Question Number 18584 by 433 last updated on 25/Jul/17 $${Prove} \\ $$$$\mathrm{sin}\:\left(\frac{\mathrm{3}\pi}{\mathrm{10}}\right)=\frac{\mathrm{1}+\sqrt{\mathrm{5}}}{\mathrm{4}} \\ $$ Answered by Tinkutara last updated on 25/Jul/17 $$\mathrm{sin}\:\mathrm{54}°\:=\:\mathrm{cos}\:\mathrm{36}°\:=\:\mathrm{1}\:−\:\mathrm{2}\:\mathrm{sin}^{\mathrm{2}} \:\mathrm{18}° \\ $$$$=\:\mathrm{1}\:−\:\frac{\mathrm{3}\:−\:\sqrt{\mathrm{5}}}{\mathrm{4}}\:=\:\frac{\sqrt{\mathrm{5}}\:+\:\mathrm{1}}{\mathrm{4}}\:\left[\because\:\mathrm{sin}\:\mathrm{18}°\:=\:\frac{\sqrt{\mathrm{5}}\:−\:\mathrm{1}}{\mathrm{4}}\right]…
Question Number 18581 by Tinkutara last updated on 25/Jul/17 $$\mathrm{In}\:\mathrm{moving}\:\mathrm{a}\:\mathrm{body}\:\mathrm{of}\:\mathrm{mass}\:{m}\:\mathrm{up}\:\mathrm{and} \\ $$$$\mathrm{down}\:\mathrm{a}\:\mathrm{rough}\:\mathrm{incline}\:\mathrm{plane}\:\mathrm{of}\:\mathrm{inclination} \\ $$$$\theta,\:\mathrm{work}\:\mathrm{done}\:\mathrm{is}\:\left(\mathrm{S}\:\mathrm{is}\:\mathrm{length}\:\mathrm{of}\:\mathrm{the}\:\mathrm{planck},\right. \\ $$$$\left.\mathrm{and}\:\mu\:\mathrm{is}\:\mathrm{coefficient}\:\mathrm{of}\:\mathrm{friction}\right). \\ $$ Answered by ajfour last updated on 25/Jul/17…
Question Number 84117 by Power last updated on 09/Mar/20 Answered by TANMAY PANACEA last updated on 09/Mar/20 $${sin}\mathrm{100}+{sin}\mathrm{20}+{sin}\mathrm{50} \\ $$$$\mathrm{2}{sin}\mathrm{60}.{cos}\mathrm{40}+{cos}\mathrm{40} \\ $$$${cos}\mathrm{40}\left(\mathrm{1}+\sqrt{\mathrm{3}}\:\right) \\ $$$$\mathrm{96}×\mathrm{2}×{sin}\mathrm{40}.{cos}\mathrm{40}+\frac{\mathrm{1}}{\mathrm{2}}\left({cos}\mathrm{30}−{cos}\mathrm{100}\right) \\…
Question Number 18575 by Tinkutara last updated on 25/Jul/17 $$\mathrm{If}\:\left(\:\right)\:\mathrm{represents}\:\mathrm{the}\:\mathrm{least}\:\mathrm{integer}\:\mathrm{function}, \\ $$$$\mathrm{then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\left(\mathrm{10}\right)\:+\:\left(\mathrm{10}\:+\:\frac{\mathrm{1}}{\mathrm{20}}\right)\:+ \\ $$$$\left(\mathrm{10}\:+\:\frac{\mathrm{2}}{\mathrm{20}}\right)\:+\:…\:+\:\left(\mathrm{10}\:+\:\frac{\mathrm{19}}{\mathrm{20}}\right)\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{219} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{200} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{220} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{221} \\ $$ Answered…
Question Number 18574 by Tinkutara last updated on 25/Jul/17 $$\mathrm{The}\:\mathrm{maximum}\:\mathrm{value}\:\mathrm{of}\:{f}\left({x}\right)\:=\:\mathrm{2}\:−\:\mid{x}\mid^{\mathrm{2}} \\ $$$$−\:\mathrm{2}{x}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{6} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{4} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{5} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{3} \\ $$ Answered by prakash…
Question Number 84109 by Power last updated on 09/Mar/20 Commented by mahdi last updated on 09/Mar/20 $$\frac{\mathrm{1}}{\mathrm{1}}+\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{5}}+…+\frac{\mathrm{1}}{\mathrm{2x}+\mathrm{1}}\approx\mathrm{ln}\left(\frac{\mathrm{2x}+\mathrm{1}}{\:\sqrt{\mathrm{x}}}\right)+\mathrm{0}.\mathrm{28861} \\ $$ Commented by mathmax by abdo last…
Question Number 84106 by jagoll last updated on 09/Mar/20 $$\int\:\frac{\mathrm{x}^{\mathrm{4}} }{\:\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{4}} }}\:\mathrm{dx}\:=\:? \\ $$ Commented by MJS last updated on 09/Mar/20 $${t}=\sqrt{\mathrm{sin}\:{x}}\:\rightarrow\:{dx}=\frac{\sqrt{\mathrm{1}−{x}^{\mathrm{4}} }}{\mathrm{2}{x}}{dt} \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}\int\left(\mathrm{sin}\:{t}\right)^{\frac{\mathrm{3}}{\mathrm{2}}}…
Question Number 18568 by Tinkutara last updated on 24/Jul/17 $$\mathrm{The}\:\mathrm{energy}\:\mathrm{required}\:\mathrm{to}\:\mathrm{dislodge}\:\mathrm{electron} \\ $$$$\mathrm{from}\:\mathrm{excited}\:\mathrm{isolated}\:\mathrm{H}-\mathrm{atom},\:\mathrm{IE}_{\mathrm{1}} \:= \\ $$$$\mathrm{13}.\mathrm{6}\:\mathrm{eV}\:\mathrm{is} \\ $$$$\left(\mathrm{1}\right)\:=\:\mathrm{13}.\mathrm{6}\:\mathrm{eV} \\ $$$$\left(\mathrm{2}\right)\:>\:\mathrm{13}.\mathrm{6}\:\mathrm{eV} \\ $$$$\left(\mathrm{3}\right)\:<\:\mathrm{13}.\mathrm{6}\:\mathrm{eV}\:\mathrm{and}\:>\:\mathrm{3}.\mathrm{4}\:\mathrm{eV} \\ $$$$\left(\mathrm{4}\right)\:\leqslant\:\mathrm{3}.\mathrm{4}\:\mathrm{eV} \\ $$…
Question Number 149637 by mnjuly1970 last updated on 06/Aug/21 Answered by iloveisrael last updated on 06/Aug/21 $$\:\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{x}^{\mathrm{2}} \sqrt{\mathrm{1}+\mathrm{x}^{−\mathrm{1}} +\mathrm{x}^{−\mathrm{4}} }\:−\mathrm{x}^{\mathrm{2}} \left(\mathrm{1}+\mathrm{x}^{−\mathrm{1}} \right)}{\mathrm{x}} \\ $$$$=\:\underset{{x}\rightarrow\infty}…
Question Number 149636 by SLVR last updated on 06/Aug/21 Answered by mr W last updated on 06/Aug/21 $${Q}\mathrm{1} \\ $$$${x}\:{is}\:{integer},\:{then}\:{x}^{\mathrm{2}} \:{also}\:{integer}. \\ $$$$\left[{x}^{\mathrm{2}} \right]={x}^{\mathrm{2}} ={x}+\mathrm{1}\:{which}\:{has}\:{no}\:{solution}.…