Question Number 214047 by ajfour last updated on 25/Nov/24 Commented by ajfour last updated on 25/Nov/24 $$\:{The}\:{L}\:{shaped}\:{rigid}\:{scale}\:{can}\:{turn}\: \\ $$$${about}\:{the}\:{pivot}\:{on}\:{a}\:{frictionless}\:{table}. \\ $$$$\:{The}\:{small}\:{mass}\:{m}\:{hits}\:{and}\:{after}\: \\ $$$${rebounding}\:{happens}\:{to}\:{find}\:{the} \\ $$$$\:{other}\:{end}.\:{Find}\:\theta,\:{if}\:\alpha\:{is}\:{measured}.…
Question Number 214040 by ajfour last updated on 25/Nov/24 Commented by ajfour last updated on 25/Nov/24 $${The}\:\bigtriangleup\:{is}\:{equilateral}.\:{Find}\:{its}\:{side}\:\boldsymbol{{s}}. \\ $$ Answered by mr W last updated…
Question Number 214059 by RoseAli last updated on 25/Nov/24 Answered by a.lgnaoui last updated on 25/Nov/24 $$\left(\mathrm{x}−\mathrm{1}\right)\left(\mathrm{x}−\mathrm{5}\right)\:=\mathrm{0}\:\:\:\: \\ $$$$\: \\ $$$$\begin{cases}{\mathrm{x}_{\mathrm{1}} \:\:\:\:=\left\{\frac{\mathrm{10}}{\mathrm{10}}\:\:,\frac{−\mathrm{10}}{−\mathrm{10}}\right\}}\\{\mathrm{x}_{\mathrm{2}} \:\:\:=\left\{\frac{\mathrm{50}}{\mathrm{10}}\:\:\:\:,\frac{−\mathrm{50}}{−\mathrm{10}}\:\:\:\right\}\:\:}\end{cases} \\ $$$$\boldsymbol{\mathrm{S}}=\left\{\frac{−\mathrm{50}}{−\mathrm{10}}\:;\:\:\frac{−\mathrm{10}}{−\mathrm{10}}\:\:;\:\frac{+\mathrm{10}}{+\mathrm{10}}\:;\:\frac{+\mathrm{50}}{+\mathrm{10}}\right\}…
Question Number 214050 by CrispyXYZ last updated on 25/Nov/24 $$\mathrm{If}\:{A}:\:{a}_{\mathrm{1}} ,\:{a}_{\mathrm{2}} ,\:…,\:{a}_{\mathrm{62}} \:\mathrm{and}\:{B}:\:{b}_{\mathrm{1}} ,\:{b}_{\mathrm{2}} ,\:…,\:{b}_{\mathrm{62}} \:\mathrm{are}\:\mathrm{two} \\ $$$$\mathrm{strictly}\:\mathrm{increasing}\:\mathrm{natural}\:\mathrm{number}\:\mathrm{sequences} \\ $$$$\mathrm{such}\:\mathrm{that}\:{a}_{\mathrm{62}} \leqslant\mathrm{755}\:\mathrm{and}\:{b}_{\mathrm{62}} \leqslant\mathrm{755}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{of}\:\underset{{i}=\mathrm{1}} {\overset{\mathrm{62}}…
Question Number 214051 by issac last updated on 25/Nov/24 $$\mathrm{evaluate}\:\int_{\mathrm{0}} ^{\:\pi} \:{e}^{\mathrm{sin}^{\mathrm{2}} \left({u}\right)} \mathrm{d}{u}…\: \\ $$$$\mathrm{i}\:\mathrm{use}\:\mathrm{Feynman}'\mathrm{s}\:\mathrm{trick}\:\mathrm{to}\:\mathrm{solve}\:\mathrm{integral} \\ $$$$\int_{\mathrm{0}} ^{\:\pi} \:{e}^{\mathrm{sin}^{\mathrm{2}} \left({u}\right)} \mathrm{d}{u}={I} \\ $$$${I}\left({t}\right)=\int_{\mathrm{0}} ^{\:\pi}…
Question Number 214012 by ajfour last updated on 24/Nov/24 Commented by ajfour last updated on 24/Nov/24 $${Outer}\:{circle}\:{radius}\:{is}\:{R}.\:{Circle}\:{with} \\ $$$${center}\:{A}\:{has}\:{radius}\:{r}={R}/\mathrm{2}. \\ $$$${If}\:\bigtriangleup{ABC}\:{is}\:{equilateral},\:{find}\:{its} \\ $$$${edge}\:{length}\:\left({say}\:{a}\right). \\ $$…
Question Number 214030 by RoseAli last updated on 24/Nov/24 Answered by A5T last updated on 24/Nov/24 $${x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{5}=\mathrm{0} \\ $$$$\Rightarrow\left({x}+\mathrm{1}\right)^{\mathrm{2}} \equiv\mathrm{6}\left({mod}\:\mathrm{10}\right) \\ $$$$\Rightarrow{x}=\mathrm{3},\mathrm{5} \\ $$…
Question Number 213999 by issac last updated on 24/Nov/24 $$\int\int…\int_{\:\mathcal{D}} \:\:{e}^{−\left({z}_{\mathrm{1}} ^{\mathrm{2}} +{z}_{\mathrm{2}} ^{\mathrm{2}} …+{z}_{{n}} ^{\mathrm{2}} \right)} \mathrm{da} \\ $$$$\mathcal{D}=\underset{\boldsymbol{\mathrm{n}}\:\boldsymbol{\mathrm{times}}} {\left[\mathrm{0},\infty\right)×\left[\mathrm{0},\infty\right)……\left[\mathrm{0},\infty\right)} \\ $$$$\int_{\mathrm{0}} ^{\:\pi} \:{e}^{−\mathrm{sin}^{\mathrm{2}}…
Question Number 214020 by ajfour last updated on 24/Nov/24 Commented by ajfour last updated on 24/Nov/24 $${Red}\:{area}\:=\:{Blue}\:{area}.\:{Find}\:{r}\:{in} \\ $$$${terms}\:{of}\:{k},\:\phi. \\ $$ Answered by dionigi last…
Question Number 214005 by RoseAli last updated on 24/Nov/24 $${find}\:{all}\:{zero}\:{divisors}\:{of}\:{Z}_{\mathrm{24}} \\ $$ Answered by TonyCWX08 last updated on 24/Nov/24 $$\mathrm{1}×\mathrm{24} \\ $$$$\mathrm{2}×\mathrm{12} \\ $$$$\mathrm{3}×\mathrm{8} \\…