Question Number 70162 by TawaTawa last updated on 01/Oct/19 Answered by mind is power last updated on 01/Oct/19 $$\Rightarrow\mathrm{1}=\left({a}+{b}\right)\left(\frac{{sin}^{\mathrm{4}} \left(\theta\right)}{{a}}+\frac{{cos}^{\mathrm{4}} \left(\theta\right)}{{b}}\right)…{S} \\ $$$$\Rightarrow\frac{{b}}{{a}}{Sin}^{\mathrm{4}} \left(\theta\right)+\frac{{a}}{{b}}{cos}^{\mathrm{4}} \left(\theta\right)+{cos}^{\mathrm{4}}…
Question Number 70163 by A8;15: last updated on 01/Oct/19 Answered by ajfour last updated on 01/Oct/19 Commented by ajfour last updated on 02/Oct/19 $$\:\:\frac{{AB}}{{BC}}={Q}=\:\frac{{x}+{y}}{\:\sqrt{{y}^{\mathrm{2}} +{z}^{\mathrm{2}}…
Question Number 4625 by Yozzis last updated on 14/Feb/16 $${Solve}\:{the}\:{following}\:{system}\:{of}\:{differential}\: \\ $$$${equations}\:{for}\:{functions}\:{x}\left({t}\right)\:{and}\:{y}\left({t}\right). \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{m}\frac{{d}^{\mathrm{2}} {x}}{{dt}^{\mathrm{2}} }=\frac{{kx}}{\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)^{\mathrm{2}} } \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{m}\frac{{d}^{\mathrm{2}} {y}}{{dt}^{\mathrm{2}} }=\frac{{ky}}{\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)^{\mathrm{2}}…
Question Number 70161 by TawaTawa last updated on 01/Oct/19 Answered by mind is power last updated on 01/Oct/19 $${let}\:{a}=\sqrt{\sqrt{\mathrm{5}}+\mathrm{2}}\:\:{b}=\sqrt{\sqrt{\mathrm{5}}−\mathrm{2}} \\ $$$${a}^{\mathrm{2}} +{b}^{\mathrm{2}} =\mathrm{2}\sqrt{\mathrm{5}} \\ $$$${ab}=\mathrm{1}…
Question Number 4624 by sanusihammed last updated on 14/Feb/16 Answered by Yozzii last updated on 15/Feb/16 $$\left(\mathrm{12}\right)\:{The}\:{equation}\:{of}\:{motion}\:{of}\:{the}\:{particle} \\ $$$${is}\:{given}\:{as} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\frac{{d}}{{ds}}\left(\frac{{v}^{\mathrm{2}} }{\mathrm{2}}\right)=−{g}−{kv}^{\mathrm{2}} . \\ $$$${v}\:{is}\:{a}\:{function}\:{of}\:{s}\:{as}\:{s}\:{and}\:{v}\:{are}\:…
Question Number 135693 by liberty last updated on 15/Mar/21 $$\Omega\:=\:\int\:\frac{{x}−\mathrm{1}}{\left({x}−\mathrm{2}\right)\left({x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{2}\right)^{\mathrm{2}} }\:{dx}\: \\ $$ Answered by MJS_new last updated on 15/Mar/21 $$\int\frac{{x}−\mathrm{1}}{\left({x}−\mathrm{2}\right)\left({x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{2}\right)^{\mathrm{2}} }{dx}= \\…
Question Number 135692 by liberty last updated on 15/Mar/21 $$ \\ $$Solve the system of congruences 2x≡1(mod5) 3x≡2(mod7) 4x≡1(mod11) Answered by floor(10²Eta[1]) last updated on…
Question Number 70159 by ajfour last updated on 01/Oct/19 Commented by ajfour last updated on 01/Oct/19 $${Under}\:{balanced}\:{conditions},\:{find} \\ $$$$\theta\:.\:{All}\:{surfaces}\:{frictionless}. \\ $$ Answered by mr W…
Question Number 4622 by sanusihammed last updated on 14/Feb/16 $${what}\:{is}\:{the}\:{value}\:{of}\:{x}\:{in}\: \\ $$$$\mathrm{2}{x}\:+\:\mathrm{5}\:=\:\mathrm{10} \\ $$ Answered by sanusihammed last updated on 14/Feb/16 $${collect}\:{the}\:{like}\:{terms} \\ $$$$\mathrm{2}{x}\:=\:\mathrm{10}\:−\:\mathrm{5} \\…
Question Number 135695 by liberty last updated on 15/Mar/21 $${What}\:{is}\:{the}\:{equation}\:{of} \\ $$$${ellipse}\:{with}\:{center}\:\left(\mathrm{1},−\mathrm{2}\right)\: \\ $$$${excentricity}\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}}\:,\:{passing} \\ $$$${through}\:\left(\mathrm{2},\:\frac{\mathrm{2}\sqrt{\mathrm{2}}−\mathrm{2}}{\mathrm{3}}\right)\: \\ $$ Answered by mr W last updated on…