Question Number 3317 by rishabh last updated on 10/Dec/15 $$\mathrm{If}\:\mathrm{cosec}\:\theta,\:\mathrm{sec}\:\theta,\:\mathrm{and}\:\mathrm{cot}\:\theta\:\mathrm{are}\:\mathrm{in}\:\mathrm{H}.\mathrm{P}.,\:\mathrm{then} \\ $$$$\frac{\mathrm{sin}\:\theta+\mathrm{tan}\:\theta}{\mathrm{cos}\:\theta}\:=\:? \\ $$ Answered by prakash jain last updated on 10/Dec/15 $$\frac{\mathrm{2}}{\mathrm{sec}\:\theta}=\frac{\mathrm{1}}{\mathrm{cosec}\:\theta}+\frac{\mathrm{1}}{\mathrm{cot}\:\theta}=\mathrm{sin}\:\theta+\mathrm{tan}\:\theta \\ $$$$\mathrm{2cos}\:\theta=\mathrm{sin}\:\theta+\mathrm{tan}\:\theta…
Question Number 3314 by Filup last updated on 10/Dec/15 $$\mathrm{Why}\:\mathrm{is}\:\mathrm{it}\:\mathrm{that}: \\ $$$$\overset{\rightarrow} {{v}}=\frac{{d}\overset{\rightarrow} {{x}}}{{dt}}\:\Rightarrow\:\overset{\rightarrow} {{x}}=\int\:\overset{\rightarrow} {{v}}\:{dt} \\ $$$$\overset{\rightarrow} {{a}}=\frac{{d}^{\mathrm{2}} \overset{\rightarrow} {{x}}}{{dt}^{\mathrm{2}} }=\frac{{d}\overset{\rightarrow} {{v}}}{{dt}} \\ $$$${v}={velocity}…
Question Number 134383 by otchereabdullai@gmail.com last updated on 03/Mar/21 $$\mathrm{In}\:\mathrm{a}\:\mathrm{course}\:\mathrm{a}\:\mathrm{student}\:\mathrm{gets}\:\mathrm{grade}\:\mathrm{C}\:\:\mathrm{if} \\ $$$$\mathrm{his}\:\mathrm{average}\:\mathrm{in}\:\:\mathrm{four}\:\mathrm{test}\:\mathrm{is}\:\mathrm{between}\: \\ $$$$\mathrm{50}\:\mathrm{and}\:\mathrm{60}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{range}\:\mathrm{of}\:\mathrm{score}\:\mathrm{X} \\ $$$$\mathrm{on}\:\mathrm{the}\:\mathrm{fourth}\:\mathrm{test}\:\mathrm{to}\:\mathrm{ensure}\:\mathrm{a}\:\mathrm{grade}\:\mathrm{C} \\ $$$$\mathrm{given}\:\mathrm{that}: \\ $$$$\left(\mathrm{a}\right)\:\mathrm{A}\:\mathrm{student}\:\mathrm{scores}\:\mathrm{65\%}\:,\:\mathrm{55\%},\:\mathrm{and} \\ $$$$\:\mathrm{45\%}\:\mathrm{in}\:\mathrm{the}\:\mathrm{first}\:\mathrm{three}\:\mathrm{test}. \\ $$$$\left(\mathrm{b}\right)\:\mathrm{A}\:\mathrm{student}\:\mathrm{score}\:\mathrm{70\%},\:\mathrm{60\%}\:\mathrm{and} \\…
Question Number 134376 by mr W last updated on 02/Mar/21 Commented by mr W last updated on 06/Mar/21 $${a}\:{solid}\:{cone}\:{of}\:{mass}\:{m}\:{is}\:{released} \\ $$$${from}\:{rest}\:{at}\:{the}\:{horizontal}\:{position} \\ $$$${on}\:{a}\:{inclined}\:{plane}\:{as}\:{shown}.\:{the}\:{cone} \\ $$$${can}\:{only}\:{roll}\:{on}\:{the}\:{plane}.\:{find}\:{the}…
Question Number 134378 by mohammad17 last updated on 02/Mar/21 $${lim}_{{x}\rightarrow\mathrm{3}} \frac{{cos}\left(\frac{\mathrm{3}\pi}{\mathrm{2}{x}}\right)}{{x}−\mathrm{3}} \\ $$ Answered by bramlexs22 last updated on 02/Mar/21 $$\underset{{x}−\mathrm{3}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{cos}\:\left(\frac{\mathrm{3}\pi}{\mathrm{2x}}\right)}{\mathrm{x}−\mathrm{3}} \\ $$$$\mathrm{let}\:\mathrm{x}−\mathrm{3}=\mathrm{w}\:\Rightarrow\:\frac{\mathrm{1}}{\mathrm{x}}=\frac{\mathrm{1}}{\mathrm{w}+\mathrm{3}} \\…
Question Number 3304 by prakash jain last updated on 09/Dec/15 $$\mathrm{Bring}\:\mathrm{up}\:\mathrm{the}\:\mathrm{topic}/\mathrm{challenge}\:\mathrm{started}\:\mathrm{by}\:\mathrm{Filup}\:\mathrm{at}\:\mathrm{the}\:\mathrm{top}. \\ $$$$\mathrm{Shall}\:\mathrm{we}\:\mathrm{start}\:\mathrm{new}\:\mathrm{topic}\:\mathrm{at}\:\mathrm{the}\:\mathrm{beginning} \\ $$$$\mathrm{of}\:\mathrm{calendar}\:\mathrm{month}? \\ $$$$\mathrm{See}\:\mathrm{older}\:\mathrm{post}\:\mathrm{dt}\:\mathrm{24}.\mathrm{11}\:\mathrm{by}\:\mathrm{Filup} \\ $$ Commented by Filup last updated on…
Question Number 134373 by mnjuly1970 last updated on 02/Mar/21 Answered by Dwaipayan Shikari last updated on 02/Mar/21 $${I}\left({a}\right)=\underset{{n}=−\infty} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\left({n}^{\mathrm{2}} +{a}^{\mathrm{2}} \right)^{\mathrm{2}} }=\frac{\mathrm{1}}{{a}^{\mathrm{4}} }+\mathrm{2}\underset{{n}=\mathrm{1}} {\overset{\infty}…
Question Number 68836 by Joel122 last updated on 16/Sep/19 $$\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{graph}\:\mathrm{of} \\ $$$$\boldsymbol{{r}}\:=\:\left(\mathrm{sin}\:{t}\right)\boldsymbol{{i}}\:+\:\left(\mathrm{2cos}\:{t}\right)\boldsymbol{{j}}\:+\:\left(\sqrt{\mathrm{3}}\mathrm{sin}\:{t}\right)\boldsymbol{{k}} \\ $$$$\mathrm{is}\:\mathrm{a}\:\mathrm{circle} \\ $$ Answered by Tanmay chaudhury last updated on 16/Sep/19 $${ix}+{jy}+{kz}=\left({sint}\right){i}+\left(\mathrm{2}{cost}\right){j}+\left(\sqrt{\mathrm{3}}\:{sint}\right){k}…
Question Number 134369 by I want to learn more last updated on 02/Mar/21 Answered by Dwaipayan Shikari last updated on 03/Mar/21 $${Vertical}\:{Velocity}\: \\ $$$${v}^{\mathrm{2}} ={u}^{\mathrm{2}}…
Question Number 68835 by MJS last updated on 16/Sep/19 $$\mathrm{reposting}\:\mathrm{this}\:\mathrm{because}\:\mathrm{it}'\mathrm{s}\:\mathrm{not}\:\mathrm{yet}\:\mathrm{solved} \\ $$$$\mathrm{correctly}.\:\mathrm{I}\:\mathrm{criticize}\:\mathrm{that}\:\mathrm{most}\:\mathrm{of}\:\mathrm{you}\:\mathrm{people} \\ $$$$\mathrm{do}\:\mathrm{not}\:\mathrm{test}\:\mathrm{if}\:\mathrm{your}\:\mathrm{solutions}\:\mathrm{fit}\:\mathrm{the}\:\mathrm{given} \\ $$$$\mathrm{equations}\:\mathrm{in}\:\mathrm{many}\:\mathrm{cases} \\ $$$$ \\ $$$${x}^{\mathrm{2}} +\mathrm{1}−\sqrt{{x}^{\mathrm{3}} +{x}}=\mathrm{6}{x} \\ $$$$ \\…