Question Number 149023 by ArielVyny last updated on 02/Aug/21 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \frac{{tsint}}{\mathrm{1}+{cos}^{\mathrm{2}} {t}}{dt}=\overset{\frac{\pi}{\mathrm{4}}} {\int}_{\mathrm{0}} \frac{{tcost}}{\mathrm{1}+{sin}^{\mathrm{2}} {t}}{dt} \\ $$$${true}\:{or}\:{false}\:?? \\ $$ Answered by mindispower last updated…
Question Number 17948 by b.e.h.i.8.3.417@gmail.com last updated on 12/Jul/17 Commented by mrW1 last updated on 12/Jul/17 $$\mathrm{area}\:\mathrm{of}\:\Delta\mathrm{ABC}=\mathrm{S}=\frac{\mathrm{1}}{\mathrm{2}}\mathrm{ah}_{\mathrm{a}} \\ $$$$\Rightarrow\frac{\mathrm{1}}{\mathrm{h}_{\mathrm{a}} }=\frac{\mathrm{1}}{\mathrm{2S}}\:\mathrm{a}=\mathrm{ka} \\ $$$$\mathrm{similarly} \\ $$$$\Rightarrow\frac{\mathrm{1}}{\mathrm{h}_{\mathrm{b}} }=\mathrm{kb}\:…
Question Number 83481 by gny last updated on 02/Mar/20 Commented by gny last updated on 02/Mar/20 $${sir}\:{could}\:{you}\:{help}\:{me}\:\:\:\:\:\:\:\:\:\:\:{Find}\:\:\alpha+\beta \\ $$ Commented by mathmax by abdo last…
Question Number 83477 by M±th+et£s last updated on 02/Mar/20 $${a}^{{b}} +{b}^{{a}} =\mathrm{1}\:\:\:{a}=?\:,\:{b}=? \\ $$$${a}\neq{b}\neq\mathrm{0} \\ $$ Commented by mr W last updated on 03/Mar/20 $${if}\:{a},{b}\in{R},\:{then}\:{i}\:{think}\:{there}\:{is}\:{no}…
Question Number 17939 by ibraheem160 last updated on 12/Jul/17 $$\int{secxdx}\: \\ $$ Commented by prakash jain last updated on 12/Jul/17 $$\mathrm{sec}\:{x}=\frac{\mathrm{sec}\:{x}\left(\mathrm{sec}\:{x}+\mathrm{tan}\:{x}\right)}{\mathrm{sec}\:{x}+\mathrm{tan}\:{x}} \\ $$$$\int\mathrm{sec}\:{x}\:\mathrm{d}{x}=\int\frac{{d}\left(\mathrm{sec}\:{x}+\mathrm{tan}\:{x}\right)}{\mathrm{sec}\:{x}+\mathrm{tan}\:{x}} \\ $$…
Question Number 149008 by Samimsultani last updated on 02/Aug/21 Commented by bramlexs22 last updated on 02/Aug/21 $$\sqrt{\mathrm{5}+\sqrt{\mathrm{24}}\:}\:=\:\sqrt{\mathrm{5}+\mathrm{2}\sqrt{\mathrm{6}}}\:=\:\sqrt{\mathrm{3}}\:+\sqrt{\mathrm{2}}\: \\ $$$$\sqrt{\mathrm{5}−\sqrt{\mathrm{24}}}\:=\:\sqrt{\mathrm{3}}−\sqrt{\mathrm{2}} \\ $$$$\left(\sqrt{\mathrm{3}}+\sqrt{\mathrm{2}}\right)^{\mathrm{x}} −\left(\sqrt{\mathrm{3}}−\sqrt{\mathrm{2}}\right)^{\mathrm{x}} \:=\:\mathrm{40}\sqrt{\mathrm{6}} \\ $$$$\mathrm{let}\:\left(\sqrt{\mathrm{3}}+\sqrt{\mathrm{2}}\right)^{\mathrm{x}}…
Question Number 17938 by Tinkutara last updated on 12/Jul/17 $$\mathrm{If}\:\mathrm{only}\:\mathrm{downward}\:\mathrm{motion}\:\mathrm{along}\:\mathrm{lines}\:\mathrm{is} \\ $$$$\mathrm{allowed},\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{total}\:\mathrm{number}\:\mathrm{of} \\ $$$$\mathrm{paths}\:\mathrm{from}\:\mathrm{point}\:\mathrm{P}\:\mathrm{to}\:\mathrm{point}\:\mathrm{Q}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{figure}\:\mathrm{below}? \\ $$ Commented by Tinkutara last updated on 12/Jul/17…
Question Number 83473 by M±th+et£s last updated on 02/Mar/20 $${solve}\:{in}\:{R} \\ $$$${sin}\left(\pi{ln}\left({x}\right)\right)+{cos}\left(\pi{ln}\left({x}\right)\right)=\mathrm{1} \\ $$ Answered by mind is power last updated on 02/Mar/20 $$\Rightarrow\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}{sin}\left(\pi{ln}\left({x}\right)\right)+\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}{cos}\left(\pi{ln}\left({x}\right)\right)=\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}} \\…
Question Number 17936 by Rishabh#1 last updated on 12/Jul/17 $$\mathrm{Two}\:\mathrm{particles}\:\mathrm{start}\:\mathrm{moving}\:\mathrm{towards} \\ $$$$\mathrm{each}\:\mathrm{other}\:\mathrm{with}\:\mathrm{constant}\:\mathrm{acceleration} \\ $$$$\mathrm{of}\:\:\mathrm{1}\:{m}/{s}^{\mathrm{2}} .\:\mathrm{If}\:\mathrm{their}\:\mathrm{initial}\:\mathrm{separation}\:\mathrm{is} \\ $$$$\mathrm{100}\:\mathrm{m},\:\mathrm{find}\:\mathrm{after}\:\mathrm{what}\:\mathrm{time}\:\mathrm{they}\:\mathrm{will} \\ $$$$\mathrm{meet}\:\mathrm{each}\:\mathrm{other} \\ $$$$\left(\mathrm{A}\right)\:\mathrm{40}{s}\:\:\:\:\left(\mathrm{B}\right)\:\mathrm{45}{s}\:\:\:\:\left(\mathrm{C}\right)\:\mathrm{50}\:{s}\:\left(\mathrm{D}\right)\mathrm{55}{s} \\ $$ Commented by…
Question Number 17935 by Rishabh#1 last updated on 12/Jul/17 $$\mathrm{Ball}\:{A}\:\mathrm{is}\:\mathrm{dropped}\:\mathrm{from}\:\mathrm{the}\:\mathrm{top}\:\mathrm{of}\:\mathrm{a}\:\mathrm{building}. \\ $$$$\mathrm{At}\:\mathrm{the}\:\mathrm{same}\:\mathrm{instant}\:\mathrm{ball}\:{B}\:\mathrm{is}\:\mathrm{thrown} \\ $$$$\mathrm{vertically}\:\mathrm{upwards}\:\mathrm{from}\:\mathrm{the}\:\mathrm{ground}. \\ $$$$\mathrm{When}\:\mathrm{the}\:\mathrm{ball}\:\mathrm{collide},\:\mathrm{they}\:\mathrm{are}\:\mathrm{moving}\:\:\mathrm{in} \\ $$$$\mathrm{opposite}\:\mathrm{directions}\:\mathrm{and}\:\mathrm{the}\:\mathrm{speed}\:\mathrm{of}\:{A}\left({u}\right) \\ $$$$\mathrm{is}\:\mathrm{twice}\:\mathrm{the}\:\mathrm{speed}\:\mathrm{of}\:{B}.\:\mathrm{The}\:\mathrm{relative}\: \\ $$$$\mathrm{velocity}\:\mathrm{of}\:\mathrm{the}\:\mathrm{ball}\:\mathrm{just}\:\mathrm{before}\:\mathrm{collision} \\ $$$$\mathrm{and}\:\mathrm{relative}\:\mathrm{acceleration}\:\mathrm{between}\:\mathrm{them} \\…