Question Number 201172 by Calculusboy last updated on 01/Dec/23 Answered by Sutrisno last updated on 01/Dec/23 $$=\int\frac{\mathrm{2}{e}^{\mathrm{2}{x}} −{e}^{{x}} }{\:\sqrt{\mathrm{3}\left({e}^{\mathrm{2}{x}} −\mathrm{2}{e}^{{x}} −\frac{\mathrm{1}}{\mathrm{3}}\right)}}{dx} \\ $$$$=\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}}\int\frac{\mathrm{2}{e}^{\mathrm{2}{x}} −{e}^{{x}} }{\:\sqrt{\left({e}^{{x}}…
Question Number 201200 by Calculusboy last updated on 01/Dec/23 Commented by Rasheed.Sindhi last updated on 02/Dec/23 $$\left(\:\left({x}−\mathrm{1}\right)^{{x}−\mathrm{1}} \:\right)^{\mathrm{1}/\mathrm{3}} =\left({x}−\mathrm{1}\right)^{\left({x}−\mathrm{1}\right)^{\mathrm{1}/\mathrm{3}} } \\ $$ Commented by Rasheed.Sindhi…
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Question Number 201166 by mnjuly1970 last updated on 01/Dec/23 Answered by mr W last updated on 01/Dec/23 $$\frac{{ah}}{\mathrm{2}}=\mathrm{4} \\ $$$$\Rightarrow{h}=\frac{\mathrm{2}×\mathrm{4}}{\:\sqrt{\mathrm{2}}}=\mathrm{4}\sqrt{\mathrm{2}} \\ $$$${h}×\mathrm{cot}\:{B}+{h}×\mathrm{cot}\:{C}={a} \\ $$$$\Rightarrow\mathrm{cot}\:{B}+\mathrm{cot}\:{C}=\frac{{a}}{{h}}=\frac{\sqrt{\mathrm{2}}}{\mathrm{4}\sqrt{\mathrm{2}}}=\frac{\mathrm{1}}{\mathrm{4}} \\…
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Question Number 201192 by Euclid last updated on 01/Dec/23 Answered by Calculusboy last updated on 01/Dec/23 $$\boldsymbol{{Solution}}:\:\boldsymbol{{Apply}}\:\boldsymbol{{I}\mathrm{n}}\:\boldsymbol{\mathrm{to}}\:\boldsymbol{{both}}\:\boldsymbol{{sides}} \\ $$$$\boldsymbol{{In}}\:\boldsymbol{{x}}^{\boldsymbol{{x}}^{\mathrm{4}} } =\boldsymbol{{In}}\mathrm{64} \\ $$$$\boldsymbol{{x}}^{\mathrm{4}} \boldsymbol{{Inx}}=\boldsymbol{{In}}\mathrm{64} \\…
Question Number 201162 by Calculusboy last updated on 01/Dec/23 Answered by Frix last updated on 01/Dec/23 $${x}={y}={z}=\mathrm{1} \\ $$ Answered by Rasheed.Sindhi last updated on…
Question Number 201190 by Calculusboy last updated on 01/Dec/23 Answered by mr W last updated on 01/Dec/23 $$\frac{\mathrm{1}}{\left(−{x}\right)^{\left(−{x}\right)} }=\frac{\mathrm{1}}{\mathrm{1000}} \\ $$$$\left(−{x}\right)^{\left(−{x}\right)} =\mathrm{1000} \\ $$$$\Rightarrow{x}=−\frac{\mathrm{4ln}\:\mathrm{10}}{{W}\left(\mathrm{4ln}\:\mathrm{10}\right)}\approx−\mathrm{5}.\mathrm{438583} \\…