Question Number 127452 by snipers237 last updated on 29/Dec/20 $$\:{Let}\:\:{a}\in\mathbb{R}^{\ast} ,\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\left({asin}\left(\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\right)+\frac{\mathrm{1}}{{a}}{cos}\left({n}\right)\right)^{{n}} =\mathrm{0} \\ $$ Answered by Ar Brandon last updated on 29/Dec/20 $$\mathrm{u}_{\mathrm{n}}…
Question Number 192990 by otchereabdullai@gmail.com last updated on 01/Jun/23 $${A}\:{fair}\:{die}\:{is}\:{tossed}\:{four}\:{times}\:.{what} \\ $$$${is}\:{the}\:{probability}\:{of}\:{obtaining}\:{a}\: \\ $$$${prime}\:{each}\:{time} \\ $$ Answered by som(math1967) last updated on 01/Jun/23 $${total}\:{outcome}=\mathrm{6}^{\mathrm{4}} \\…
Question Number 127453 by Eric002 last updated on 29/Dec/20 $${find}\:{the}\:{equation}\:{of}\:{all}\:{faces}\:{of}\:{pyramid} \\ $$$${bounded}\:{by}:\:{the}\:{plan}\:{Oxy};\:{the}\:{plan}\:{Oyz}; \\ $$$${the}\:{plan}\:{passing}\:{through}\:{the}\:{points} \\ $$$$\left(\mathrm{0};\mathrm{0};\mathrm{3}\right),\left(\mathrm{0};\mathrm{1};\mathrm{0}\right)\:{and}\:{being}\:{parallel}\:{to}\:{the} \\ $$$${axis}\:{Ox};\:{the}\:{plan}\:{passing}\:{through}\:{the} \\ $$$${point}\:\left(\mathrm{0};\mathrm{0};\mathrm{3}\right)\:{and}\:{the}\:{line}\:\frac{{x}−\mathrm{2}}{−\mathrm{4}}=\frac{{y}}{\mathrm{3}}=\frac{{z}}{\mathrm{3}} \\ $$ Terms of Service…
Question Number 192985 by MM42 last updated on 01/Jun/23 $${prove}\:{it}\:: \\ $$$${lim}_{{n}\rightarrow\infty} \:\underset{{i}=\mathrm{1}} {\overset{{n}} {\prod}}{cos}\frac{\theta}{\mathrm{2}^{{i}} }=\frac{{sin}\theta}{\theta} \\ $$$${then}\:{show}\:: \\ $$$${im}_{{n}\rightarrow\infty} \:{cos}\frac{\pi}{\mathrm{4}}{cos}\frac{\pi}{\mathrm{8}}…{cos}\frac{\pi}{\mathrm{2}^{{n}+\mathrm{1}} }\:=\frac{\mathrm{2}}{\pi} \\ $$$$ \\…
Question Number 61915 by aseerimad last updated on 11/Jun/19 $$\mathrm{1}+{iw}+\left({iw}\right)^{\mathrm{2}} +\left({iw}\right)^{\mathrm{3}} +………\left({iw}\right)^{\mathrm{989}} =? \\ $$$$ \\ $$$${ans}=\:\:\:\:\frac{\mathrm{2}}{\mathrm{1}−{iw}}\:\:\:\:\:\:{answer}\:{is}\:{correct}. \\ $$$${pls}\:{help}\:..\:{how}\:{to}\:{do}\:{this}? \\ $$$${TIA} \\ $$ Answered by…
Question Number 192987 by Mingma last updated on 01/Jun/23 Answered by ajfour last updated on 01/Jun/23 $${let}\:{left}\:{vertical}=\mathrm{2} \\ $$$$\mathrm{2cos}\:\theta={c}\mathrm{cos}\:{x} \\ $$$$\mathrm{sin}\:\theta={c}\mathrm{sin}\:{x} \\ $$$$\mathrm{4cos}\:\theta\mathrm{cos}\:\theta={c}\mathrm{cos}\:\left(\pi−{x}−\theta\right) \\ $$$$……….\:\:\:\:\:\:\:\:………..\:\:\:\:\:\:\:………..…
Question Number 61912 by ajfour last updated on 11/Jun/19 Commented by ajfour last updated on 11/Jun/19 $${Find}\:{maximum}\:{side}\:{length}\:{of} \\ $$$${equilateral}\:{triangle}\:{ABC}. \\ $$$$\left({The}\:{radii}\:{of}\:{the}\:{circles}\:{are}\:{p},{q},{r}\right). \\ $$ Terms of…
Question Number 127446 by mnjuly1970 last updated on 29/Dec/20 $$\:\:\:\:\:\:\:\:\:\:…{challanging}\:\:{integral}… \\ $$$$\:\:\:\:\:\:{prove}\:\:{that}\::: \\ $$$$\:\:\:\:\:\Omega=\int_{\mathrm{0}} ^{\:\infty} \left({cos}\left({x}\right)−\frac{\mathrm{1}}{\mathrm{1}+{x}^{\mathrm{2}} \:}\right)\frac{{dx}}{{x}}\:=\:−\gamma\:\: \\ $$$$ \\ $$ Answered by mindispower last…
Question Number 61907 by naka3546 last updated on 11/Jun/19 Commented by MJS last updated on 12/Jun/19 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{n}}=\infty\:\Rightarrow\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\:\sqrt[{{k}}]{{n}}}=\infty\:\mathrm{for}\:{k}\in\mathbb{N}^{\bigstar} \\ $$$$ \\ $$$$\mathrm{calculating}\:\Omega_{{n}}…
Question Number 192979 by Red1ight last updated on 01/Jun/23 $$\mathrm{Can}\:\mathrm{this}\:\mathrm{be}\:\mathrm{optimized}\:\left(\mathrm{getting}\:\mathrm{the}\:\mathrm{minimum}\right)\:\mathrm{using}\:\mathrm{backprobagation}? \\ $$$$ \\ $$$$\alpha\left({x}_{{i}} ,{y}_{{i}} ,{h}_{{i}} \right)=\left({h}_{{i}} −{x}_{{i}} \right)^{\mathrm{2}} +{y}_{{i}} ^{\mathrm{2}} \\ $$$$\beta\left({y}_{{i}} ,{h}_{{i}} \right)={y}_{{i}}…