Question Number 72027 by mathmax by abdo last updated on 23/Oct/19 $${if}\:{a}+{b}+{c}\:=\mathrm{3}\:\:{and}\:{a}^{\mathrm{3}} \:+{b}^{\mathrm{3}} \:+{c}^{\mathrm{3}} =\mathrm{27}\:{find}\:{a}^{\mathrm{2}} \:+{b}^{\mathrm{2}} \:+{c}^{\mathrm{2}} \\ $$ Commented by Rasheed.Sindhi last updated on…
Question Number 137563 by liberty last updated on 04/Apr/21 $${let}\:\frac{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }{{x}^{\mathrm{2}} −{y}^{\mathrm{2}} }+\frac{{x}^{\mathrm{2}} −{y}^{\mathrm{2}} }{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }={k} \\ $$$${find}\:{the}\:{value}\:{of}\:\frac{{x}^{\mathrm{8}} +{y}^{\mathrm{8}} }{{x}^{\mathrm{8}} −{y}^{\mathrm{8}} }+\frac{{x}^{\mathrm{8}} −{y}^{\mathrm{8}}…
Question Number 72024 by mathmax by abdo last updated on 23/Oct/19 $${calculate}\:{lim}_{{n}\rightarrow+\infty} \:\:\:\int_{\mathrm{0}} ^{{n}} \left(\mathrm{1}−\frac{{x}}{{n}}\right)^{{n}} {ln}\left(\mathrm{1}+{x}\right){dx} \\ $$ Commented by mathmax by abdo last updated…
Question Number 72025 by mathmax by abdo last updated on 23/Oct/19 $${calculate}\:\:\int_{\mathrm{0}} ^{\infty} \:{e}^{−\alpha{x}} {ln}\left({x}\right){dx}\:\:{with}\:\alpha>\mathrm{0} \\ $$ Commented by mathmax by abdo last updated on…
Question Number 6488 by Rasheed Soomro last updated on 29/Jun/16 Commented by Rasheed Soomro last updated on 29/Jun/16 $${Centres}\:{of}\:{the}\:{arcs}\:\:{are}\:\mathrm{A},\mathrm{B}\:{and}\:\mathrm{C}. \\ $$$${Also}\:{determine}\:{the}\:{measures}\:{of}\:{the}\:{sides} \\ $$$${of}\:\bigtriangleup\mathrm{DFH}. \\ $$$${May}\:{be}\:{treated}\:{as}\:{separate}\:{question}\left(\:{labled}\right.…
Question Number 6487 by Temp last updated on 29/Jun/16 $$\mathrm{Prove}\:\mathrm{and}\:\mathrm{show}\:\mathrm{why}: \\ $$$$\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}{H}_{{k}} =\left({n}+\mathrm{1}\right)\left({H}_{{n}+\mathrm{1}} −\mathrm{1}\right) \\ $$$$\mathrm{Where}: \\ $$$${H}_{{k}} =\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+…+\frac{\mathrm{1}}{{k}} \\ $$ Commented by…
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Question Number 72023 by mathmax by abdo last updated on 23/Oct/19 $${find}\:{lim}_{{n}\rightarrow+\infty} \:\:\:\sum_{\mathrm{1}\leqslant{i}<{j}\leqslant{n}} \:\:\frac{\mathrm{1}}{\left({ij}\right)^{\mathrm{2}} } \\ $$ Commented by mathmax by abdo last updated on…
Question Number 137559 by liberty last updated on 04/Apr/21 $$ \\ $$What is the volume of tetrahedron ABCD, whose vertices have the coordinates A (2,…
Question Number 72020 by mathmax by abdo last updated on 23/Oct/19 $${calculate}\:\sum_{{k}=\mathrm{0}} ^{{n}} \:{C}_{{n}} ^{{k}} \:{cos}\left(\frac{{k}\pi}{\mathrm{2}{n}}\right) \\ $$ Commented by mathmax by abdo last updated…