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Question Number 198497 Answers: 0 Comments: 0

∫_0 ^∞ ((e^(at) −e^(−at) )/(e^(πt) −e^(−πt) )) dt

$$\:\:\:\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{e}^{\mathrm{at}} −\mathrm{e}^{−\mathrm{at}} }{\mathrm{e}^{\pi\mathrm{t}} −\mathrm{e}^{−\pi\mathrm{t}} }\:\mathrm{dt} \\ $$

Question Number 198496 Answers: 1 Comments: 0

A nice series If , Ω = Σ_(n=2) ^∞ (( 1)/(n^( 2) +n −1)) =(( π tan( aπ ))/( b)) ⇒ find the value of (b/a) = ?

$$ \\ $$$$\:\:\:\:\:\:\:\:\:{A}\:{nice}\:\:{series} \\ $$$$\:\:{If}\:,\:\:\Omega\:=\:\underset{{n}=\mathrm{2}} {\overset{\infty} {\sum}}\:\frac{\:\mathrm{1}}{{n}^{\:\mathrm{2}} \:+{n}\:−\mathrm{1}}\:=\frac{\:\pi\:{tan}\left(\:{a}\pi\:\right)}{\:{b}} \\ $$$$\:\:\:\:\:\Rightarrow\:{find}\:{the}\:{value}\:{of}\:\:\:\frac{{b}}{{a}}\:=\:? \\ $$$$\:\:\:\:\:\:\:\:\: \\ $$

Question Number 198489 Answers: 2 Comments: 0

Question Number 198483 Answers: 3 Comments: 0

resoudre dans ]−π;π] cosx+cos2x+cos3x=0

$$\left.{r}\left.{esoudre}\:{dans}\:\right]−\pi;\pi\right] \\ $$$${cosx}+{cos}\mathrm{2}{x}+{cos}\mathrm{3}{x}=\mathrm{0}\: \\ $$

Question Number 198482 Answers: 2 Comments: 0

x^2 + 1 =0 resoudre dans C

$${x}^{\mathrm{2}} \:+\:\mathrm{1}\:=\mathrm{0}\:{resoudre}\:{dans}\:\mathbb{C} \\ $$

Question Number 198479 Answers: 2 Comments: 2

Question Number 198477 Answers: 1 Comments: 2

find the Area (ABCD)

$$\mathrm{find}\:\mathrm{the}\:\mathrm{Area}\:\left(\mathrm{ABCD}\right) \\ $$

Question Number 198474 Answers: 2 Comments: 0

16000 = (x^3 /((1−x)^2 )) x=?

$$\mathrm{16000}\:=\:\frac{\mathrm{x}^{\mathrm{3}} }{\left(\mathrm{1}−\mathrm{x}\right)^{\mathrm{2}} }\: \\ $$$$\:\mathrm{x}=? \\ $$

Question Number 198470 Answers: 0 Comments: 0

Question Number 198465 Answers: 0 Comments: 1

The furier series approximation to the forcing function is given by f(t)=5[1+(4/π)((/)((sin120πt)/1)+((sin360πt)/2)+((sin600πt)/3) +.........)] The transfer function for this problem T(s)=((X(s))/(f(s)))=(1/(ms^2 +cs+k)) =(1/(0.001s+1)) 1. plot the amplitude spectrum 2.Obtain the expression for steady displacement X(t)

$${The}\:{furier}\:{series}\:{approximation}\:{to}\: \\ $$$${the}\:{forcing}\:{function}\:{is}\:{given}\:{by}\: \\ $$$${f}\left({t}\right)=\mathrm{5}\left[\mathrm{1}+\frac{\mathrm{4}}{\pi}\left(\frac{}{}\frac{{sin}\mathrm{120}\pi{t}}{\mathrm{1}}+\frac{{sin}\mathrm{360}\pi{t}}{\mathrm{2}}+\frac{{sin}\mathrm{600}\pi{t}}{\mathrm{3}}\right.\right. \\ $$$$\left.\:\left.\:\:\:\:\:+.........\right)\right] \\ $$$${The}\:{transfer}\:{function}\:{for}\:{this} \\ $$$${problem}\:\:{T}\left({s}\right)=\frac{{X}\left({s}\right)}{{f}\left({s}\right)}=\frac{\mathrm{1}}{{ms}^{\mathrm{2}} +{cs}+{k}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\frac{\mathrm{1}}{\mathrm{0}.\mathrm{001}{s}+\mathrm{1}} \\ $$$$\mathrm{1}.\:{plot}\:{the}\:{amplitude}\:{spectrum}\: \\ $$$$\mathrm{2}.{Obtain}\:{the}\:{expression}\:{for}\:{steady}\: \\ $$$$\:\:\:\:\:\:\:\:{displacement}\:{X}\left({t}\right) \\ $$

Question Number 198460 Answers: 0 Comments: 0

In △ABC holds: Π (1 + (1/a) tan (A/2)) ≥ (1 + (1/(3R)))^3

$$\mathrm{In}\:\:\:\bigtriangleup\mathrm{ABC}\:\:\:\mathrm{holds}: \\ $$$$\Pi\:\left(\mathrm{1}\:+\:\frac{\mathrm{1}}{\mathrm{a}}\:\mathrm{tan}\:\frac{\mathrm{A}}{\mathrm{2}}\right)\:\geqslant\:\left(\mathrm{1}\:+\:\frac{\mathrm{1}}{\mathrm{3R}}\right)^{\mathrm{3}} \\ $$

Question Number 198451 Answers: 0 Comments: 0

Solve the EDP x(y−z)(∂U/∂x)+y(z−x)(∂U/∂y)=z(x−y)

$${Solve}\:{the}\:{EDP} \\ $$$${x}\left({y}−{z}\right)\frac{\partial{U}}{\partial{x}}+{y}\left({z}−{x}\right)\frac{\partial{U}}{\partial{y}}={z}\left({x}−{y}\right) \\ $$

Question Number 198449 Answers: 0 Comments: 2