Question Number 167036 by HongKing last updated on 05/Mar/22 $$\mathrm{Evaluate}: \\ $$$$\Omega\:=\:\int\:\mathrm{620}\:\left(\mathrm{x}^{\mathrm{2017}} \:-\:\mathrm{69}\:\mathrm{x}^{\mathrm{126}} \right)^{\mathrm{15}} \:\mathrm{dx} \\ $$ Answered by mr W last updated on 05/Mar/22…
Question Number 167037 by HongKing last updated on 05/Mar/22 $$\mathrm{If}\:\:\:\:\:\mathrm{I}\:=\:\int_{-\mathrm{1}} ^{\:-\mathrm{8}} \:\frac{\mathrm{1}}{\mathrm{x}^{\frac{\mathrm{2}}{\mathrm{3}}} \:−\:\mathrm{x}}\:\mathrm{dx} \\ $$$$\mathrm{then}\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:\:\mathrm{81}\boldsymbol{\mathrm{e}}^{\boldsymbol{\mathrm{I}}} \:? \\ $$ Answered by ghakhan last updated on 05/Mar/22…
Question Number 101498 by bemath last updated on 03/Jul/20 $$\mathrm{If}\:\mathrm{4}^{\mathrm{x}} \:=\:\mathrm{5}^{\mathrm{y}} \:=\:\mathrm{20}^{\mathrm{z}} \:. \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{z}\:\mathrm{in}\:\mathrm{term}\:\mathrm{of}\:\mathrm{x}\:\mathrm{and}\:\mathrm{y}. \\ $$$$\bigstar\spadesuit \\ $$ Commented by bobhans last updated on…
Question Number 167038 by HongKing last updated on 05/Mar/22 $$\mathrm{Find}\:\mathrm{all}\:\mathrm{values}\:\mathrm{of}\:\:\mathrm{a}\:\:\mathrm{and}\:\:\mathrm{b} \\ $$$$\mathrm{such}\:\mathrm{that}\:\:\mathrm{y}=\mathrm{0},\mathrm{5x}^{\mathrm{2}} +\left(\mathrm{a}+\mathrm{b}\right)\mathrm{x}+\mathrm{ab} \\ $$$$\mathrm{is}\:\mathrm{always}\:\mathrm{positive} \\ $$ Commented by mr W last updated on 05/Mar/22…
Question Number 101489 by bramlex last updated on 03/Jul/20 Answered by john santu last updated on 03/Jul/20 $$\mathrm{let}\:\sqrt[{\mathrm{3}\:}]{\mathrm{x}−\mathrm{3}}\:=\:{h}\:\mathrm{and}\:\sqrt[{\mathrm{3}\:\:}]{\mathrm{x}+\mathrm{4}}\:=\:{t} \\ $$$$\Leftrightarrow\:\mathrm{5}{ht}\:+\:\mathrm{4}{h}^{\mathrm{2}} \:+\:{t}^{\mathrm{2}} \:=\:\mathrm{0} \\ $$$$\left(\mathrm{4}{h}+{t}\right)\left({h}+{t}\right)\:=\:\mathrm{0} \\…
Question Number 167027 by Tawa11 last updated on 04/Mar/22 Commented by cortano1 last updated on 05/Mar/22 $$\:\begin{cases}{\mathrm{log}\:_{\mathrm{8}} \left(\mathrm{p}+\mathrm{2}\right)+\mathrm{log}\:_{\mathrm{8}} \mathrm{q}=\mathrm{r}−\frac{\mathrm{1}}{\mathrm{3}}}\\{\mathrm{log}\:_{\mathrm{8}} \left(\mathrm{p}−\mathrm{2}\right)−\mathrm{log}\:_{\mathrm{8}} \mathrm{q}=\mathrm{2r}+\mathrm{1}}\end{cases} \\ $$$$\Rightarrow\left(\mathrm{1}\right)+\left(\mathrm{2}\right)\equiv\:\mathrm{log}\:_{\mathrm{8}} \left(\mathrm{p}^{\mathrm{2}} −\mathrm{4}\right)=\mathrm{3r}+\frac{\mathrm{2}}{\mathrm{3}}…
Question Number 167010 by mnjuly1970 last updated on 04/Mar/22 Answered by LowLevelLump last updated on 04/Mar/22 $${h}\left({x}\right)={f}\left({x}−\mathrm{ln}\:\mathrm{2}\right)+{a} \\ $$$$\mathrm{ln}\:\left(\frac{\mathrm{1}}{\mathrm{2}}{e}^{\mathrm{2}{x}} −{e}^{{x}} +\mathrm{1}\right)=\mathrm{ln}\:\left({e}^{\mathrm{2}\left({x}−\mathrm{ln}\:\mathrm{2}\right)} −{e}^{{x}−\mathrm{ln}\:\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{2}}\right)+{a} \\ $$$$\mathrm{ln}\:\left(\frac{\mathrm{1}}{\mathrm{2}}{e}^{\mathrm{2}{x}}…
Question Number 167007 by mathlove last updated on 04/Mar/22 Answered by Rasheed.Sindhi last updated on 04/Mar/22 $$\mathrm{3}^{\frac{{x}+\mathrm{6}}{\mathrm{3}}} +\mathrm{9}.\mathrm{2}.\mathrm{3}^{\frac{{x}}{\mathrm{3}}} =\mathrm{9} \\ $$$$\mathrm{3}^{\mathrm{2}} .\mathrm{3}^{\frac{{x}}{\mathrm{3}}} +\mathrm{9}.\mathrm{2}.\mathrm{3}^{\frac{{x}}{\mathrm{3}}} =\mathrm{9} \\…
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Question Number 101425 by pete last updated on 02/Jul/20 $$\mathrm{A}\:\mathrm{student}\:\mathrm{wrote}\:\mathrm{three}\:\mathrm{papers}\:\mathrm{in}\:\mathrm{mathematics} \\ $$$$\mathrm{examinations}.\:\mathrm{Her}\:\mathrm{marks}\:\mathrm{for}\:\mathrm{the}\:\mathrm{two}\:\mathrm{of} \\ $$$$\mathrm{papers}\:\mathrm{were}\:\mathrm{77}\:\mathrm{and}\:\mathrm{72}\:\mathrm{respectively}.\:\mathrm{To} \\ $$$$\mathrm{obtain}\:\mathrm{grade}\:\mathrm{A},\:\mathrm{an}\:\mathrm{average}\:\mathrm{of}\:\mathrm{not}\:\mathrm{less} \\ $$$$\mathrm{than}\:\mathrm{75}\:\mathrm{marks}\:\mathrm{is}\:\mathrm{required}\:\mathrm{for}\:\mathrm{the}\:\mathrm{three} \\ $$$$\mathrm{papers}.\:\mathrm{How}\:\mathrm{many}\:\mathrm{marks}\:\mathrm{must}\:\mathrm{she}\:\mathrm{get} \\ $$$$\mathrm{in}\:\mathrm{the}\:\mathrm{third}\:\mathrm{paper}\:\mathrm{to}\:\mathrm{get}\:\mathrm{grade}\:\mathrm{A}? \\ $$ Commented…