Question Number 1132 by 123456 last updated on 24/Jun/15 $$\mathrm{let}\:\mathrm{S}=\left\{\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{5}\right\},\:\mathrm{if}\:\mathrm{A},\mathrm{B},\mathrm{C}\:\mathrm{is}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{A}\cap\mathrm{B}\cap\mathrm{C}=\varnothing \\ $$$$\mathrm{A}\cap\mathrm{B}\neq\varnothing \\ $$$$\mathrm{A}\cap\mathrm{C}\neq\varnothing \\ $$$$\mathrm{how}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{be}\:\mathrm{choose}\:\mathrm{A},\mathrm{B}\:\mathrm{and} \\ $$$$\mathrm{C} \\ $$ Commented by Faaiz…
Question Number 132201 by SOMEDAVONG last updated on 12/Feb/21 $$\mathrm{A}=\underset{{x}\rightarrow\frac{\pi}{\mathrm{2}}} {\mathrm{lim}}\frac{\mathrm{sin}^{\mathrm{50}} \mathrm{x}+\mathrm{5sin}^{\mathrm{30}} \mathrm{x}−\mathrm{6}}{\mathrm{cos}^{\mathrm{20}} \mathrm{x}+\mathrm{cos}^{\mathrm{40}} \mathrm{2x}−\mathrm{1}} \\ $$ Answered by bemath last updated on 12/Feb/21 Answered…
Question Number 66667 by naka3546 last updated on 18/Aug/19 Commented by naka3546 last updated on 18/Aug/19 $$\frac{\left[{PBQ}\right]}{\left[{PQCA}\right]}\:\:=\:\:? \\ $$ Commented by MJS last updated on…
Question Number 1130 by 123456 last updated on 22/Jun/15 $${f}:\mathbb{R}\rightarrow\mathbb{R} \\ $$$${f}\left({xy}\right)+{f}\left({x}+{y}\right)={f}\left({x}\right){f}\left({y}\right)+{f}\left({x}\right)+{f}\left({y}\right) \\ $$$${f}\left(−\mathrm{1}\right)=? \\ $$$${f}\left(\mathrm{0}\right)=? \\ $$$${f}\left(+\mathrm{1}\right)=? \\ $$ Answered by prakash jain last…
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Question Number 1125 by 123456 last updated on 18/Jun/15 $${f}:\mathbb{R}\rightarrow\mathbb{R} \\ $$$${g}:\mathbb{R}\rightarrow\mathbb{R} \\ $$$${f}\left({x}+{y}\right)={f}\left({x}\right)+{g}\left({y}\right) \\ $$$${g}\left({xy}\right)={f}\left({x}\right){g}\left({y}\right) \\ $$$${f}\left({x}\right)=? \\ $$$${g}\left({x}\right)=? \\ $$ Commented by 123456…
Question Number 132198 by benjo_mathlover last updated on 12/Feb/21 $$\mathrm{If}\:\begin{cases}{\mathrm{16}^{{a}+{b}} \:=\:\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}}\\{\mathrm{16}^{{b}+{c}} \:=\:\mathrm{2}}\\{\mathrm{16}^{{a}+{c}} \:=\:\mathrm{2}\sqrt{\mathrm{2}}}\end{cases} \\ $$$$\:\mathrm{then}\:\mathrm{c}\:=\:\_\_\: \\ $$ Answered by EDWIN88 last updated on 12/Feb/21 $$\mathrm{eq}\left(\mathrm{1}\right)\:\mathrm{16}^{\mathrm{2}\left(\mathrm{a}+\mathrm{b}\right)}…
Question Number 1124 by 123456 last updated on 17/Jun/15 $$\mathrm{lets}\:{f}:\left[\mathrm{0},\mathrm{1}\right]\rightarrow\mathbb{R}\:\mathrm{given}\:\mathrm{by} \\ $$$${f}\left({x}\right)=\begin{cases}{{x}}&{{x}\in\mathbb{Q}}\\{\mathrm{1}−{x}}&{{x}\notin\mathbb{Q}}\end{cases} \\ $$$$\mathrm{is}\:{f}\:\mathrm{continuos}\:\mathrm{at}\:{x}=\mathrm{1}/\mathrm{2}? \\ $$$$\mathrm{is}\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}{fdx}\:\mathrm{riemann}\:\mathrm{integrable}? \\ $$$$\mathrm{is}\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}{fdx}\:\mathrm{lebesgue}\:\mathrm{integable}? \\ $$ Commented…
Question Number 132192 by benjo_mathlover last updated on 12/Feb/21 $$\:\int\:\frac{\mathrm{dx}}{\mathrm{csc}\:\mathrm{x}\:+\:\mathrm{sec}\:\mathrm{x}} \\ $$ Answered by Dwaipayan Shikari last updated on 12/Feb/21 $$\int\frac{{sinx}\:{cosx}}{{sinx}+{cosx}}{dx} \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}}\int{sinx}+{cosx}−\frac{\mathrm{1}}{{sinx}+{cosx}}{dx} \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}}\left({sinx}−{cosx}\right)−\int\frac{{dt}}{\mathrm{1}−{t}^{\mathrm{2}}…
Question Number 132195 by aurpeyz last updated on 12/Feb/21 $${Aspherical}\:{satelite}\:{orbiting}\:{Earth}\:{is} \\ $$$${lighted}\:{on}\:{one}\:{side}\:{by}\:{the}\:{sun}\:{with}\:{intensity} \\ $$$$\mathrm{340}{W}/{m}^{\mathrm{2}} .\:{If}\:{the}\:{radius}\:{of}\:{the}\: \\ $$$${satelite}\:{is}\:\mathrm{1}{m}.\:{what}\:{power}\:{is}\: \\ $$$${incident}\:{upon}\:{it}? \\ $$ Answered by ajfour last…