Question Number 140596 by nadovic last updated on 10/May/21 $$ \\ $$$$\mathrm{A}\:\mathrm{class}\:\mathrm{contains}\:\mathrm{20}\:\mathrm{students}\:\mathrm{of}\:\mathrm{whom}\:\mathrm{2} \\ $$$$\mathrm{are}\:\mathrm{men}\:\mathrm{and}\:\mathrm{8}\:\mathrm{are}\:\mathrm{women}.\:\mathrm{A}\:\mathrm{random} \\ $$$$\mathrm{sample}\:\mathrm{of}\:\mathrm{2}\:\mathrm{students}\:\mathrm{is}\:\mathrm{taken}\:\mathrm{from}\:\mathrm{the} \\ $$$$\mathrm{class}\:\mathrm{without}\:\mathrm{replacement}.\:\left(\mathrm{random}\right. \\ $$$$\mathrm{imlies}\:\mathrm{that}\:\mathrm{each}\:\mathrm{student}\:\mathrm{has}\:\mathrm{an}\:\mathrm{equal} \\ $$$$\left.\mathrm{chance}\:\mathrm{of}\:\mathrm{appearing}\:\mathrm{in}\:\mathrm{the}\:\mathrm{sample}\right) \\ $$$$\left({a}\right)\:\mathrm{Use}\:\mathrm{a}\:\mathrm{diagram}\:\mathrm{to}\:\mathrm{illustrate}\:\mathrm{the}\:\mathrm{possible} \\…
Question Number 75063 by mathmax by abdo last updated on 06/Dec/19 $${calculate}\:\:\sum_{{n}=\mathrm{1}} ^{\mathrm{17}} \:\:\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}^{\mathrm{3}} } \\ $$ Commented by mathmax by abdo last updated…
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Question Number 9525 by Joel575 last updated on 12/Dec/16 $$\mathrm{If}\:{x}_{\mathrm{1}} ,\:{x}_{\mathrm{2}} ,\:{x}_{\mathrm{3}} ,\:…,\:{x}_{\mathrm{2009}\:} \in\:\mathbb{R} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{from} \\ $$$$\left(\mathrm{cos}\:{x}_{\mathrm{1}} \right)\left(\mathrm{sin}\:{x}_{\mathrm{2}} \right)\:+\:\left(\mathrm{cos}\:{x}_{\mathrm{2}} \right)\left(\mathrm{sin}\:{x}_{\mathrm{3}} \right)\:+\:…\:+\:\left(\mathrm{cos}\:{x}_{\mathrm{2008}} \right)\left(\mathrm{sin}\:{x}_{\mathrm{2009}} \right)\:+\:\left(\mathrm{cos}\:{x}_{\mathrm{2009}} \right)\left(\mathrm{sin}\:{x}_{\mathrm{1}}…
Question Number 75058 by behi83417@gmail.com last updated on 07/Dec/19 $$\boldsymbol{\mathrm{in}}\:\boldsymbol{\mathrm{triangle}}:\:\:\boldsymbol{\mathrm{ABC}}: \\ $$$$\boldsymbol{\mathrm{a}}=\sqrt{\mathrm{2}\:},\boldsymbol{\mathrm{b}}−\boldsymbol{\mathrm{c}}=\frac{\sqrt{\mathrm{2}}+\mathrm{1}}{\mathrm{2}},\overset{} {\boldsymbol{\mathrm{B}}}−\overset{} {\boldsymbol{\mathrm{C}}}=\frac{\boldsymbol{\pi}}{\mathrm{2}} \\ $$$$\boldsymbol{\mathrm{find}}:\:\:\boldsymbol{\mathrm{h}}_{\boldsymbol{\mathrm{a}}} ,\:\:\boldsymbol{\mathrm{S}}_{\boldsymbol{\mathrm{ABC}}\:\:} ,\boldsymbol{\mathrm{d}}_{\boldsymbol{\mathrm{a}}\:\:\:} ,\:\boldsymbol{\mathrm{R}}\:\:\:\:,\overset{} {\boldsymbol{\mathrm{A}}}. \\ $$ Commented by mr…
Question Number 9523 by Joel575 last updated on 12/Dec/16 $$\mathrm{3}{a}\:=\:\left({b}\:+\:{c}\:+\:{d}\right)^{\mathrm{2014}} \\ $$$$\mathrm{3}{b}\:=\:\left({a}\:+\:{c}\:+\:{d}\right)^{\mathrm{2014}} \\ $$$$\mathrm{3}{c}\:=\:\left({a}\:+\:{b}\:+\:{d}\right)^{\mathrm{2014}} \\ $$$$\mathrm{3}{d}\:=\:\left({a}\:+\:{b}\:+\:{c}\right)^{\mathrm{2014}} \\ $$$$\mathrm{Find}\:\mathrm{all}\:\mathrm{the}\:\mathrm{solution}\:\mathrm{of}\:\left({a},\:{b},\:{c},\:{d}\right)\:\mathrm{if}\:{a},\:{b},\:{c},\:{d}\:\in\:\mathbb{R} \\ $$ Answered by mrW last updated…
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Question Number 9520 by ridwan balatif last updated on 12/Dec/16 $$\int\frac{\mathrm{sinxcosx}}{\mathrm{4}+\mathrm{sin}^{\mathrm{4}} \mathrm{x}}\mathrm{dx}=…? \\ $$ Answered by mrW last updated on 12/Dec/16 $$\mathrm{u}=\mathrm{sin}\:\mathrm{x} \\ $$$$\mathrm{du}=\mathrm{cos}\:\mathrm{xdx} \\…
Question Number 140589 by bramlexs22 last updated on 09/May/21 $$\:{x}^{−\mathrm{log}\:_{\mathrm{2}} \:{x}\:+\mathrm{4}} \:<\:\frac{{x}}{\mathrm{16}} \\ $$ Answered by MJS_new last updated on 10/May/21 $${x}^{\mathrm{4}−\mathrm{log}_{\mathrm{2}} \:{x}} \in\mathbb{R}\:\Rightarrow\:{x}>\mathrm{0} \\…
Question Number 140588 by mnjuly1970 last updated on 09/May/21 $$\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…….{Advanced}\:….\bigstar\bigstar\bigstar….{Calculus}……. \\ $$$$\:\:\:\:\:\:\:\:{evaluation}\:{the}\:{value}\:{of}\:: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\phi}\::=\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} {sin}^{\mathrm{2}} \left({x}\right).{ln}\left({sin}\left({x}\right)\right){dx} \\ $$$$\:\:\:\:\:\:\:\:\:\:{solution}:: \\ $$$$\:\:\:\:\:\:\:\xi\:\left({a}\right):=\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} {sin}^{\mathrm{2}+{a}}…