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Question Number 38862 Answers: 0 Comments: 0

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Question Number 38860 Answers: 0 Comments: 0

Question Number 38859 Answers: 0 Comments: 0

Question Number 38858 Answers: 0 Comments: 0

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Question Number 38853 Answers: 0 Comments: 1

Question Number 39030 Answers: 2 Comments: 3

1) let f(x) = ∫_0 ^∞ (dt/(1+x^2 t^4 )) with x >0 find a simple form of f(x) 2) calculate ∫_0 ^(+∞) (dt/(1+t^4 )) 3) calculate ∫_0 ^∞ (dt/(1+3t^4 ))

$$\left.\mathrm{1}\right)\:{let}\:{f}\left({x}\right)\:=\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dt}}{\mathrm{1}+{x}^{\mathrm{2}} {t}^{\mathrm{4}} }\:\:{with}\:{x}\:>\mathrm{0} \\ $$$${find}\:{a}\:{simple}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\:\int_{\mathrm{0}} ^{+\infty} \:\:\:\frac{{dt}}{\mathrm{1}+{t}^{\mathrm{4}} } \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\frac{{dt}}{\mathrm{1}+\mathrm{3}{t}^{\mathrm{4}} } \\ $$

Question Number 38849 Answers: 1 Comments: 1

Question Number 38847 Answers: 0 Comments: 0

Question Number 38836 Answers: 0 Comments: 0

Question Number 38825 Answers: 1 Comments: 4

Question Number 38822 Answers: 1 Comments: 1

The incident wave set up on a string of length fixed at each end is given by: y_1 =Asin(kx−wt) i)what is the equation of motion of the reflected wave,y_2 . ii)obtain the resultant,y=y_1 +y_2 of the two waves. iii)what type of resultant wave is this? iv)for what values of x will the amplitud of the resultant wave become zero? v)for what values of x will y be maximum?

$${The}\:{incident}\:{wave}\:{set}\:{up}\:{on}\:{a}\:{string} \\ $$$${of}\:{length}\:{fixed}\:{at}\:{each}\:{end}\:{is}\:{given} \\ $$$${by}:\:\:\:{y}_{\mathrm{1}} ={Asin}\left({kx}−{wt}\right) \\ $$$$\left.{i}\right){what}\:{is}\:{the}\:{equation}\:{of}\:{motion} \\ $$$${of}\:{the}\:{reflected}\:{wave},{y}_{\mathrm{2}} . \\ $$$$\left.{ii}\right){obtain}\:{the}\:{resultant},{y}={y}_{\mathrm{1}} +{y}_{\mathrm{2}} \\ $$$${of}\:{the}\:{two}\:{waves}. \\ $$$$\left.{iii}\right){what}\:{type}\:{of}\:{resultant}\:{wave}\:{is} \\ $$$${this}? \\ $$$$\left.{iv}\right){for}\:{what}\:{values}\:{of}\:{x}\:{will}\:{the} \\ $$$${amplitud}\:{of}\:{the}\:{resultant}\:{wave}\: \\ $$$${become}\:{zero}? \\ $$$$\left.{v}\right){for}\:{what}\:{values}\:{of}\:{x}\:{will}\:{y}\:{be} \\ $$$${maximum}? \\ $$

Question Number 38816 Answers: 1 Comments: 0

Two waves are represented by y_1 =Asinωt and y_2 =Asin(ωt−δ). What is the resultant of the two waves? ii)determine the amplitude of the resultant wave and under which condition will it be constructive or destructive.

$${Two}\:{waves}\:{are}\:{represented}\:{by} \\ $$$${y}_{\mathrm{1}} ={Asin}\omega{t}\:{and}\:{y}_{\mathrm{2}} ={Asin}\left(\omega{t}−\delta\right). \\ $$$${What}\:{is}\:{the}\:{resultant}\:{of}\:{the}\:{two} \\ $$$${waves}? \\ $$$$\left.{ii}\right){determine}\:{the}\:{amplitude}\:{of}\:{the} \\ $$$${resultant}\:{wave}\:{and}\:{under}\:{which} \\ $$$${condition}\:{will}\:{it}\:{be}\:{constructive}\:{or} \\ $$$${destructive}. \\ $$

Question Number 38812 Answers: 0 Comments: 1

Can you remember this formula and the question behind it? 𝚽=mn−𝚺_(i=1) ^m 𝚺_(j=1) ^n sign[gcd(i,j)−1] The first prize goes to that one who can tell the # of the initial question.

$${Can}\:{you}\:{remember}\:{this}\:{formula}\:{and} \\ $$$${the}\:{question}\:{behind}\:{it}? \\ $$$$\:\:\:\:\boldsymbol{\Phi}=\boldsymbol{{mn}}−\underset{\boldsymbol{{i}}=\mathrm{1}} {\overset{\boldsymbol{{m}}} {\boldsymbol{\sum}}}\:\underset{\boldsymbol{{j}}=\mathrm{1}} {\overset{\boldsymbol{{n}}} {\boldsymbol{\sum}}}\:\boldsymbol{{sign}}\left[\boldsymbol{{gcd}}\left(\boldsymbol{{i}},\boldsymbol{{j}}\right)−\mathrm{1}\right] \\ $$$${The}\:{first}\:{prize}\:{goes}\:{to}\:{that}\:{one}\:{who} \\ $$$${can}\:{tell}\:{the}\:#\:{of}\:{the}\:{initial}\:{question}. \\ $$

Question Number 38804 Answers: 1 Comments: 3

let A_n = ∫_0 ^n (((−1)^x )/(2[x] +1))dx 1) calculate A_n 2) find lim_(n→+∞) A_n

$${let}\:\:{A}_{{n}} =\:\int_{\mathrm{0}} ^{{n}} \:\:\:\frac{\left(−\mathrm{1}\right)^{{x}} }{\mathrm{2}\left[{x}\right]\:+\mathrm{1}}{dx} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow+\infty} \:{A}_{{n}} \\ $$

Question Number 38802 Answers: 2 Comments: 0

solve: y′′(1 + 4x^2 ) − 8y = 0

$$\mathrm{solve}:\:\:\:\mathrm{y}''\left(\mathrm{1}\:+\:\mathrm{4x}^{\mathrm{2}} \right)\:−\:\mathrm{8y}\:=\:\mathrm{0} \\ $$

Question Number 39029 Answers: 2 Comments: 0

∫((3−5(√(1−(1/x)))))^(1/3) dx=? ∫(1/((3−5(√(1−(1/x)))))^(1/3) )dx=?

$$\int\sqrt[{\mathrm{3}}]{\mathrm{3}−\mathrm{5}\sqrt{\mathrm{1}−\frac{\mathrm{1}}{{x}}}}{dx}=? \\ $$$$\int\frac{\mathrm{1}}{\sqrt[{\mathrm{3}}]{\mathrm{3}−\mathrm{5}\sqrt{\mathrm{1}−\frac{\mathrm{1}}{{x}}}}}{dx}=? \\ $$

Question Number 38786 Answers: 0 Comments: 5

Question Number 38775 Answers: 1 Comments: 2

Question Number 38765 Answers: 0 Comments: 10

App notification problem has been fixed. Please report if u are still not able to get notification. Issue was on server side so no app updates are needed.

$$\mathrm{App}\:\mathrm{notification}\:\mathrm{problem}\:\mathrm{has} \\ $$$$\mathrm{been}\:\mathrm{fixed}.\:\mathrm{Please}\:\mathrm{report}\:\mathrm{if}\:\mathrm{u}\:\mathrm{are} \\ $$$$\mathrm{still}\:\mathrm{not}\:\mathrm{able}\:\mathrm{to}\:\mathrm{get}\:\mathrm{notification}. \\ $$$$ \\ $$$$\mathrm{Issue}\:\mathrm{was}\:\mathrm{on}\:\mathrm{server}\:\mathrm{side}\:\mathrm{so}\:\mathrm{no}\:\mathrm{app} \\ $$$$\mathrm{updates}\:\mathrm{are}\:\mathrm{needed}. \\ $$

Question Number 38762 Answers: 2 Comments: 2

Question Number 38759 Answers: 0 Comments: 2

3+3=

$$\mathrm{3}+\mathrm{3}= \\ $$

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