Question Number 75802 by pete last updated on 17/Dec/19 $$\mathrm{A}\:\mathrm{fair}\:\mathrm{die}\:\mathrm{is}\:\mathrm{thrown}\:\mathrm{4}\:\mathrm{times}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{probability}\:\mathrm{of}\:\mathrm{obtaining}\:\mathrm{a}\:\mathrm{6}\:\mathrm{twice}? \\ $$ Answered by MJS last updated on 17/Dec/19 $$\frac{\mathrm{1}}{\mathrm{6}}×\frac{\mathrm{1}}{\mathrm{6}}×\frac{\mathrm{5}}{\mathrm{6}}×\frac{\mathrm{5}}{\mathrm{6}}×\begin{pmatrix}{\mathrm{4}}\\{\mathrm{2}}\end{pmatrix}\:=\frac{\mathrm{25}}{\mathrm{216}}\approx\mathrm{11}.\mathrm{57\%} \\ $$ Commented…
Question Number 141336 by cesarL last updated on 17/May/21 $$\int\mathrm{sin}\:\left(\mathrm{ln}\:\left({x}\right)\right){dx}=?\:\:{Please} \\ $$ Answered by Dwaipayan Shikari last updated on 17/May/21 $${log}\left({x}\right)={u} \\ $$$$\int{e}^{{u}} {sin}\left({u}\right){du}=\boldsymbol{\Phi} \\…
Question Number 10265 by Tawakalitu ayo mi last updated on 31/Jan/17 $$\mathrm{From}\:\mathrm{the}\:\mathrm{top}\:\mathrm{of}\:\mathrm{a}\:\mathrm{100}\:\mathrm{m}\:\mathrm{high}\:\mathrm{building},\:\mathrm{a}\:\mathrm{man} \\ $$$$\mathrm{observes}\:\mathrm{the}\:\mathrm{top}\:\mathrm{of}\:\mathrm{a}\:\mathrm{tree}\:\mathrm{at}\:\mathrm{an}\:\mathrm{angle}\:\mathrm{of} \\ $$$$\mathrm{depression}\:\mathrm{30}°.\:\mathrm{If}\:\mathrm{the}\:\mathrm{tree}\:\mathrm{is}\:\mathrm{50}\:\mathrm{m}\:\mathrm{tall},\:\mathrm{the} \\ $$$$\mathrm{angle}\:\mathrm{of}\:\mathrm{depression}\:\mathrm{of}\:\mathrm{the}\:\mathrm{foot}\:\mathrm{of}\:\mathrm{the}\:\mathrm{tree}\:\mathrm{is} \\ $$$$\mathrm{viewed}\:\mathrm{by}\:\mathrm{the}\:\mathrm{man}\:\mathrm{is}\:? \\ $$ Answered by sandy_suhendra…
Question Number 141333 by cesarL last updated on 17/May/21 $$\int{x}^{\mathrm{2}} \mathrm{cos}\:\left(\frac{{x}}{\mathrm{2}}\right){dx} \\ $$ Answered by qaz last updated on 17/May/21 $$\int{x}^{\mathrm{2}} \mathrm{cos}\:\frac{{x}}{\mathrm{2}}{dx} \\ $$$$=\mathrm{2}{x}^{\mathrm{2}} \mathrm{sin}\:\frac{{x}}{\mathrm{2}}−\mathrm{4}\int{x}\mathrm{sin}\:\frac{{x}}{\mathrm{2}}{dx}…
Question Number 75796 by ~blr237~ last updated on 17/Dec/19 $$\mathrm{let}\:\mathrm{be}\:\mathrm{a},\mathrm{b}\:\mathrm{such}\:\mathrm{as}\:\mathrm{a}^{\mathrm{2}} −\mathrm{b}^{\mathrm{2}} =\mathrm{ab} \\ $$$$\mathrm{find}\:\:\mathrm{out}\:\mathrm{Z}=\frac{\mathrm{a}^{\mathrm{n}} +\mathrm{b}^{\mathrm{n}} }{\mathrm{a}^{\mathrm{n}} −\mathrm{b}^{\mathrm{n}} }\:\:\mathrm{when}\:\:\mathrm{a}\neq\mathrm{0} \\ $$$$ \\ $$ Answered by mr…
Question Number 141328 by mnjuly1970 last updated on 17/May/21 $$……\:{Evaluate}: \\ $$$$\:\:\:\:\:\mathscr{F}\::=\underset{{n}=\mathrm{2}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} \zeta\left({n}\right)}{{n}+\mathrm{1}}\:=? \\ $$$$……. \\ $$ Answered by Dwaipayan Shikari last updated…
Question Number 75795 by ~blr237~ last updated on 17/Dec/19 $$\mathrm{Find}\:\mathrm{out}\:\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{argsh}\left(\mathrm{x}\right)}{\mathrm{x}}\mathrm{dx} \\ $$ Commented by mathmax by abdo last updated on 18/Dec/19 $${let}\:{A}\:=\int_{\mathrm{0}} ^{\infty}…
Question Number 75793 by ~blr237~ last updated on 17/Dec/19 $$\mathrm{Prove}\:\mathrm{that}\:\int_{\mathrm{0}} ^{\infty} \left(\frac{\mathrm{arctanx}}{\mathrm{x}\sqrt{\mathrm{log2}}}\right)^{\mathrm{2}} \mathrm{dx}=\:\pi \\ $$ Commented by mathmax by abdo last updated on 18/Dec/19 $${let}\:{I}\:=\int_{\mathrm{0}}…
Question Number 141320 by mnjuly1970 last updated on 17/May/21 $$\:\:\:\:\:\:\:……{nice}\:……{calculuus}….. \\ $$$$\:\:\:\:{prove}\:\:{that}:: \\ $$$$\:\:\:\:\boldsymbol{\phi}:=\int_{\mathrm{0}} ^{\:\infty} \int_{\mathrm{0}} ^{\:\infty} \frac{\mathscr{A}\:{rctan}\left({x}^{\mathrm{2}} {y}^{\mathrm{2}} \right)}{{x}^{\mathrm{4}} +{y}^{\mathrm{4}} }{dxdy}=\frac{\pi^{\mathrm{2}} \sqrt{\mathrm{2}}}{\mathrm{16}} \\ $$$$…..…
Question Number 10250 by jaikar last updated on 31/Jan/17 Commented by jaikar last updated on 31/Jan/17 $${please}\:{Q}\:{no}.\:\mathrm{10} \\ $$$$ \\ $$ Answered by ridwan balatif…