Question Number 142977 by mohammad17 last updated on 08/Jun/21 Commented by mohammad17 last updated on 08/Jun/21 $${can}\:{you}\:{solve}\:{by}\:{Gramar}\:{rulle} \\ $$ Commented by mohammad17 last updated on…
Question Number 77442 by aliesam last updated on 06/Jan/20 $${prove}\:{that} \\ $$$$\underset{{x}\rightarrow\infty} {{lim}}\:\left(\mid\frac{{x}^{{x}^{\mathrm{2}} } \left({x}+\mathrm{2}\right)^{\left({x}+\mathrm{1}\right)^{\mathrm{2}} } }{\left({x}+\mathrm{1}\right)^{\mathrm{2}{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{1}} }\mid\right)={e} \\ $$ Answered by aliesam last…
Question Number 11902 by FilupS last updated on 04/Apr/17 $$\mathrm{Assuming}\:\mathrm{it}\:\mathrm{rained}\:\mathrm{at}\:\mathrm{a}\:\mathrm{constant}\:\mathrm{rate}, \\ $$$$\mathrm{and}\:\mathrm{the}\:\mathrm{rain}\:\mathrm{fell}\:\mathrm{at}\:\mathrm{angle}\:\theta\:\mathrm{to}\:\mathrm{the}\:\mathrm{ground} \\ $$$$\left(\mathrm{see}\:\mathrm{diagram}\right),\:\mathrm{determine}\:\mathrm{if}\:\mathrm{walking}\:\mathrm{or} \\ $$$$\mathrm{running}\:\mathrm{causes}\:\mathrm{you}\:\mathrm{to}\:\mathrm{get}\:\mathrm{more}/\mathrm{less}\:\mathrm{wet}, \\ $$$$\mathrm{or}\:\mathrm{of}\:\mathrm{it}\:\mathrm{makes}\:\mathrm{no}\:\mathrm{difference}\:\mathrm{for}: \\ $$$$\: \\ $$$$\mathrm{1}.\:\:\:\theta=\mathrm{90}°\:\:\left(\mathrm{downwards}\right) \\ $$$$\mathrm{2}.\:\theta<\mathrm{90}°\:\:\left(\mathrm{the}\:\mathrm{rain}\:\mathrm{is}\:\mathrm{moving}\:\mathrm{on}\:\mathrm{the}\right. \\…
Question Number 11901 by ahmet last updated on 04/Apr/17 $$\frac{\mathrm{7}{cos}^{\mathrm{2}} {x}+{sin}^{\mathrm{2}} {x}−\mathrm{3}}{\mathrm{2}{cos}^{\mathrm{2}} {x}−{sin}^{\mathrm{2}} {x}}=? \\ $$$${czm}\because\:\:\frac{\mathrm{7}{cos}^{\mathrm{2}} {x}+\mathrm{1}−{cos}^{\mathrm{2}} {x}−\mathrm{3}}{\mathrm{2}{cos}^{\mathrm{2}} {x}−{sin}^{\mathrm{2}} {x}} \\ $$$$\frac{\mathrm{6}{cos}^{\mathrm{2}} {x}−\mathrm{2}}{\mathrm{2}{cos}^{\mathrm{2}} {x}−\left(\mathrm{1}−{cos}^{\mathrm{2}} {x}\right)}=\frac{\mathrm{6}{cos}^{\mathrm{2}}…
Question Number 11900 by @ANTARES_VY last updated on 04/Apr/17 $$\boldsymbol{\mathrm{Calculate}}. \\ $$$$\boldsymbol{\mathrm{cos}}\frac{\boldsymbol{\pi}}{\mathrm{7}}×\boldsymbol{\mathrm{cos}}\frac{\mathrm{4}\boldsymbol{\pi}}{\mathrm{7}}×\boldsymbol{\mathrm{cos}}\frac{\mathrm{5}\boldsymbol{\pi}}{\mathrm{7}}. \\ $$ Answered by ajfour last updated on 04/Apr/17 $$=\:\mathrm{cos}\:\frac{\pi}{\mathrm{7}}\mathrm{cos}\:\frac{\mathrm{4}\pi}{\mathrm{7}}\left[−\mathrm{cos}\:\left(\pi−\frac{\mathrm{5}\pi}{\mathrm{7}}\right)\:\right] \\ $$$$=\:−\mathrm{cos}\:\frac{\pi}{\mathrm{7}}\mathrm{cos}\:\frac{\mathrm{4}\pi}{\mathrm{7}}\mathrm{cos}\:\frac{\mathrm{2}\pi}{\mathrm{7}} \\…
Question Number 11899 by ahmet last updated on 04/Apr/17 $${f}'\left({x}\right)=\left\{_{\mathrm{3}\:\:\:\:\:;{x}>\mathrm{2}} ^{\mathrm{2}{x}\:\:;\:{x}\leqslant\mathrm{2}} \right. \\ $$$${f}\left(\mathrm{2}\right)=\mathrm{1}\:{ise}\:{f}\left(\mathrm{1}\right)+{f}\left(\mathrm{3}\right)=? \\ $$$${czm}\because\:{f}\left({x}\right)=\left\{_{\mathrm{3}{x}+{c}_{\mathrm{2}} \:;\:{x}>\mathrm{2}} ^{{x}^{\mathrm{2}} +{c}_{\mathrm{1}} \:;{x}\leqslant\mathrm{2}} \right. \\ $$$${f}\left(\mathrm{2}\right)={x}^{\mathrm{2}} +{c}_{\mathrm{1}} \:{dir}…
Question Number 142968 by bramlexs22 last updated on 08/Jun/21 $${Given}\:{p}<{x}<{q}\:{is}\:{solution}\:{set} \\ $$$${inequality}\:\mathrm{1}+\mathrm{2}^{{x}} +\mathrm{2}^{\mathrm{2}{x}} +\mathrm{2}^{\mathrm{3}{x}} +…>\mathrm{2} \\ $$$${for}\:{x}\neq\mathrm{1}.\:{find}\:{the}\:{value}\:{of}\: \\ $$$$\mathrm{5}{p}−\mathrm{3}{q}\:. \\ $$ Answered by mr W…
Question Number 11898 by tawa last updated on 04/Apr/17 $$\left(\mathrm{a}\right) \\ $$$$\mathrm{You}\:\mathrm{are}\:\mathrm{listening}\:\mathrm{to}\:\mathrm{your}\:\mathrm{favourite}\:\mathrm{song}\:\mathrm{on}\:\mathrm{a}\:\mathrm{CD}.\:\mathrm{You}\:\mathrm{note}\:\mathrm{that}\:\mathrm{the}\:\mathrm{sound} \\ $$$$\mathrm{wave}\:\mathrm{has}\:\mathrm{a}\:\mathrm{pleasant}\:\mathrm{frequency}\:\mathrm{of}\:\mathrm{12}\:\mathrm{Hertz}. \\ $$$$\left(\mathrm{i}\right)\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{velovity}\:\mathrm{of}\:\mathrm{the}\:\mathrm{sound}\:\mathrm{wave} \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{What}\:\mathrm{wavelenght}\:\mathrm{are}\:\mathrm{the}\:\mathrm{wave}\:\mathrm{moving}\:\mathrm{at} \\ $$$$\left(\mathrm{iii}\right)\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{period} \\ $$$$\left(\mathrm{b}\right) \\ $$$$\mathrm{60}\:\mathrm{complete}\:\mathrm{waves}\:\mathrm{pass}\:\mathrm{a}\:\mathrm{particular}\:\mathrm{point}\:\mathrm{in}\:\mathrm{4}\:\mathrm{secs},\:\mathrm{if}\:\mathrm{the}\:\mathrm{distance}\:\mathrm{between} \\…
Question Number 142971 by 0731619 last updated on 08/Jun/21 Commented by wassel last updated on 11/Jun/21 $$\left(\sqrt{{x}}−\frac{\mathrm{1}}{\:\sqrt{{x}}}\right)^{\mathrm{2}} ={x}+\frac{\mathrm{1}}{{x}}−\mathrm{2}=\frac{\mathrm{1}}{\mathrm{2}}−\mathrm{2}=−\frac{\mathrm{3}}{\mathrm{2}}\:=\frac{\mathrm{3}}{\mathrm{2}}{i}^{\mathrm{2}} \\ $$$$\sqrt{{x}}−\frac{\mathrm{1}}{\:\sqrt{{x}}}=\pm{i}\sqrt{\frac{\mathrm{3}}{\mathrm{2}}\:\:}\: \\ $$ Answered by Rasheed.Sindhi…
Question Number 142970 by mnjuly1970 last updated on 08/Jun/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:……….{CALCULUS}……….. \\ $$$$\:\:\:\:\:\:\:{prove}\:{that}::\:\: \\ $$$$\:\:\:\:\:\:\boldsymbol{\phi}:=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}−\mathrm{1}} \left(\left({n}−\mathrm{1}\right)!\right)^{\mathrm{2}} }{\left(\mathrm{2}{n}\right)!}=\mathrm{2}{log}^{\mathrm{2}} \left(\varphi\right) \\ $$$$\:\:\:\:\varphi={golden}\:{ratio}…. \\ $$$$\:\:\:\:…………. \\ $$…