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Question Number 87516 by mary_ last updated on 04/Apr/20 $$\begin{cases}{\mathrm{2}^{\frac{{x}+{y}}{\mathrm{3}}} +\mathrm{2}^{\frac{{x}+{y}}{\mathrm{6}}} =\mathrm{6}}\\{{x}^{\mathrm{2}} +\mathrm{5}{y}^{\mathrm{2}} =\mathrm{6}{xy}}\end{cases} \\ $$ Answered by TANMAY PANACEA. last updated on 04/Apr/20 $${x}^{\mathrm{2}}…
Question Number 153054 by daus last updated on 04/Sep/21 Answered by bobhans last updated on 04/Sep/21 $$\begin{cases}{{g}\left({x}\right)=\mathrm{1}−\mathrm{2}{x}}\\{{f}\left({x}\right)={kx}^{\mathrm{2}} +{m}}\end{cases}\:\Rightarrow\left({f}\bullet{g}\right)\left({x}\right)={x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{5} \\ $$$$\Rightarrow{k}\left(\mathrm{1}−\mathrm{2}{x}\right)^{\mathrm{2}} +{m}\:=\:{x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{5} \\ $$$$\Rightarrow{k}\left(\mathrm{4}{x}^{\mathrm{2}}…
Question Number 21977 by Tinkutara last updated on 08/Oct/17 $$\mathrm{Let}\:{n}\:\mathrm{be}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{ways}\:\mathrm{in}\:\mathrm{which} \\ $$$$\mathrm{5}\:\mathrm{boys}\:\mathrm{and}\:\mathrm{5}\:\mathrm{girls}\:\mathrm{stand}\:\mathrm{in}\:\mathrm{a}\:\mathrm{queue}\:\mathrm{in} \\ $$$$\mathrm{such}\:\mathrm{a}\:\mathrm{way}\:\mathrm{that}\:\mathrm{all}\:\mathrm{the}\:\mathrm{girls}\:\mathrm{stand} \\ $$$$\mathrm{consecutively}\:\mathrm{in}\:\mathrm{the}\:\mathrm{queue}.\:\mathrm{Let}\:\mathrm{m}\:\mathrm{be} \\ $$$$\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{ways}\:\mathrm{in}\:\mathrm{which}\:\mathrm{5}\:\mathrm{boys} \\ $$$$\mathrm{and}\:\mathrm{5}\:\mathrm{girls}\:\mathrm{can}\:\mathrm{stand}\:\mathrm{in}\:\mathrm{a}\:\mathrm{queue}\:\mathrm{in}\:\mathrm{such} \\ $$$$\mathrm{a}\:\mathrm{way}\:\mathrm{that}\:\mathrm{exactly}\:\mathrm{four}\:\mathrm{girls}\:\mathrm{stand} \\ $$$$\mathrm{consecutively}\:\mathrm{in}\:\mathrm{the}\:\mathrm{queue}.\:\mathrm{Then}\:\mathrm{the} \\…
Question Number 153050 by DELETED last updated on 04/Sep/21 Answered by DELETED last updated on 04/Sep/21 $$\mathrm{M}\overset{+\mathrm{4}} {\mathrm{n}}\overset{−\mathrm{2}} {\mathrm{O}}_{\mathrm{2}} \rightarrow\Sigma\mathrm{biloks}=\mathrm{0}\: \\ $$$$\mathrm{Mn}+\left(−\mathrm{2}×\mathrm{2}\right)=\mathrm{0}\:\rightarrow\mathrm{Mn}−\mathrm{4}=\mathrm{0} \\ $$$$\mathrm{Mn}=+\mathrm{4}\: \\…
Question Number 87511 by M±th+et£s last updated on 04/Apr/20 Answered by TANMAY PANACEA. last updated on 04/Apr/20 $${t}={x}^{\mathrm{3}} \rightarrow\frac{{dt}}{\mathrm{3}}={x}^{\mathrm{2}} {dx} \\ $$$$\int_{{ln}\mathrm{3}} ^{{ln}\mathrm{4}} \frac{\mathrm{1}}{\mathrm{3}}×\frac{{sint}}{{sint}+{sin}\left({ln}\mathrm{12}−{t}\right)}{dt}\:={I} \\…
Question Number 87508 by M±th+et£s last updated on 04/Apr/20 Commented by M±th+et£s last updated on 04/Apr/20 $${ABCD}\:{is}\:{parallelogram} \\ $$$${find}\:{the}\:{area}\:{of}\:{the}\:{green}\:{triangle} \\ $$ Terms of Service Privacy…
Question Number 21973 by Joel577 last updated on 08/Oct/17 $$\Delta{ABC}\:\mathrm{with}\:\mathrm{sides}\:{a},\:{b},\:{c}\:\in\:\mathbb{Z}\:\mathrm{and}\:\angle{A}\:=\:\mathrm{3}\angle{B} \\ $$$$\mathrm{If}\:\mathrm{its}\:\mathrm{circumference}\:\mathrm{is}\:\mathrm{minimum},\:\mathrm{then} \\ $$$$\mathrm{find}\:{a},\:{b},\:{c} \\ $$ Commented by Rasheed.Sindhi last updated on 08/Oct/17 $$\mathrm{Let}\:\angle\mathrm{B}=\theta\Rightarrow\angle\mathrm{A}=\mathrm{3}\theta\:,\:\angle\mathrm{C}=\pi−\mathrm{4}\theta \\…
Question Number 153046 by Tawa11 last updated on 04/Sep/21 Commented by Tawa11 last updated on 04/Sep/21 $$\mathrm{If}\:\mathrm{real}\:\mathrm{numbers}\:\:\mathrm{x}\:\:\mathrm{and}\:\:\mathrm{y}\:\:\:\mathrm{satisfies}\:\mathrm{the}\:\mathrm{system}\:\mathrm{shown},\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\mathrm{x}^{\mathrm{3}} \:\:\:+\:\:\:\mathrm{y}^{\mathrm{3}} \\ $$ Answered by mr…
Question Number 153041 by nadovic last updated on 04/Sep/21 $$\mathrm{A}\:\mathrm{ball}\:\mathrm{is}\:\mathrm{thrown}\:\mathrm{vertically}\:\mathrm{upwards} \\ $$$$\mathrm{with}\:\mathrm{a}\:\mathrm{velocity}\:\mathrm{of}\:\mathrm{10}\:{ms}^{−\mathrm{1}} \:\mathrm{from}\:\mathrm{a}\:\mathrm{point} \\ $$$$\mathrm{75}{m}\:\mathrm{above}\:\mathrm{the}\:\mathrm{ground}.\:\mathrm{How}\:\mathrm{long}\:\mathrm{will} \\ $$$$\mathrm{it}\:\mathrm{take}\:\mathrm{the}\:\mathrm{ball}\:\mathrm{to}\:\mathrm{strike}\:\mathrm{the}\:\mathrm{ground}? \\ $$ Answered by mr W last updated…