Question Number 175010 by Mastermind last updated on 16/Aug/22 $$\:\mathrm{A}\:\mathrm{ball}\:\mathrm{of}\:\boldsymbol{\mathrm{p}}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{0}.\mathrm{25kg}\:\mathrm{losses}\:\frac{\mathrm{1}}{\mathrm{3}}\:\mathrm{of}\: \\ $$$$\mathrm{its}\:\mathrm{velocity}\:\mathrm{when}\:\mathrm{it}\:\mathrm{makes}\:\mathrm{an}\:\mathrm{head}\:\mathrm{on} \\ $$$$\mathrm{collision}\:\mathrm{with}\:\mathrm{an}\:\mathrm{identical}\:\mathrm{ball}\:\boldsymbol{\mathrm{q}}\:\mathrm{at}\:\mathrm{rest}. \\ $$$$\mathrm{After}\:\mathrm{collision},\:\boldsymbol{\mathrm{q}}\:\mathrm{moves}\:\mathrm{off}\:\mathrm{with}\:\mathrm{a}\:\mathrm{velocity} \\ $$$$\mathrm{of}\:\mathrm{2ms}^{−\mathrm{1}} \:\mathrm{in}\:\mathrm{the}\:\mathrm{original}\:\mathrm{direction}\:\mathrm{of}\:\boldsymbol{\mathrm{p}}. \\ $$$$\mathrm{Calculate}\:\mathrm{the}\:\mathrm{initial}\:\mathrm{velocity}\:\mathrm{of}\:\boldsymbol{\mathrm{p}}. \\ $$ Commented by…
Question Number 43889 by SNILL JAMES last updated on 17/Sep/18 $${if}\:{tan}\:{A}\:+\:{tan}\:{B}=\mathrm{90} \\ $$$${find}\:{taAtanB} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 17/Sep/18 $${tan}\left({A}+{B}\right)=\frac{{tanA}+{tanB}}{\mathrm{1}−{tanAtanB}} \\ $$$$\mathrm{1}−{tanAtanB}=\frac{\mathrm{90}}{{tan}\left({A}+{B}\right)}…
Question Number 174950 by Mastermind last updated on 14/Aug/22 $$\mathrm{Have}\:\mathrm{you}\:\mathrm{seen}\:\mathrm{this}\:\mathrm{method}\:\mathrm{of}\:\mathrm{solving} \\ $$$$\mathrm{quadratic}\:\mathrm{problem}? \\ $$$$\mathrm{x}^{\mathrm{2}} −\mathrm{x}−\mathrm{12}=\mathrm{0} \\ $$$$\mathrm{y}'=\pm\sqrt{\mathrm{b}^{\mathrm{2}} −\mathrm{4ac}} \\ $$ Answered by peter frank last…
Question Number 43874 by peter frank last updated on 16/Sep/18 $${in}\:\Delta\:{ABC},{prove}\:{that} \\ $$$$\:\frac{{a}+{b}−{c}}{{a}+{b}+{c}}\:=\:\mathrm{tan}\:\frac{{A}}{\mathrm{2}}\mathrm{tan}\:\frac{{B}}{\mathrm{2}}\: \\ $$ Answered by ajfour last updated on 16/Sep/18 $$\frac{{a}+{b}−{c}}{{a}+{b}+{c}}=\frac{\mathrm{sin}\:{A}+\mathrm{sin}\:{B}−\mathrm{sin}\:\left({A}+{B}\right)}{\mathrm{sin}\:{A}+\mathrm{sin}\:{B}+\mathrm{sin}\:\left({A}+{B}\right)} \\ $$$$\:\:\:\:\:\:\:\:\:=\:\frac{\mathrm{2sin}\:\left(\frac{{A}+{B}}{\mathrm{2}}\right)\left[\mathrm{cos}\:\left(\frac{{A}−{B}}{\mathrm{2}}\right)−\mathrm{cos}\:\left(\frac{{A}+{B}}{\mathrm{2}}\right)\right]}{\mathrm{2sin}\:\left(\frac{{A}+{B}}{\mathrm{2}}\right)\left[\mathrm{cos}\:\left(\frac{{A}−{B}}{\mathrm{2}}\right)+\mathrm{cos}\:\left(\frac{{A}+{B}}{\mathrm{2}}\right)\right]}…
Question Number 174928 by Mastermind last updated on 14/Aug/22 $$\mathrm{How}\:\mathrm{many}\:\mathrm{digits}\:\mathrm{does}\:\mathrm{1000}^{\mathrm{1000}} \:\mathrm{have}? \\ $$$$ \\ $$$$ \\ $$$$\mathrm{Mastermind} \\ $$ Answered by Ar Brandon last updated…
Question Number 43796 by gunawan last updated on 15/Sep/18 Answered by MrW3 last updated on 15/Sep/18 $$\sqrt{\mathrm{2}}{R}+{R}+\frac{\mathrm{1}}{\mathrm{2}}=\frac{\mathrm{1}}{\mathrm{2}}×\sqrt{\mathrm{2}} \\ $$$$\mathrm{2}\left(\sqrt{\mathrm{2}}+\mathrm{1}\right){R}=\left(\sqrt{\mathrm{2}}−\mathrm{1}\right) \\ $$$${R}=\frac{\sqrt{\mathrm{2}}−\mathrm{1}}{\mathrm{2}\left(\sqrt{\mathrm{2}}+\mathrm{1}\right)}=\frac{\left(\sqrt{\mathrm{2}}−\mathrm{1}\right)^{\mathrm{2}} }{\mathrm{2}\left(\mathrm{2}−\mathrm{1}\right)}=\frac{\mathrm{3}−\mathrm{2}\sqrt{\mathrm{2}}}{\mathrm{2}}=\frac{\mathrm{3}}{\mathrm{2}}−\sqrt{\mathrm{2}} \\ $$ Commented…
Question Number 43789 by Junaid555 last updated on 15/Sep/18 $$\:{plz}\:{solve}\:{it}\:{for}\:{me}\:{i}\:{am}\:{learning} \\ $$$$ \\ $$$$\:\:\sqrt[{\mathrm{3}}]{\frac{\mathrm{81}}{\mathrm{125}}} \\ $$ Answered by MJS last updated on 15/Sep/18 $$\sqrt[{{n}}]{\frac{{a}}{{b}}}=\frac{\sqrt[{{n}}]{{a}}}{\:\sqrt[{{n}}]{{b}}}\:\:\:\:\:\sqrt[{{n}}]{{a}×{b}}=\sqrt[{{n}}]{{a}}×\sqrt[{{n}}]{{b}} \\…
Question Number 174853 by Mastermind last updated on 12/Aug/22 $$\mathrm{By}\:\mathrm{first}\:\mathrm{principle},\:\mathrm{solve}\:\mathrm{cos}^{\mathrm{2}} \mathrm{x}\:+\:\mathrm{sin}^{\mathrm{2}} \mathrm{x}=\mathrm{1} \\ $$ Commented by daus last updated on 13/Aug/22 $${what}\:{do}\:{you}\:{means}\:{by}\:{first}\:{principle}? \\ $$ Commented…
Question Number 174770 by Mastermind last updated on 10/Aug/22 $$\int\left(\frac{\mathrm{sinx}}{\:\sqrt{\mathrm{x}}}\right)\mathrm{dx} \\ $$$$ \\ $$$$\mathrm{Mastermind} \\ $$ Answered by Frix last updated on 10/Aug/22 $$\int\frac{\mathrm{sin}\:{x}}{\:\sqrt{{x}}}{dx}\overset{\left(\ast\right)} {=}\sqrt{\mathrm{2}\pi}\int\mathrm{sin}\:\frac{\pi{u}^{\mathrm{2}}…
Question Number 43694 by Tawa1 last updated on 14/Sep/18 $$\mathrm{Using}\:\mathrm{the}\:\mathrm{method}\:\mathrm{of}\:\mathrm{dimension},\:\mathrm{derive}\:\mathrm{an}\:\mathrm{expression}\:\mathrm{for}\:\mathrm{the}\:\mathrm{velocity} \\ $$$$\mathrm{of}\:\mathrm{sound}\:\mathrm{waves}\:\left(\mathrm{v}\right)\:\mathrm{through}\:\mathrm{a}\:\mathrm{medium}.\:\mathrm{Assume}\:\mathrm{that}\:\mathrm{the}\:\mathrm{velocity}\: \\ $$$$\mathrm{depends}\:\mathrm{on}:\:\:\left(\mathrm{i}\right)\:\mathrm{Modulus}\:\mathrm{of}\:\mathrm{elasticity}\:\left(\mathrm{E}\right)\:\mathrm{of}\:\mathrm{the}\:\mathrm{medium} \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{The}\:\mathrm{density}\:\mathrm{of}\:\mathrm{the}\:\mathrm{medium}\:\left(\rho\right),\:\mathrm{take}\:\mathrm{the}\:\mathrm{constant}\:\mathrm{K}\:=\:\mathrm{1} \\ $$ Answered by alex041103 last updated on 14/Sep/18…