\:\mathrm{old}\:\mathrm{is}\:\mathrm{the}\:\mathrm{woman}? \\ $$

Question Number 41084 Answers: 1 Comments: 0

∫ (x^3 /(x^6 + 1)) dx

$$\int\:\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{x}^{\mathrm{6}} \:+\:\mathrm{1}}\:\mathrm{dx} \\ $$

Question Number 41079 Answers: 1 Comments: 0

In a triangle the length of the two larger sides are 24 and 22, respectively. If the angles are in AP, then the third side is

$$\mathrm{In}\:\mathrm{a}\:\mathrm{triangle}\:\mathrm{the}\:\mathrm{length}\:\mathrm{of}\:\mathrm{the}\:\mathrm{two} \\ $$$$\mathrm{larger}\:\mathrm{sides}\:\mathrm{are}\:\mathrm{24}\:\mathrm{and}\:\mathrm{22},\:\mathrm{respectively}. \\ $$$$\mathrm{If}\:\mathrm{the}\:\mathrm{angles}\:\mathrm{are}\:\mathrm{in}\:\mathrm{AP},\:\mathrm{then}\:\mathrm{the}\:\mathrm{third} \\ $$$$\mathrm{side}\:\mathrm{is} \\ $$

Question Number 41078 Answers: 1 Comments: 3

∫_0 ^1 ((sin x + 2cos x)/(3sin x + 4cos x))dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{sin}\:{x}\:+\:\mathrm{2cos}\:{x}}{\mathrm{3sin}\:{x}\:+\:\mathrm{4cos}\:{x}}{dx} \\ $$

Question Number 41066 Answers: 1 Comments: 0

Question Number 41063 Answers: 0 Comments: 1

Question Number 41062 Answers: 0 Comments: 3

Question Number 41054 Answers: 0 Comments: 1

calculate ∫_0 ^(π/2) (x^2 /(sin^2 x))dx .

$${calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\frac{{x}^{\mathrm{2}} }{{sin}^{\mathrm{2}} {x}}{dx}\:. \\ $$

Question Number 41053 Answers: 4 Comments: 1

let I = ∫_0 ^(π/2) cos^6 x dx and J = ∫_0 ^(π/2) sin^6 xdx 1)cslculate I +J and I−J 2)find the value of I and J

$${let}\:{I}\:=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:{cos}^{\mathrm{6}} {x}\:{dx}\:{and} \\ $$$${J}\:=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:{sin}^{\mathrm{6}} {xdx} \\ $$$$\left.\mathrm{1}\right){cslculate}\:{I}\:+{J}\:\:{and}\:{I}−{J} \\ $$$$\left.\mathrm{2}\right){find}\:{the}\:{value}\:{of}\:{I}\:{and}\:{J} \\ $$

Question Number 41052 Answers: 0 Comments: 1

find the value of ∫_(π/6) ^(π/4) (x/(1+cos^2 x))dxr

$${find}\:{the}\:{value}\:{of}\:\:\int_{\frac{\pi}{\mathrm{6}}} ^{\frac{\pi}{\mathrm{4}}} \:\:\frac{{x}}{\mathrm{1}+{cos}^{\mathrm{2}} {x}}{dxr} \\ $$

Question Number 41051 Answers: 0 Comments: 1

find the value of Σ_(n=1) ^∞ ((2n+3)/(n^2 (n+1)^2 ))

$${find}\:{the}\:{value}\:{of}\:\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{\mathrm{2}{n}+\mathrm{3}}{{n}^{\mathrm{2}} \left({n}+\mathrm{1}\right)^{\mathrm{2}} } \\ $$

Question Number 41049 Answers: 0 Comments: 2

calculate ∫_(−(π/4)) ^(π/4) (x^2 /(cos^2 x))dx

$${calculate}\:\:\:\int_{−\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{4}}} \:\:\frac{{x}^{\mathrm{2}} }{{cos}^{\mathrm{2}} {x}}{dx} \\ $$

Question Number 41044 Answers: 1 Comments: 0

Question Number 41038 Answers: 1 Comments: 5

Question Number 41032 Answers: 1 Comments: 0

(a/(x−a)) +(b/(x−b))=2.find x.

$$\frac{{a}}{{x}−{a}}\:+\frac{{b}}{{x}−{b}}=\mathrm{2}.{find}\:{x}. \\ $$

Question Number 41027 Answers: 1 Comments: 0

Question Number 41026 Answers: 1 Comments: 0

Question Number 41023 Answers: 0 Comments: 1

Question Number 47179 Answers: 1 Comments: 0

Question Number 47182 Answers: 0 Comments: 3

calculate ∫_0 ^1 e^(−x) (√(1−(√x)))dx

$${calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{e}^{−{x}} \sqrt{\mathrm{1}−\sqrt{{x}}}{dx}\: \\ $$

Question Number 41016 Answers: 1 Comments: 1

Question Number 41028 Answers: 1 Comments: 0

if 1/u = (√((x2 + y2 +z2))) then x∂u/∂x + y∂u/∂y + z∂u/∂z = ?

$${if}\:\mathrm{1}/{u}\:=\:\sqrt{\left({x}\mathrm{2}\:+\:{y}\mathrm{2}\:+{z}\mathrm{2}\right)} \\ $$$${then}\:{x}\partial{u}/\partial{x}\:+\:{y}\partial{u}/\partial{y}\:+\:{z}\partial{u}/\partial{z}\:=\:? \\ $$

Question Number 41009 Answers: 1 Comments: 1

Question Number 41003 Answers: 2 Comments: 0

The LCM and GCF of x,18 and 60 are 360 and 6 respectively. find the value of x

$$\boldsymbol{\mathrm{The}}\:\boldsymbol{\mathrm{LCM}}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{GCF}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{{x}},\mathrm{18}\:\boldsymbol{\mathrm{and}}\:\mathrm{60} \\ $$$$\boldsymbol{\mathrm{are}}\:\mathrm{360}\:\boldsymbol{\mathrm{and}}\:\mathrm{6}\:\boldsymbol{\mathrm{respectively}}. \\ $$$$\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{value}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{{x}} \\ $$

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