Question Number 125080 by ZiYangLee last updated on 08/Dec/20 $$\mathrm{How}\:\mathrm{many}\:\mathrm{positive}\:\mathrm{integers}\:\mathrm{less}\:\mathrm{than} \\ $$$$\mathrm{200}\:\mathrm{have}\:\mathrm{exaxtly}\:\mathrm{6}\:\mathrm{positive}\:\mathrm{factors}? \\ $$ Answered by mr W last updated on 08/Dec/20 $${say}\:{such}\:{a}\:{number}\:{is} \\ $$$${n}={p}^{{a}}…
Question Number 59516 by naka3546 last updated on 11/May/19 Answered by tanmay last updated on 11/May/19 $$\bigtriangleup=\frac{\mathrm{1}}{\mathrm{2}}{r}\left({a}+{b}+{c}\right)=\sqrt{{s}\left({s}−{a}\right)\left({s}−{b}\right)\left({s}−{c}\right)\:} \\ $$$${s}=\frac{{a}+{b}+{c}}{\mathrm{2}}=\frac{\mathrm{2}{x}+\mathrm{2}{y}+\mathrm{2}{z}}{\mathrm{2}}={x}+{y}+{z} \\ $$$$ \\ $$$$\frac{{x}+{y}+{z}}{\mathrm{3}}\geqslant\left({xyz}\right)^{\frac{\mathrm{1}}{\mathrm{3}}} \\ $$$${x}+{y}+{z}\geqslant\mathrm{3}\left({xyz}\right)^{\frac{\mathrm{1}}{\mathrm{3}}}…
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Question Number 190583 by 073 last updated on 06/Apr/23 Answered by mr W last updated on 06/Apr/23 $${f}\left(\mathrm{2}\right)=\mathrm{2}\sqrt{\mathrm{3}} \\ $$$${f}'\left(\mathrm{2}\right)=\mathrm{tan}\:\mathrm{60}°=\sqrt{\mathrm{3}} \\ $$$${g}'\left({x}\right)=\mathrm{2}{xf}\left({x}\right)+{x}^{\mathrm{2}} {f}'\left({x}\right) \\ $$$${g}'\left(\mathrm{2}\right)=\mathrm{2}×\mathrm{2}{f}\left(\mathrm{2}\right)+\mathrm{2}^{\mathrm{2}}…
Question Number 190580 by 073 last updated on 06/Apr/23 Answered by a.lgnaoui last updated on 06/Apr/23 $$\left(\mathrm{11}+\mathrm{2}×\mathrm{4}\right)−\mathrm{1}=\mathrm{18} \\ $$$$\Rightarrow{Answwer}=\left(\mathrm{E}\right) \\ $$ Terms of Service Privacy…
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Question Number 190579 by 073 last updated on 06/Apr/23 Answered by a.lgnaoui last updated on 06/Apr/23 $$\mathrm{2}\left({a}+{b}+{c}\right)=\mathrm{2}{x}^{\mathrm{2}} +\mathrm{8}{x}+\mathrm{0} \\ $$$${a}+{b}+{c}={x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{0} \\ $$$${m}+{n}+{p}=\mathrm{1}+\mathrm{4}=\mathrm{5} \\ $$$${Answer}=\left(\boldsymbol{\mathrm{D}}\right)…
Question Number 190578 by 073 last updated on 06/Apr/23 Answered by a.lgnaoui last updated on 06/Apr/23 $${squart}:\:\:\:\:\mathrm{4}\:\:\:\:{cotes}\:\Rightarrow\overset{−} {\mathrm{3}},\overset{−} {\mathrm{5}},\overset{−} {\mathrm{7}} \\ $$$${triangle}\:\:\mathrm{3}\:\:\:{cotes}\:\Rightarrow\mathrm{3}:\:{yes}\left(\mathrm{1}\right) \\ $$$${polygone}\:\mathrm{5}\:\:\:{cotes}\Rightarrow\mathrm{5}:{yes}\left(\mathrm{1}\right) \\…
Question Number 190564 by Best1 last updated on 06/Apr/23 Answered by a.lgnaoui last updated on 06/Apr/23 $$\bullet\mathrm{1}\boldsymbol{{a}}\:\:\:\:{perimetere}\left(\boldsymbol{{p}}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\left[\:\left(\mathrm{2},\mathrm{8}×\mathrm{2}\right)+\mathrm{1},\mathrm{6}\right]+\frac{\mathrm{1},\mathrm{6}×\pi}{\mathrm{2}} \\ $$$$\:\:\:=\mathrm{7},\mathrm{1}+\frac{\mathrm{4}\pi}{\mathrm{5}}\Rightarrow\:\:\:\:\boldsymbol{{p}}=\mathrm{9},\mathrm{61}{m} \\ $$$$\:\bullet\mathrm{2}\boldsymbol{{a}}\:\:\:\:\boldsymbol{{A}}{rea}\: \\ $$$$\:=\left(\mathrm{2},\mathrm{8}×\mathrm{1},\mathrm{6}\:\right)\:\:+\pi\left(\mathrm{0},\mathrm{8}\right)^{\mathrm{2}}…
Question Number 125028 by ngahcedric last updated on 07/Dec/20 Answered by Dwaipayan Shikari last updated on 07/Dec/20 $$\int_{\mathrm{0}} ^{\mathrm{4}} {x}^{{n}} \left(\mathrm{16}−{x}^{\mathrm{2}} \right)^{\frac{\mathrm{1}}{\mathrm{2}}} {dx}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{x}=\mathrm{4}{t} \\ $$$$=\mathrm{4}\int_{\mathrm{0}}…