Question Number 78060 by aliesam last updated on 13/Jan/20 Commented by aliesam last updated on 13/Jan/20 $${the}\:{triangle}\:{is}\:{equilateral} \\ $$ Answered by ajfour last updated on…
Question Number 12525 by tawa last updated on 24/Apr/17 $$\mathrm{Use}\:\mathrm{the}\:\mathrm{substitution}\:\:\mathrm{t}\:=\:\mathrm{sin}\left(\theta\right)\:\mathrm{to}\:\mathrm{solve}\:\mathrm{the}\:\mathrm{equation}\: \\ $$$$\mathrm{2sin}^{\mathrm{4}} \left(\theta\right)\:−\:\mathrm{9sin}^{\mathrm{3}} \left(\theta\right)\:+\:\mathrm{14sin}^{\mathrm{2}} \left(\theta\right)\:−\:\mathrm{9sin}\left(\theta\right)\:+\:\mathrm{2}\:=\:\mathrm{0},\:\: \\ $$$$\mathrm{for}\:\mathrm{possible}\:\mathrm{values}\:\mathrm{of}\:\theta\:\mathrm{in}\:\mathrm{the}\:\mathrm{range}\:\:\mathrm{0}\:\leqslant\:\theta\:\leqslant\:\mathrm{2}\pi \\ $$ Answered by mrW1 last updated on…
Question Number 143598 by mohammad17 last updated on 16/Jun/21 Commented by mohammad17 last updated on 16/Jun/21 $${help}\:{me}\:{sir} \\ $$ Commented by mohammad17 last updated on…
Question Number 143593 by pticantor last updated on 16/Jun/21 $${soit}\:\left(\boldsymbol{{X}}_{{i}} \right),{i}\in\left\{\mathrm{1},\mathrm{2},……,{n}\right\}\:{une}\:{suite}\:{de}\:{variable}\:{a}\boldsymbol{{leartoire}}\:\boldsymbol{{independante}} \\ $$$$\left(\boldsymbol{{iid}}\right)\:\boldsymbol{{suivant}}\:\boldsymbol{{la}}\:\boldsymbol{{loi}}\:\boldsymbol{{binomiale}}\:\boldsymbol{{B}}\left(\boldsymbol{{n}},\boldsymbol{{p}}\right)\: \\ $$$$\boldsymbol{{montrer}}\:\boldsymbol{{que}}\:\overset{\_} {\boldsymbol{{X}}}_{\boldsymbol{{n}}} \boldsymbol{{converge}}\:\boldsymbol{{en}}\:\boldsymbol{{loi}}\:\boldsymbol{{vers}}\:\boldsymbol{{E}}\left(\boldsymbol{{X}}\right) \\ $$$$\mathrm{2}−\:\boldsymbol{{montrer}}\:\boldsymbol{{que}}\:\frac{\mathrm{1}}{\boldsymbol{{n}}}\underset{{i}=\mathrm{1}} {\overset{\mathrm{2}} {\sum}}\boldsymbol{{X}}_{\boldsymbol{{i}}\:\:} ^{\mathrm{2}} \boldsymbol{{converge}}\:\boldsymbol{{en}}\:\boldsymbol{{loi}}\:\:\boldsymbol{{vers}}\:\:\:\:\:\:\:\:\boldsymbol{{E}}\:\left(\boldsymbol{{X}}^{\mathrm{2}} \right) \\…
Question Number 143595 by ZiYangLee last updated on 16/Jun/21 $$\mathrm{If}\:{f}\left({x}\right)=\frac{\mathrm{10}^{{x}} −\mathrm{10}^{−{x}} }{\mathrm{10}^{{x}} +\mathrm{10}^{−{x}} },\:\mathrm{find}\:{f}^{\:−\mathrm{1}} \left({x}\right). \\ $$ Answered by bobhans last updated on 16/Jun/21 $${let}\:\mathrm{10}^{{x}}…
Question Number 78056 by ajfour last updated on 13/Jan/20 Answered by ajfour last updated on 13/Jan/20 $${It}\:{is}\:{from}\:{aid}\:{of}\:{another} \\ $$$${diagram}\:{that}\:{x}^{\mathrm{3}} −{x}=\mathrm{2}{c}\:\:\:\:….\left({i}\right) \\ $$$${From}\:{here} \\ $$$${first}\:{let}\:{AH}={r} \\…
Question Number 143588 by bobhans last updated on 16/Jun/21 Answered by EDWIN88 last updated on 16/Jun/21 $$\mathrm{F}\left(\mathrm{x}\right)=\underset{\mathrm{4}} {\overset{\mathrm{8x}} {\int}}\:\mathrm{f}\left(\mathrm{t}\right)\:\mathrm{dt}\:=\:\sqrt{\mathrm{2}+\mathrm{x}^{\mathrm{2}} }\:+\:\mathrm{c}\: \\ $$$$\mathrm{F}\:'\left(\mathrm{x}\right)=\:\mathrm{8f}\left(\mathrm{8x}\right)=\frac{\mathrm{x}}{\:\sqrt{\mathrm{2}+\mathrm{x}^{\mathrm{2}} }}\: \\ $$$$\mathrm{F}'\left(\mathrm{x}\right)=\mathrm{f}\left(\mathrm{8x}\right)=\frac{\mathrm{x}}{\mathrm{8}\sqrt{\mathrm{2}+\mathrm{x}^{\mathrm{2}}…
Question Number 143591 by mathdanisur last updated on 16/Jun/21 $${a};{b};{c}>\mathrm{0}\:\:{and}\:\:{a}+{b}+{c}={k} \\ $$$$\boldsymbol{{min}}\left(\frac{\mathrm{1}}{\mathrm{1}+{a}^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{\mathrm{1}+{b}^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{\mathrm{1}+{c}^{\mathrm{2}} }\right)=? \\ $$ Answered by Olaf_Thorendsen last updated on 16/Jun/21 $$\mathrm{Let}\:{f}\left({a},{b},{c}\right)\:=\:\frac{\mathrm{1}}{\mathrm{1}+{a}^{\mathrm{2}}…
Question Number 12517 by tawa last updated on 24/Apr/17 $$\mathrm{A}\:\mathrm{spring}\:\mathrm{stretches}\:\mathrm{by}\:\mathrm{15cm}\:\mathrm{when}\:\mathrm{a}\:\mathrm{mass}\:\mathrm{of}\:\mathrm{300g}\:\mathrm{hangs}\:\mathrm{down}\:\mathrm{from}\:\mathrm{it}. \\ $$$$\mathrm{if}\:\mathrm{the}\:\mathrm{spring}\:\mathrm{is}\:\mathrm{then}\:\mathrm{strethed}\:\mathrm{an}\:\mathrm{additional}\:\mathrm{10cm}\:\mathrm{and}\:\mathrm{realeased},\:\mathrm{calculate} \\ $$$$\left(\mathrm{a}\right)\:\mathrm{the}\:\mathrm{spring}\:\mathrm{constant} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{Angular}\:\mathrm{velocity} \\ $$$$\left(\mathrm{c}\right)\:\mathrm{The}\:\mathrm{amplitude}\:\mathrm{of}\:\mathrm{the}\:\mathrm{oscillation} \\ $$$$\left(\mathrm{d}\right)\:\mathrm{The}\:\mathrm{maximum}\:\mathrm{velocity} \\ $$$$\left(\mathrm{e}\right)\:\mathrm{The}\:\mathrm{maximum}\:\mathrm{acceleration}\:\mathrm{of}\:\mathrm{the}\:\mathrm{mass} \\ $$$$\left(\mathrm{f}\right)\:\mathrm{The}\:\mathrm{period}\:\mathrm{T}\:\mathrm{and}\:\mathrm{frequency}\:\mathrm{f} \\…
Question Number 143584 by Huy last updated on 16/Jun/21 $$\begin{cases}{{x}^{\mathrm{2}} −{xy}+{y}^{\mathrm{2}} =\mathrm{7}}\\{\left({x}+\mathrm{3}\right)\left({y}−\mathrm{2}\right)=\sqrt{{xy}+\mathrm{3}}+\sqrt{{xy}−\mathrm{2}}}\end{cases} \\ $$$${Find}\:{x},{y} \\ $$ Answered by MJS_new last updated on 16/Jun/21 $$\mathrm{assuming}\:\mathrm{both}\:\sqrt{{xy}+\mathrm{3}}\:\mathrm{and}\:\sqrt{{xy}−\mathrm{2}}\:\mathrm{are}\:\in\mathbb{N} \\…