Question Number 135472 by mr W last updated on 13/Mar/21 $${for}\:{x}+{y}+{z}=\mathrm{10}\:{with}\:{x},{y},{z}\in\mathbb{N} \\ $$$${find}\:\Sigma\frac{\mathrm{10}!}{{x}!{y}!{z}!} \\ $$ Answered by Ñï= last updated on 13/Mar/21 $$\Sigma\begin{pmatrix}{\:\:\:\mathrm{10}}\\{{x},{y},{z}}\end{pmatrix}=\left(\mathrm{1}+\mathrm{1}+\mathrm{1}\right)^{\mathrm{10}} =\mathrm{3}^{\mathrm{10}} \\…
Question Number 69939 by mr W last updated on 29/Sep/19 $${x},{y},{z}\:\in\:{Z}^{+} \\ $$$${find}\:{all}\:{solutions}\:{of}\:\boldsymbol{{xy}}=\left(\boldsymbol{{x}}+\boldsymbol{{y}}\right)\boldsymbol{{z}} \\ $$ Commented by Rasheed.Sindhi last updated on 29/Sep/19 $${k}\in\mathbb{Z}^{+} \:{in}\:{the}\:{following}. \\…
Question Number 4399 by alib last updated on 22/Jan/16 $${Solve}\:{for}\:{x} \\ $$$$ \\ $$$${x}^{\mathrm{2}\:{log}\:_{\mathrm{2}} \:{x}} =\mathrm{8} \\ $$ Commented by Rasheed Soomro last updated on…
Question Number 4397 by moussapk last updated on 20/Jan/16 $$\int\left(\frac{\mathrm{1}}{{sin}\left({x}\right)}{dx}\right. \\ $$ Answered by Yozzii last updated on 20/Jan/16 $${I}=\int\frac{\mathrm{1}}{{sinx}}{dx}=\int{cosecxdx} \\ $$$${I}=\int\frac{{cosecx}\left({cosecx}+{cotx}\right)}{{cosecx}+{cotx}}{dx} \\ $$$${I}=\int\frac{{cosec}^{\mathrm{2}} {x}+{cotxcosecx}}{{cosecx}+{cotx}}{dx}…
Question Number 135467 by benjo_mathlover last updated on 13/Mar/21 Answered by EDWIN88 last updated on 13/Mar/21 $$\begin{vmatrix}{\alpha\:\:\:\:\:\beta\:\:\:\:\:\:\gamma}\\{\beta\:\:\:\:\:\gamma\:\:\:\:\:\:\alpha}\\{\gamma\:\:\:\:\:\alpha\:\:\:\:\:\beta}\end{vmatrix}=\:\alpha\left(\beta\gamma−\alpha^{\mathrm{2}} \right)−\beta\left(\beta^{\mathrm{2}} −\alpha\gamma\right)+\gamma\left(\alpha\beta−\gamma^{\mathrm{2}} \right) \\ $$$$=\alpha\beta\gamma−\alpha^{\mathrm{3}} −\beta^{\mathrm{3}} +\alpha\beta\gamma+\alpha\beta\gamma−\gamma^{\mathrm{3}} \\…
Question Number 4392 by Rasheed Soomro last updated on 18/Jan/16 $$\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\mathrm{n}}\mathrm{x}^{\frac{\mathrm{1}}{\mathrm{n}}} =?\:\:\:,\:\mathrm{x}>\mathrm{1} \\ $$ Commented by Yozzii last updated on 18/Jan/16 $$ \\…
Question Number 4390 by Rasheed Soomro last updated on 17/Jan/16 Answered by Rasheed Soomro last updated on 20/Jan/16 Commented by Rasheed Soomro last updated on…
Question Number 4389 by Yozzii last updated on 17/Jan/16 $$\int_{−\infty} ^{\infty} \int_{−\infty} ^{\infty} \sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }{exp}\left(\frac{−\mathrm{1}}{\mathrm{2}}\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)\right){dydx}=? \\ $$ Commented by prakash jain last…
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Question Number 4387 by Rasheed Soomro last updated on 17/Jan/16 Commented by Rasheed Soomro last updated on 17/Jan/16 $$\mathrm{In}\:\mathrm{the}\:\mathrm{trapezium}\:\mathrm{m}\angle\mathrm{A}=\mathrm{m}\angle\mathrm{B}=\frac{\pi}{\mathrm{2}}\:\mathrm{rad}. \\ $$$$\mathrm{m}\overline {\mathrm{AB}}=\mathrm{m}\overline {\mathrm{AD}}=\mathrm{x}\:\mathrm{units}\:\mathrm{and}\:\mathrm{m}\overline {\mathrm{BC}}=\mathrm{2x}\:\mathrm{units}. \\…