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Question Number 27526    Answers: 1   Comments: 0

(256)^(0.16) ×(256)^(0.09) =?

$$\left(\mathrm{256}\right)^{\mathrm{0}.\mathrm{16}} ×\left(\mathrm{256}\right)^{\mathrm{0}.\mathrm{09}} =? \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 27189    Answers: 1   Comments: 0

let give S_(n ) = Σ_(p=1) ^(p=n) arctan ((1/(2p^2 )) ) find lim_(n−>∝) S_n .

$${let}\:{give}\:{S}_{{n}\:} =\:\sum_{{p}=\mathrm{1}} ^{{p}={n}} \:{arctan}\:\left(\frac{\mathrm{1}}{\mathrm{2}{p}^{\mathrm{2}} }\:\right)\:\:{find}\:{lim}_{{n}−>\propto} \:{S}_{{n}} \:\:. \\ $$

Question Number 27187    Answers: 0   Comments: 1

find I= ∫_0 ^∝ ((cosx)/(cosh(x)))dx

$${find}\:{I}=\:\:\int_{\mathrm{0}} ^{\propto} \:\frac{{cosx}}{{cosh}\left({x}\right)}{dx} \\ $$

Question Number 27186    Answers: 1   Comments: 1

find I=∫_0 ^π (dx/(cosx +2sinx)) .

$${find}\:{I}=\int_{\mathrm{0}} ^{\pi} \:\:\frac{{dx}}{{cosx}\:+\mathrm{2}{sinx}}\:. \\ $$

Question Number 27185    Answers: 0   Comments: 0

find ∫∫_D (x+y)^2 e^(x^2 −y^2 ) dxdy with D={(x,y)∈R^(2 ) /0<x<1 and 0<y<1−x }.

$${find}\:\:\int\int_{{D}} \left({x}+{y}\right)^{\mathrm{2}} \:{e}^{{x}^{\mathrm{2}} −{y}^{\mathrm{2}} } {dxdy}\:{with} \\ $$$${D}=\left\{\left({x},{y}\right)\in{R}^{\mathrm{2}\:} /\mathrm{0}<{x}<\mathrm{1}\:{and}\:\mathrm{0}<{y}<\mathrm{1}−{x}\:\right\}. \\ $$

Question Number 27184    Answers: 0   Comments: 1

calculate in terms of x f(x)= ∫_0 ^(π/(2 )) (dt/(1+xsint)) .

$${calculate}\:{in}\:{terms}\:{of}\:{x}\:\:\:{f}\left({x}\right)=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}\:}} \frac{{dt}}{\mathrm{1}+{xsint}}\:. \\ $$

Question Number 27183    Answers: 1   Comments: 0

find the value of I= ∫_0 ^1 ((t−1)/(lnt))dt .

$${find}\:{the}\:{value}\:{of}\:{I}=\:\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{t}−\mathrm{1}}{{lnt}}{dt}\:. \\ $$

Question Number 27182    Answers: 0   Comments: 1

find the value of I_a = ∫∫_D_a e^(−((x^2 +y^2 )/2)) dxdy with D_a ={(x,y)∈R^2 / x^2 +y^2 ≤ a^2 }

$$\:{find}\:{the}\:{value}\:{of}\:{I}_{{a}} =\:\int\int_{{D}_{{a}} } {e}^{−\frac{{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} }{\mathrm{2}}} {dxdy}\:\:{with} \\ $$$${D}_{{a}} \:=\left\{\left({x},{y}\right)\in\mathbb{R}^{\mathrm{2}} \:/\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} \leqslant\:{a}^{\mathrm{2}} \:\:\right\} \\ $$

Question Number 27168    Answers: 0   Comments: 4

Question Number 27159    Answers: 0   Comments: 0

(√(1−x^(6 ) )) +(√(1−y^6 )) =k^3 (x^3 −y^3 ) then prove that (dy/dx)=((x^2 (√(1−x^2 )))/(y^2 (√(1−y^(2Δ) ))))

$$\sqrt{\mathrm{1}−{x}^{\mathrm{6}\:} \:}\:+\sqrt{\mathrm{1}−{y}^{\mathrm{6}} }\:={k}^{\mathrm{3}} \left({x}^{\mathrm{3}} −{y}^{\mathrm{3}} \right)\:\:\:{then}\:{prove}\:{that}\:\:\:\frac{{dy}}{{dx}}=\frac{{x}^{\mathrm{2}} \sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}{{y}^{\mathrm{2}} \sqrt{\mathrm{1}−{y}^{\mathrm{2}\Delta} }} \\ $$$$ \\ $$$$ \\ $$

Question Number 27144    Answers: 1   Comments: 1

Let A={x,y,z} and B={1,2}. Find the number of relations from A to B.

$${Let}\:{A}=\left\{{x},{y},{z}\right\}\:{and}\:{B}=\left\{\mathrm{1},\mathrm{2}\right\}.\:{Find} \\ $$$${the}\:{number}\:{of}\:{relations}\:{from}\:{A}\:{to} \\ $$$${B}. \\ $$

Question Number 27128    Answers: 1   Comments: 0

A body resting on a rough horizontal plane require a pull of 18N inclined at 30° to the plane first to move it.It was found that a push of 22N inclined at 30° to the plane just moved the body. Determine the weight and coefficient of friction.

$${A}\:{body}\:{resting}\:{on}\:{a}\:{rough} \\ $$$${horizontal}\:{plane}\:{require}\:{a}\:{pull}\:{of} \\ $$$$\mathrm{18}{N}\:{inclined}\:{at}\:\mathrm{30}°\:{to}\:{the}\:{plane} \\ $$$${first}\:{to}\:{move}\:{it}.{It}\:{was}\:{found} \\ $$$${that}\:{a}\:{push}\:{of}\:\mathrm{22}{N}\:{inclined}\:{at}\:\mathrm{30}° \\ $$$${to}\:{the}\:{plane}\:{just}\:{moved}\:{the}\:{body}. \\ $$$${Determine}\:{the}\:{weight}\:{and}\: \\ $$$${coefficient}\:{of}\:{friction}. \\ $$

Question Number 27117    Answers: 1   Comments: 0

Question Number 27112    Answers: 0   Comments: 2

Question Number 27104    Answers: 0   Comments: 1

sin45^(o ) cos45^o +(√(3 sin 60°=?))

$$\mathrm{sin45}^{{o}\:} \mathrm{cos45}^{{o}} +\sqrt{\mathrm{3}\:\:\:\mathrm{sin}\:\mathrm{60}°=?} \\ $$

Question Number 27103    Answers: 0   Comments: 1

the intrest on a certain sum of money at the end of 6.25 year was (5/(16)) of the sum itself.what is the rate percent?

$$\mathrm{the}\:\mathrm{intrest}\:\mathrm{on}\:\mathrm{a}\:\mathrm{certain}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{money}\:\mathrm{at}\:\mathrm{the} \\ $$$$\mathrm{end}\:\mathrm{of}\:\mathrm{6}.\mathrm{25}\:\mathrm{year}\:\mathrm{was}\:\frac{\mathrm{5}}{\mathrm{16}}\:\mathrm{of}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{itself}.\mathrm{what} \\ $$$$\mathrm{is}\:\mathrm{the}\:\mathrm{rate}\:\mathrm{percent}? \\ $$

Question Number 27102    Answers: 1   Comments: 0

Question Number 27101    Answers: 1   Comments: 0

Question Number 27111    Answers: 1   Comments: 0

Question Number 27098    Answers: 0   Comments: 2

let give S(x) = Σ_(n=1) ^∝ (x^n /n) and W(x)= Σ_(n=1) ^∝ (((−1)^n x^n )/n^2 ) calculate S(x).W(x). in that we know /x/<1.

$${let}\:{give}\:{S}\left({x}\right)\:=\:\sum_{{n}=\mathrm{1}} ^{\propto} \frac{{x}^{{n}} }{{n}}\:\:{and}\:\:{W}\left({x}\right)=\:\:\sum_{{n}=\mathrm{1}} ^{\propto} \frac{\left(−\mathrm{1}\right)^{{n}} {x}^{{n}} }{{n}^{\mathrm{2}} } \\ $$$${calculate}\:\:\:{S}\left({x}\right).{W}\left({x}\right).\:\:\:{in}\:{that}\:{we}\:{know}\:/{x}/<\mathrm{1}. \\ $$

Question Number 27097    Answers: 1   Comments: 2

let give H_n = Σ_(k=1) ^(n ) (1/k) for p fixed from N find lim_(n−>∝) H_(n+p) − H_n .

$${let}\:{give}\:\:\:{H}_{{n}} \:=\:\sum_{{k}=\mathrm{1}} ^{{n}\:\:} \:\frac{\mathrm{1}}{{k}}\:\:\:\:{for}\:{p}\:\:{fixed}\:{from}\:\mathbb{N}\: \\ $$$${find}\:\:{lim}_{{n}−>\propto} \:\:{H}_{{n}+{p}} \:\:\:−\:\:{H}_{{n}} \:\:. \\ $$

Question Number 27094    Answers: 1   Comments: 2

if 1+x+x^2 =0 find the value of A= (x+(1/x))^6 +( x^2 +(1/x^2 ))^6 +... ( x^(100) +(1/x^(100) ))^6 .

$${if}\:\mathrm{1}+{x}+{x}^{\mathrm{2}} =\mathrm{0}\:{find}\:{the}\:{value}\:{of}\: \\ $$$${A}=\:\left({x}+\frac{\mathrm{1}}{{x}}\right)^{\mathrm{6}} \:+\left(\:{x}^{\mathrm{2}} +\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right)^{\mathrm{6}} \:\:+...\:\left(\:\:{x}^{\mathrm{100}} +\frac{\mathrm{1}}{{x}^{\mathrm{100}} }\right)^{\mathrm{6}} \:. \\ $$

Question Number 27083    Answers: 1   Comments: 0

∫3x^2 /x^6 +1

$$\int\mathrm{3}{x}^{\mathrm{2}} /{x}^{\mathrm{6}} +\mathrm{1} \\ $$$$ \\ $$

Question Number 27081    Answers: 1   Comments: 0

let give f(x)= (x/(4x^2 −1)) find f^((n)) (x) .

$${let}\:{give}\:{f}\left({x}\right)=\:\:\frac{{x}}{\mathrm{4}{x}^{\mathrm{2}} −\mathrm{1}}\:\:{find}\:{f}^{\left({n}\right)} \left({x}\right)\:\:. \\ $$

Question Number 27076    Answers: 0   Comments: 1

Question Number 27073    Answers: 1   Comments: 0

∫ln x×cos 2ln xdx

$$\int\mathrm{ln}\:{x}×\mathrm{cos}\:\mathrm{2ln}\:{xdx} \\ $$

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