Question Number 74037 by akshaypalsra8@gmail.com last updated on 18/Nov/19 $$\int_{\mathrm{0}^{} } ^{\Pi/\mathrm{2}} {x}\mathrm{cos}^{{n}} {xdx}\:\:\:{by}\:{reduction}\:{formula} \\ $$ Answered by mind is power last updated on 18/Nov/19…
Question Number 8498 by Chantria last updated on 13/Oct/16 Commented by Rasheed Soomro last updated on 13/Oct/16 $$\frac{\mathrm{2a}^{\mathrm{2}} }{\mathrm{3a}+\mathrm{bc}}×\sqrt{\frac{\mathrm{1}}{\mathrm{b}+\mathrm{c}}}×\frac{\mathrm{18ab}}{\left(\mathrm{3b}\right)^{\mathrm{2}} −\mathrm{5c}} \\ $$$$=\frac{\mathrm{2a}^{\mathrm{2}} }{\mathrm{3a}+\mathrm{bc}}×\frac{\mathrm{1}}{\:\sqrt{\mathrm{b}+\mathrm{c}}}×\frac{\mathrm{18ab}}{\mathrm{9b}^{\mathrm{2}} −\mathrm{5c}} \\…
Question Number 139561 by physicstutes last updated on 28/Apr/21 $$\mathrm{Near}\:\mathrm{the}\:\mathrm{shore}\:\mathrm{a}\:\mathrm{fisherman}\:\mathrm{jumps}\:\mathrm{out}\:\mathrm{of}\:\mathrm{his}\:\mathrm{boat}\:\mathrm{with}\:\mathrm{a}\:\mathrm{velocity} \\ $$$$\mathrm{of}\:\mathrm{5}.\mathrm{00}\:\mathrm{ms}^{−\mathrm{1}} \:\mathrm{and}\:\mathrm{lands}\:\mathrm{on}\:\mathrm{the}\:\mathrm{shore}\:\mathrm{0}.\mathrm{650}\:\mathrm{afterwards}.\mathrm{The}\:\mathrm{boat} \\ $$$$\mathrm{moves}\:\mathrm{backwards}.\:\mathrm{The}\:\mathrm{respective}\:\mathrm{masses}\:\mathrm{of}\:\mathrm{the}\:\mathrm{fisherman}\:\mathrm{and} \\ $$$$\mathrm{the}\:\mathrm{boat}\:\mathrm{are}\:\mathrm{85}.\mathrm{0}\:\mathrm{kg}\:\mathrm{and}\:\mathrm{165}\:\mathrm{kg}\:\mathrm{and}\:\mathrm{the}\:\mathrm{frictional}\:\mathrm{force}\:\mathrm{between} \\ $$$$\mathrm{the}\:\mathrm{boat}\:\mathrm{and}\:\mathrm{water}\:\mathrm{is}\:\mathrm{negligible}.\:\mathrm{What}\:\mathrm{will}\:\mathrm{be}\:\mathrm{the}\:\mathrm{distance}\:\mathrm{between} \\ $$$$\mathrm{the}\:\mathrm{fisherman}\:\mathrm{and}\:\mathrm{the}\:\mathrm{both}\:\mathrm{at}\:\mathrm{the}\:\mathrm{instant}\:\mathrm{when}\:\mathrm{he}\:\mathrm{just}\:\mathrm{lands}\:\mathrm{on}\:\mathrm{the} \\ $$$$\mathrm{shore}? \\ $$…
Question Number 74026 by mathmax by abdo last updated on 17/Nov/19 $${U}_{{n}} {is}\:{a}\:{sequence}\:{wich}\:{verfy}\: \\ $$$$\forall{n}\:\in{N}\:\:\:\:\:\:\:\:\mathrm{2}^{{n}} \left(\:{U}_{{n}} +{U}_{{n}+\mathrm{1}} \right)=\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{U}_{{n}} \:{interms}\:{of}\:{n} \\ $$$$\left.\mathrm{2}\right)\:{is}\:\left({U}_{{n}} \right)\:{cojverhent}\:? \\…
Question Number 139560 by Dwaipayan Shikari last updated on 28/Apr/21 $$\underset{{n}_{\mathrm{1}} +\mathrm{2}{n}_{\mathrm{2}} +\mathrm{3}{n}_{\mathrm{3}} +..+{rn}_{{r}} ={n}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{{n}_{\mathrm{1}} !{n}_{\mathrm{2}} !{n}_{\mathrm{3}} !..{n}_{{r}} !\mathrm{1}^{{n}_{\mathrm{1}} } \mathrm{2}^{{n}_{\mathrm{2}} } \mathrm{3}^{{n}_{\mathrm{3}}…
Question Number 8490 by fernandodantas1996 last updated on 14/Oct/16 $${show}\:{thats}\:{true}: \\ $$$$\int_{−\infty} ^{+\infty} {e}^{−{x}^{\mathrm{2}} } =\:\sqrt{\pi} \\ $$ Commented by prakash jain last updated on…
Question Number 74024 by ajfour last updated on 18/Nov/19 $$\begin{cases}{{h}^{\mathrm{2}} +{y}^{\mathrm{2}} +\left({k}−{z}\right)^{\mathrm{2}} ={s}^{\mathrm{2}} }\\{{a}^{\mathrm{2}} +\left({b}−{y}\right)^{\mathrm{2}} +{z}^{\mathrm{2}} ={s}^{\mathrm{2}} }\\{{ah}+{y}\left({y}−{b}\right)+{z}\left({z}−{k}\right)=\mathrm{0}}\\{\frac{{h}+{a}}{\mathrm{2}}+{yz}−\left({b}−{y}\right)\left({k}−{z}\right)=\mathrm{1}}\\{{b}+{a}\left({k}−{z}\right)+{hz}=\mathrm{1}}\\{{k}+{h}\left({b}−{y}\right)+{ay}=\mathrm{1}}\end{cases} \\ $$$${Find}\:\:{s}_{{min}} \:{or}\:{at}\:{least}\:{express} \\ $$$$\:{s}={f}\left({y}\right)\:{or}\:{g}\left({z}\right). \\ $$…
Question Number 8488 by Basant007 last updated on 12/Oct/16 $${find}\:{y}_{{n}} \:{if}\:{y}=\mathrm{cos}\:\mathrm{2}{x} \\ $$ Commented by FilupSmith last updated on 13/Oct/16 $${y}_{{n}} =\frac{{d}^{{n}} {y}}{{dx}^{{n}} } \\…
Question Number 139556 by mnjuly1970 last updated on 28/Apr/21 $$\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:……..\:{advanced}\:…\:…\:…\:{calculus}…….. \\ $$$$\:\:\:\Phi=\:{lim}_{{n}\rightarrow\infty} \left\{\int_{\mathrm{1}} ^{\:{n}} \frac{{x}}{\left[{x}\right]^{\mathrm{2}} }\:{dx}\:−\psi\left({n}+\mathrm{1}\right)\right\}=? \\ $$$$\:\:\:\:{solution}: \\ $$$$\:\:\:\:\:\Phi_{{n}} =\int_{\mathrm{1}} ^{\:{n}} \frac{{x}}{\left[{x}\right]^{\mathrm{2}}…
Question Number 8486 by PradipGos. last updated on 12/Oct/16 $$\underset{−\infty} {\overset{\infty} {\int}}{e}^{−\mathrm{2}\mid{x}\overset{} {\mid}\:} \left(\mathrm{1}−\mathrm{cos}\:\mathrm{2}\alpha{x}\right){dx}=???? \\ $$$${solve}\:{this}\:……. \\ $$$$ \\ $$$$ \\ $$ Answered by Yozzias…