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AllQuestion and Answers: Page 1678

Question Number 37642 Answers: 1 Comments: 0

3^(3(√(250))+7^(3(√(16))−4^(3(√(54))) ) )

$$\mathrm{3}^{\mathrm{3}\sqrt{\mathrm{250}}+\mathrm{7}^{\mathrm{3}\sqrt{\mathrm{16}}−\mathrm{4}^{\mathrm{3}\sqrt{\mathrm{54}}} } } \\ $$

Question Number 37636 Answers: 1 Comments: 1

find ∫_0 ^6 (x^2 −x+1)e^([−2x]) dx .

$${find}\:\:\int_{\mathrm{0}} ^{\mathrm{6}} \left({x}^{\mathrm{2}} −{x}+\mathrm{1}\right){e}^{\left[−\mathrm{2}{x}\right]} {dx}\:. \\ $$

Question Number 37635 Answers: 0 Comments: 1

let a>0 find the value of f(a) = ∫_0 ^(+∞) e^(−(t^2 +(a/t^2 ))) dt

$${let}\:{a}>\mathrm{0}\:\:{find}\:{the}\:{value}\:{of}\: \\ $$$${f}\left({a}\right)\:=\:\int_{\mathrm{0}} ^{+\infty} \:{e}^{−\left({t}^{\mathrm{2}} \:\:+\frac{{a}}{{t}^{\mathrm{2}} }\right)} {dt}\: \\ $$

Question Number 37634 Answers: 1 Comments: 1

find ∫_0 ^(+∞) e^(−(t^2 +(1/t^2 ))) dt

$${find}\:\int_{\mathrm{0}} ^{+\infty} \:\:{e}^{−\left({t}^{\mathrm{2}} \:+\frac{\mathrm{1}}{{t}^{\mathrm{2}} }\right)} {dt} \\ $$

Question Number 37633 Answers: 1 Comments: 0

find ∫_0 ^(+∞) [ x e^(−x) ]dx

$${find}\:\:\int_{\mathrm{0}} ^{+\infty} \left[\:\:{x}\:{e}^{−{x}} \right]{dx} \\ $$

Question Number 37632 Answers: 1 Comments: 1

Question Number 37627 Answers: 3 Comments: 0

Given {x} = x − ⌊x⌋ How many real solutions from equation {x} + {x^2 } = 1 with −10 ≤ x ≤ 10 ?

$$\mathrm{Given}\:\left\{{x}\right\}\:=\:{x}\:−\:\lfloor{x}\rfloor \\ $$$$\mathrm{How}\:\mathrm{many}\:\mathrm{real}\:\mathrm{solutions}\:\mathrm{from}\:\mathrm{equation} \\ $$$$\left\{{x}\right\}\:+\:\left\{{x}^{\mathrm{2}} \right\}\:=\:\mathrm{1} \\ $$$$\mathrm{with}\:−\mathrm{10}\:\leqslant\:{x}\:\leqslant\:\mathrm{10}\:? \\ $$

Question Number 37602 Answers: 0 Comments: 4

find the value of f(a)= ∫_0 ^∞ ((x^2 −1)/((x^4 +a^4 )^2 ))dx 2) calculate ∫_0 ^∞ ((x^2 −1)/((x^4 +1)^2 ))dx

$${find}\:{the}\:{value}\:{of} \\ $$$${f}\left({a}\right)=\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{x}^{\mathrm{2}} −\mathrm{1}}{\left({x}^{\mathrm{4}} \:\:\:+{a}^{\mathrm{4}} \right)^{\mathrm{2}} }{dx} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\:\frac{{x}^{\mathrm{2}} \:−\mathrm{1}}{\left({x}^{\mathrm{4}} \:+\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$

Question Number 37601 Answers: 0 Comments: 2

let give n inyehr natural≥1 find tbe value of A_n = ∫_0 ^∞ (dx/((x^2 +1)(x^(2 ) +2)....(x^2 +n)))

$${let}\:{give}\:{n}\:{inyehr}\:{natural}\geqslant\mathrm{1}\:{find}\:{tbe}\:{value}\:{of} \\ $$$${A}_{{n}} =\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)\left({x}^{\mathrm{2}\:} +\mathrm{2}\right)....\left({x}^{\mathrm{2}} \:+{n}\right)} \\ $$

Question Number 37600 Answers: 2 Comments: 0

n integr natural calculate ∫_0 ^∞ (dx/((x+1)(x+2)......(x+n)))

$${n}\:{integr}\:{natural}\:{calculate} \\ $$$$\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\frac{{dx}}{\left({x}+\mathrm{1}\right)\left({x}+\mathrm{2}\right)......\left({x}+{n}\right)} \\ $$

Question Number 37591 Answers: 1 Comments: 0

if the circle x^2 +y^2 −2y−8=0 and x^2 +y^2 −24x+hy=0 cut orthogonally, determine the value of h.

$$\boldsymbol{\mathrm{if}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{circle}}\:\boldsymbol{{x}}^{\mathrm{2}} +\boldsymbol{{y}}^{\mathrm{2}} −\mathrm{2}\boldsymbol{{y}}−\mathrm{8}=\mathrm{0} \\ $$$$\boldsymbol{\mathrm{and}}\:\boldsymbol{{x}}^{\mathrm{2}} +\boldsymbol{{y}}^{\mathrm{2}} −\mathrm{24}\boldsymbol{{x}}+\boldsymbol{{hy}}=\mathrm{0}\:\boldsymbol{\mathrm{cut}}\:\boldsymbol{\mathrm{orthogonally}}, \\ $$$$\boldsymbol{\mathrm{determine}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{value}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{{h}}. \\ $$$$ \\ $$

Question Number 37587 Answers: 2 Comments: 2

calculate ∫_0 ^(2π) (dx/(2cos^2 x +(√3) sin^2 x))

$${calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\:\:\:\frac{{dx}}{\mathrm{2}{cos}^{\mathrm{2}} {x}\:+\sqrt{\mathrm{3}}\:{sin}^{\mathrm{2}} {x}} \\ $$

Question Number 37582 Answers: 1 Comments: 3

Question Number 37579 Answers: 1 Comments: 0

a=((−1)/(2x^2 )) with x=1 and v=0 at t=0 find time that particle takes to reach x=0.25m .

$${a}=\frac{−\mathrm{1}}{\mathrm{2}{x}^{\mathrm{2}} }\:\:{with}\:{x}=\mathrm{1}\:{and}\:{v}=\mathrm{0}\:{at}\:{t}=\mathrm{0} \\ $$$${find}\:{time}\:{that}\:{particle}\:{takes}\:{to} \\ $$$${reach}\:{x}=\mathrm{0}.\mathrm{25}{m}\:. \\ $$

Question Number 37568 Answers: 2 Comments: 0

let α and β the roots of the equation x^2 −2mx −1 =0 find interms of the real m A = α^2 +β^2 B =α^3 +β^3 c =α^4 +β^4 D= α^6 +β^6

$${let}\:\alpha\:{and}\:\beta\:{the}\:{roots}\:{of}\:{the}\:{equation} \\ $$$${x}^{\mathrm{2}} \:−\mathrm{2}{mx}\:−\mathrm{1}\:=\mathrm{0}\:\:{find}\:{interms}\:{of}\:{the}\:{real}\:{m} \\ $$$${A}\:=\:\alpha^{\mathrm{2}} \:+\beta^{\mathrm{2}} \\ $$$${B}\:=\alpha^{\mathrm{3}} \:+\beta^{\mathrm{3}} \\ $$$${c}\:=\alpha^{\mathrm{4}} \:+\beta^{\mathrm{4}} \\ $$$${D}=\:\alpha^{\mathrm{6}} \:+\beta^{\mathrm{6}} \\ $$

Question Number 37553 Answers: 0 Comments: 2

Question Number 37517 Answers: 1 Comments: 5

Question Number 37485 Answers: 2 Comments: 1

Question Number 37464 Answers: 1 Comments: 2

36x^2 y^2 -42x^3 y^3 +24x^5 y^4

$$\mathrm{36}\boldsymbol{{x}}^{\mathrm{2}} \boldsymbol{{y}}^{\mathrm{2}} -\mathrm{42}\boldsymbol{{x}}^{\mathrm{3}} \boldsymbol{{y}}^{\mathrm{3}} +\mathrm{24}\boldsymbol{{x}}^{\mathrm{5}} \boldsymbol{{y}}^{\mathrm{4}} \\ $$

Question Number 37462 Answers: 1 Comments: 0

If x+3 is the common factor of the expressions ax^2 +bx+1 and px^2 +qx−3, then ((−(9a+3p))/(3b+q)) = ____.

$$\mathrm{If}\:{x}+\mathrm{3}\:\mathrm{is}\:\mathrm{the}\:\mathrm{common}\:\mathrm{factor}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{expressions}\:{ax}^{\mathrm{2}} +{bx}+\mathrm{1}\:\mathrm{and}\: \\ $$$${px}^{\mathrm{2}} +{qx}−\mathrm{3},\:\mathrm{then}\:\frac{−\left(\mathrm{9}{a}+\mathrm{3}{p}\right)}{\mathrm{3}{b}+{q}}\:=\:\_\_\_\_. \\ $$

Question Number 37451 Answers: 2 Comments: 1

∫_0 ^( 2π) ((a^2 sin^2 θdθ)/(√(a^2 sin^2 θ+b^2 cos^2 θ))) = ?

$$\int_{\mathrm{0}} ^{\:\mathrm{2}\pi} \frac{{a}^{\mathrm{2}} \mathrm{sin}\:^{\mathrm{2}} \theta{d}\theta}{\sqrt{{a}^{\mathrm{2}} \mathrm{sin}\:^{\mathrm{2}} \theta+{b}^{\mathrm{2}} \mathrm{cos}\:^{\mathrm{2}} \theta}}\:=\:? \\ $$

Question Number 37449 Answers: 1 Comments: 0

∫_0 ^1 ((3x^3 −x^2 +2x+4)/(√(x^2 −3x+2))) dx=

$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{3}{x}^{\mathrm{3}} −{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{4}}{\sqrt{{x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{2}}}\:{dx}= \\ $$

Question Number 37447 Answers: 2 Comments: 5

Question Number 37432 Answers: 2 Comments: 0

∫(dα/((1/2)tan α +2cot (α/2)))=? ∫(dβ/(2tan (β/2) +(1/2)cot β))=?

$$\int\frac{{d}\alpha}{\frac{\mathrm{1}}{\mathrm{2}}\mathrm{tan}\:\alpha\:+\mathrm{2cot}\:\frac{\alpha}{\mathrm{2}}}=? \\ $$$$\int\frac{{d}\beta}{\mathrm{2tan}\:\frac{\beta}{\mathrm{2}}\:+\frac{\mathrm{1}}{\mathrm{2}}\mathrm{cot}\:\beta}=? \\ $$

Question Number 37425 Answers: 1 Comments: 0

∫((x^5 −3x^4 −23x^3 +51x^2 +94x−120)/(8x^3 (√(42+x−x^2 ))))dx=?

$$\int\frac{{x}^{\mathrm{5}} −\mathrm{3}{x}^{\mathrm{4}} −\mathrm{23}{x}^{\mathrm{3}} +\mathrm{51}{x}^{\mathrm{2}} +\mathrm{94}{x}−\mathrm{120}}{\mathrm{8}{x}^{\mathrm{3}} \sqrt{\mathrm{42}+{x}−{x}^{\mathrm{2}} }}{dx}=? \\ $$

Question Number 37424 Answers: 0 Comments: 0

solve for Z(x,t)if Z_n =x^2 t subjected Z(x,0)=x^2 and Z(1,t)=cost

$$\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{for}}\:\boldsymbol{{Z}}\left(\boldsymbol{{x}},\boldsymbol{{t}}\right)\boldsymbol{\mathrm{if}}\:\boldsymbol{\mathrm{Z}}_{\boldsymbol{\mathrm{n}}} =\boldsymbol{{x}}^{\mathrm{2}} \boldsymbol{{t}}\:\:\boldsymbol{\mathrm{subjected}}\:\boldsymbol{{Z}}\left(\boldsymbol{{x}},\mathrm{0}\right)=\boldsymbol{{x}}^{\mathrm{2}} \\ $$$$\boldsymbol{\mathrm{and}}\:\boldsymbol{{Z}}\left(\mathrm{1},\boldsymbol{{t}}\right)=\boldsymbol{\mathrm{cos}{t}} \\ $$

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