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Question Number 81647 by john santu last updated on 14/Feb/20 $$\mathrm{how}\:\mathrm{to}\:\mathrm{prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{number}\: \\ $$$$\mathrm{is}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{3},\:\mathrm{then}\:\mathrm{the}\:\mathrm{number} \\ $$$$\mathrm{of}\:\mathrm{numbers}\:\mathrm{is}\:\mathrm{a}\:\mathrm{multiple}\:\mathrm{of}\:\mathrm{3} \\ $$ Commented by mr W last updated on 14/Feb/20…
Question Number 147183 by mathdanisur last updated on 18/Jul/21 $${prove}\:{that} \\ $$$$\boldsymbol{{e}}^{\sqrt{\mathrm{2}}\:+\:\sqrt{\mathrm{3}}} \:>\:\frac{\mathrm{13}\:+\:\mathrm{2}\sqrt{\mathrm{6}}}{\mathrm{2}} \\ $$ Answered by mindispower last updated on 18/Jul/21 $$\Leftrightarrow{e}^{\sqrt{\mathrm{2}}+\sqrt{\mathrm{3}}} >\mathrm{1}+\mathrm{3}+\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{5}+\mathrm{2}\sqrt{\mathrm{6}}\right)\left({E}\right) \\…
Question Number 147169 by mathdanisur last updated on 18/Jul/21 $$\underset{{x}\rightarrow\mathrm{0}} {{lim}}\left(\frac{\mathrm{3}^{\boldsymbol{{x}}} \:+\:\mathrm{5}^{\boldsymbol{{x}}} \:+\:\mathrm{6}^{\boldsymbol{{x}}} }{\mathrm{3}}\right)^{\frac{\mathrm{1}}{\boldsymbol{{x}}}} =\:? \\ $$ Commented by gsk2684 last updated on 18/Jul/21 $$\underset{{x}\rightarrow\mathrm{0}}…
Question Number 147146 by mathdanisur last updated on 18/Jul/21 Answered by mr W last updated on 18/Jul/21 $${h}=\frac{\mathrm{2}{S}}{{a}}=\frac{\mathrm{2}×\mathrm{12}}{\mathrm{4}}=\mathrm{6}\:{sm} \\ $$$${V}=\mathrm{2}\pi×\mathrm{12}×\frac{\mathrm{6}}{\mathrm{3}}=\mathrm{48}\pi\:{sm}^{\mathrm{3}} \\ $$ Commented by mathdanisur…
Question Number 147137 by mathdanisur last updated on 18/Jul/21 Answered by bramlexs22 last updated on 18/Jul/21 $$\mathrm{AB}\:=\:\mathrm{DC} \\ $$$$\Rightarrow\begin{pmatrix}{\:\:−\mathrm{4}}\\{\mathrm{m}−\mathrm{7}}\\{\:\:\:\:\:\mathrm{16}}\end{pmatrix}\:=\:\begin{pmatrix}{\mathrm{3}−\mathrm{n}}\\{−\mathrm{10}}\\{\mathrm{p}−\mathrm{10}}\end{pmatrix} \\ $$$$\:\blacktriangle\begin{cases}{\mathrm{n}=\mathrm{7}}\\{\mathrm{m}=−\mathrm{3}}\\{\mathrm{p}=\mathrm{26}}\end{cases}\:\:\Rightarrow\mathrm{m}+\mathrm{n}+\mathrm{p}\:=\:\mathrm{30} \\ $$ Commented by…
Question Number 81598 by zainal tanjung last updated on 03/Mar/20 $$\mathrm{fog}\left(\mathrm{x}\right)=\mathrm{8x}+\mathrm{3} \\ $$$$\mathrm{g}\left(\mathrm{x}\right)=\mathrm{2x}−\mathrm{1} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)=…..? \\ $$$$ \\ $$$$\mathrm{gof}\left(\mathrm{x}\right)=\mathrm{6x}+\mathrm{1} \\ $$$$\mathrm{g}\left(\mathrm{x}\right)=\mathrm{5x}+\mathrm{1} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)=…..? \\ $$$$…
Question Number 81596 by zainal tanjung last updated on 14/Feb/20 $$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{3x}+\mathrm{1}\:,\:\:\mathrm{g}\left(\mathrm{x}\right)=\mathrm{2x}+\mathrm{3} \\ $$$$\left.\mathrm{a}\right).\:\mathrm{fog}\left(\mathrm{x}\right)=…. \\ $$$$\left.\mathrm{b}\right).\:\mathrm{gof}\left(\mathrm{x}\right)=…. \\ $$ Commented by Tony Lin last updated on 14/Feb/20…
Question Number 81597 by zainal tanjung last updated on 14/Feb/20 $$\mathrm{fog}\left(\mathrm{x}\right)=\mathrm{5x}+\mathrm{6} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{2x}+\mathrm{1} \\ $$$$\mathrm{g}\left(\mathrm{x}\right)=…..? \\ $$ Commented by Tony Lin last updated on 14/Feb/20…
Question Number 147134 by mathdanisur last updated on 18/Jul/21 $$\sqrt{\mathrm{2}{sin}\left({x}\right)−\mathrm{1}}\:\centerdot\:{sin}\left({x}\right)\:>\:\mathrm{0} \\ $$ Commented by hknkrc46 last updated on 18/Jul/21 $$\blacktriangleright\:\mathrm{2sin}\:\boldsymbol{{x}}\:−\:\mathrm{1}\:>\:\mathrm{0}\:\:\wedge\:\mathrm{sin}\:\boldsymbol{{x}}\:>\:\mathrm{0} \\ $$$$\Rightarrow\:\mathrm{sin}\:\boldsymbol{{x}}\:>\:\frac{\mathrm{1}}{\mathrm{2}}\:\wedge\:\mathrm{sin}\:\boldsymbol{{x}}\:>\:\mathrm{0}\:\equiv\:\mathrm{sin}\:\boldsymbol{{x}}\:>\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\blacktriangleright\:\frac{\boldsymbol{\pi}}{\mathrm{6}}\:<\:\boldsymbol{{x}}\:<\:\frac{\mathrm{5}\boldsymbol{\pi}}{\mathrm{6}}\:\: \\…