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Question Number 69939 Answers: 2 Comments: 12

x,y,z ∈ Z^+ find all solutions of xy=(x+y)z

$${x},{y},{z}\:\in\:{Z}^{+} \\ $$$${find}\:{all}\:{solutions}\:{of}\:\boldsymbol{{xy}}=\left(\boldsymbol{{x}}+\boldsymbol{{y}}\right)\boldsymbol{{z}} \\ $$

Question Number 69912 Answers: 1 Comments: 0

(√(xy)) + 3 = y Find (dy/dx) .

$$\sqrt{{xy}}\:\:+\:\:\mathrm{3}\:\:=\:\:{y} \\ $$$${Find}\:\:\frac{{dy}}{{dx}}\:\:. \\ $$

Question Number 69906 Answers: 1 Comments: 7

Notifications are working now. We are still working on other issues. No app update is needed. The changes were only on server side.

$$\mathrm{Notifications}\:\mathrm{are}\:\mathrm{working}\:\mathrm{now}. \\ $$$$\mathrm{We}\:\mathrm{are}\:\mathrm{still}\:\mathrm{working}\:\mathrm{on}\:\mathrm{other}\:\mathrm{issues}. \\ $$$$ \\ $$$$\mathrm{No}\:\mathrm{app}\:\mathrm{update}\:\mathrm{is}\:\mathrm{needed}.\:\mathrm{The}\:\mathrm{changes} \\ $$$$\mathrm{were}\:\mathrm{only}\:\mathrm{on}\:\mathrm{server}\:\mathrm{side}. \\ $$

Question Number 69901 Answers: 1 Comments: 2

Question Number 70718 Answers: 1 Comments: 1

∫_0 ^1 ((tan^(−1) x)/(1+x))dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{tan}^{−\mathrm{1}} \mathrm{x}}{\mathrm{1}+\mathrm{x}}\mathrm{dx} \\ $$

Question Number 69894 Answers: 0 Comments: 3

∫ ((2x^5 −x)/(x^3 −2))dx

$$\int\:\frac{\mathrm{2}{x}^{\mathrm{5}} −{x}}{{x}^{\mathrm{3}} −\mathrm{2}}{dx} \\ $$

Question Number 69966 Answers: 0 Comments: 1

Question Number 69878 Answers: 0 Comments: 3

Question Number 69874 Answers: 0 Comments: 3

Hi We are still working on solving android api update and notification related issues. The solution of these problem will take a few more weeks. Sorry about the inconvenience caused and we thank you for your patience.

$$\mathrm{Hi} \\ $$$$ \\ $$$$\mathrm{We}\:\mathrm{are}\:\mathrm{still}\:\mathrm{working}\:\mathrm{on}\:\mathrm{solving} \\ $$$$\mathrm{android}\:\mathrm{api}\:\mathrm{update}\:\mathrm{and}\:\mathrm{notification} \\ $$$$\mathrm{related}\:\mathrm{issues}.\:\mathrm{The}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{these} \\ $$$$\mathrm{problem}\:\mathrm{will}\:\mathrm{take}\:\mathrm{a}\:\mathrm{few}\:\mathrm{more}\:\mathrm{weeks}. \\ $$$$ \\ $$$$\mathrm{Sorry}\:\mathrm{about}\:\mathrm{the}\:\mathrm{inconvenience} \\ $$$$\mathrm{caused}\:\mathrm{and}\:\mathrm{we}\:\mathrm{thank}\:\mathrm{you}\:\mathrm{for}\:\mathrm{your} \\ $$$$\mathrm{patience}. \\ $$$$ \\ $$$$ \\ $$

Question Number 69871 Answers: 1 Comments: 0

Here, m^2 −n^(2 ) = 4(√(mn ))and tanθ+sinθ= m then prove that, tanθ−sinθ= n.

$$\mathrm{Here},\:\mathrm{m}^{\mathrm{2}} −\mathrm{n}^{\mathrm{2}\:\:} =\:\mathrm{4}\sqrt{\mathrm{mn}\:}\mathrm{and}\:\mathrm{tan}\theta+\mathrm{sin}\theta=\:\mathrm{m} \\ $$$$\mathrm{then}\:\mathrm{prove}\:\mathrm{that},\:\mathrm{tan}\theta−\mathrm{sin}\theta=\:\mathrm{n}. \\ $$

Question Number 69873 Answers: 0 Comments: 1

Question Number 69866 Answers: 1 Comments: 0

Question Number 69851 Answers: 0 Comments: 0

A convex mirror of radius of curvature 30cm forms a real image 20cm from its surface.Find whether the imavect is erect or inverted.Please explain how possible this is. Thanks in advance.

$${A}\:{convex}\:{mirror}\:{of}\:{radius}\:{of}\:{curvature} \\ $$$$\mathrm{30}{cm}\:{forms}\:{a}\:{real}\:{image}\:\mathrm{20}{cm}\:{from}\:{its} \\ $$$${surface}.{Find}\:{whether}\:{the}\:{imavect}\:{is} \\ $$$${erect}\:{or}\:{inverted}.{Please}\:{explain}\:{how}\: \\ $$$${possible}\:{this}\:{is}. \\ $$$$ \\ $$$${Thanks}\:{in}\:{advance}. \\ $$

Question Number 69847 Answers: 1 Comments: 0

A plane is travelling at 500km/hr eastward. wind blows at 90km/hr southward. find the velocity and direction if the plane rlative to the ground.

$${A}\:{plane}\:{is}\:{travelling}\:{at}\:\mathrm{500}{km}/{hr}\:{eastward}. \\ $$$${wind}\:{blows}\:{at}\:\mathrm{90}{km}/{hr}\:{southward}. \\ $$$${find}\:{the}\:{velocity}\:{and}\:{direction}\:{if}\:{the}\:{plane}\:{rlative}\:{to}\:{the}\:{ground}. \\ $$

Question Number 69846 Answers: 1 Comments: 0

Find the x−component and y−component of a 25N force acting at 210° angle

$${Find}\:{the}\:{x}−{component}\:{and}\:{y}−{component}\:{of}\:{a}\:\mathrm{25}{N}\:{force}\:{acting}\:{at}\:\mathrm{210}°\:{angle} \\ $$

Question Number 69836 Answers: 1 Comments: 2

Question Number 69829 Answers: 2 Comments: 2

Question Number 69827 Answers: 2 Comments: 0

The acceleration of a particle moving in a straight line is defined as a=6t−20 m/s^2 , where t is in seconds. Knowing that s=0m when t=3s and that t=5sec when v=2m/s. Determine the total distance travelled when t=11s.

$${The}\:{acceleration}\:{of}\:{a}\:{particle}\:{moving} \\ $$$${in}\:{a}\:{straight}\:{line}\:{is}\:{defined}\:{as}\:{a}=\mathrm{6}{t}−\mathrm{20} \\ $$$${m}/{s}^{\mathrm{2}} ,\:{where}\:{t}\:{is}\:{in}\:{seconds}.\:{Knowing} \\ $$$${that}\:{s}=\mathrm{0}{m}\:{when}\:{t}=\mathrm{3}{s}\:{and}\:{that}\:{t}=\mathrm{5}{sec} \\ $$$${when}\:{v}=\mathrm{2}{m}/{s}.\:{Determine}\:{the}\:{total} \\ $$$${distance}\:{travelled}\:{when}\:{t}=\mathrm{11}{s}. \\ $$

Question Number 69809 Answers: 2 Comments: 2

lim_(x→∞) xsin (π/x)

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:{x}\mathrm{sin}\:\frac{\pi}{{x}} \\ $$

Question Number 69803 Answers: 0 Comments: 2

1)find f(α) =∫_0 ^∞ ((cos(αx))/((x^4 +1)^2 ))dx with α real 2) find the value of ∫_0 ^∞ ((cos(2x))/((x^4 +1)^2 ))dx 3) find nature of the serie Σf(n)

$$\left.\mathrm{1}\right){find}\:\:\:{f}\left(\alpha\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{cos}\left(\alpha{x}\right)}{\left({x}^{\mathrm{4}} +\mathrm{1}\right)^{\mathrm{2}} }{dx}\:\:{with}\:\alpha\:{real} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{cos}\left(\mathrm{2}{x}\right)}{\left({x}^{\mathrm{4}} +\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$$$\left.\mathrm{3}\right)\:{find}\:{nature}\:{of}\:{the}\:{serie}\:\Sigma{f}\left({n}\right) \\ $$

Question Number 69795 Answers: 0 Comments: 1

let p(x)=(x+in)^n −n^n with n integr natural 1) find the roots of p(x) 2)factorize p(x) inside C[x] 3) decompose the fraction F(x)=(1/(p(x)))

$${let}\:{p}\left({x}\right)=\left({x}+{in}\right)^{{n}} −{n}^{{n}} \:{with}\:{n}\:{integr}\:{natural} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{the}\:{roots}\:{of}\:{p}\left({x}\right) \\ $$$$\left.\mathrm{2}\right){factorize}\:{p}\left({x}\right)\:{inside}\:{C}\left[{x}\right] \\ $$$$\left.\mathrm{3}\right)\:{decompose}\:{the}\:{fraction}\:{F}\left({x}\right)=\frac{\mathrm{1}}{{p}\left({x}\right)} \\ $$

Question Number 69794 Answers: 1 Comments: 2

let p(x)=(x+1)^6 −e^(iα) with α real 1) find the roots of p(x) 2) factorize p(x)inside C[x] 3)factorize p(x)inside R[x]