Question Number 71868 by naka3546 last updated on 21/Oct/19 Commented by prakash jain last updated on 21/Oct/19 $${f}\left({n}\right)=\mathrm{0} \\ $$ Commented by mr W last…
Question Number 137398 by mohammad17 last updated on 02/Apr/21 Commented by mohammad17 last updated on 02/Apr/21 $${please}\:{sir}\:{help}\:{me} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 71819 by Maclaurin Stickker last updated on 20/Oct/19 $${There}\:{are}\:\mathrm{3}\:{tangent}\:{circumferences} \\ $$$${inscribed}\:{in}\:{an}\:{isosceles}\:{right}\:{triangle} \\ $$$${Two}\:{of}\:{these}\:{circumferences}\:{have} \\ $$$${radius}\:\boldsymbol{{R}}\:{and}\:{are}\:{tangent}\:{to}\:{the}\: \\ $$$${hypotenuse}\:{and}\:{to}\:{the}\:{two}\:{cathetus}. \\ $$$${The}\:{smaller}\:{circumference}\:{has}\: \\ $$$${radius}\:\boldsymbol{{r}}\:{and}\:{is}\:{tangent}\:{to}\:{the}\:{two} \\ $$$${cathetus}.\:{How}\:{can}\:{I}\:{find}\:{the}\:{radius}…
Question Number 137349 by mohammad17 last updated on 01/Apr/21 Commented by mohammad17 last updated on 01/Apr/21 $${help}\:{me}\:{sir}\:{please}\:? \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 137340 by SLVR last updated on 01/Apr/21 Answered by SLVR last updated on 02/Apr/21 $${kindly}\:{provide}\:{the}\:{solution}\:{please} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 6257 by 314159 last updated on 20/Jun/16 $${Given}\:{that}\:{a}\:{and}\:{b}\:{are}\:{positive}\:{real}\:{number} \\ $$$${such}\:{that}\:{b}<\mathrm{4}{a}+\mathrm{1},{show}\:{that}\:\frac{\mathrm{2}{a}+{b}}{\mathrm{4}{a}+\mathrm{1}}<\sqrt{\mathrm{4}{a}^{\mathrm{2}} +{b}}\:. \\ $$ Answered by Yozzii last updated on 20/Jun/16 $$\frac{\mathrm{2}{a}+{b}}{\mathrm{4}{a}+\mathrm{1}}<\sqrt{\mathrm{4}{a}^{\mathrm{2}} +{b}}\:\:\:\:\:\:{a},{b}>\mathrm{0} \\…
Question Number 137321 by mathocean1 last updated on 01/Apr/21 $${H}\left({x}\right)=\frac{\mathrm{8}}{{x}−\mathrm{2}}\:{and}\:{f}\left({x}\right)=\frac{{x}^{\mathrm{2}} +\mathrm{3}{x}+\mathrm{6}}{\mathrm{2}{x}−\mathrm{4}} \\ $$$$\left.\mathrm{1}\right){Calculate}\:{the}\:{surface}\:{V}_{\boldsymbol{{n}}} \:{of} \\ $$$${area}\:{limited}\:{by}\:{the}\:{the}\:{line} \\ $$$${x}=\mathrm{6};\:{x}=\mathrm{6}+\boldsymbol{{n}}\:\left({n}\in\mathbb{N}^{\ast} \right)\:{and}\:{the} \\ $$$${curve}\:{of}\:{H}\left({x}\right)\:{and}\:{f}\left({x}\right)\:{in}\:{function} \\ $$$${of}\:\boldsymbol{{n}}. \\ $$$$\left.\mathrm{2}\right)\:{Knowing}\:{that}\:\mathrm{1}^{\mathrm{2}}…
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Question Number 71759 by naka3546 last updated on 19/Oct/19 Commented by Prithwish sen last updated on 19/Oct/19 $$\boldsymbol{\mathrm{x}}=\:\frac{\mathrm{1}}{\mathrm{3}}.\frac{\mathrm{1}}{\mathrm{3}}.\frac{\mathrm{2}}{\mathrm{4}}.\frac{\mathrm{3}}{\mathrm{5}}………\frac{\mathrm{998}}{\mathrm{1000}}.\frac{\mathrm{999}}{\mathrm{1001}}\:=\:\frac{\mathrm{2}×\mathrm{1001001}}{\mathrm{3×1000}×\mathrm{1001}}\approx\mathrm{0}.\mathrm{67} \\ $$$$\therefore\:\mathrm{100x}\:\approx\:\mathrm{67} \\ $$$$\boldsymbol{\mathrm{By}}\:\boldsymbol{\mathrm{considering}} \\ $$$$\frac{\boldsymbol{\mathrm{n}}^{\mathrm{3}} −\mathrm{1}}{\boldsymbol{\mathrm{n}}^{\mathrm{3}}…
Question Number 137279 by Ñï= last updated on 31/Mar/21 $$\int\frac{{dx}}{\mathrm{sin}\:\left({a}+{x}\right)\mathrm{cos}\:\left({b}+{x}\right)}=? \\ $$ Answered by Ar Brandon last updated on 31/Mar/21 $$\mathcal{I}=\int\frac{\mathrm{dx}}{\mathrm{sin}\left(\mathrm{a}+\mathrm{x}\right)\mathrm{cos}\left(\mathrm{b}+\mathrm{x}\right)} \\ $$$$\:\:\:=\frac{\mathrm{1}}{\mathrm{cos}\left(\mathrm{a}−\mathrm{b}\right)}\int\frac{\mathrm{cos}\left(\mathrm{a}−\mathrm{b}\right)}{\mathrm{sin}\left(\mathrm{a}+\mathrm{x}\right)\mathrm{cos}\left(\mathrm{b}+\mathrm{x}\right)}\mathrm{dx} \\ $$$$\:\:\:=\frac{\mathrm{1}}{\mathrm{cos}\left(\mathrm{a}−\mathrm{b}\right)}\int\frac{\mathrm{cos}\left[\left(\mathrm{x}+\mathrm{a}\right)−\left(\mathrm{x}+\mathrm{b}\right)\right]}{\mathrm{sin}\left(\mathrm{a}+\mathrm{x}\right)\mathrm{cos}\left(\mathrm{b}+\mathrm{x}\right)}\mathrm{dx}…