Question Number 16919 by rustylee last updated on 28/Jun/17 $${ax}\mathrm{2}+{bx}+{c}=\mathrm{0} \\ $$ Answered by RasheedSoomro last updated on 28/Jun/17 $${ax}^{\mathrm{2}} +{bx}+{c}=\mathrm{0}\Rightarrow \\ $$$$\:\:\:\:\:\:\:\:\:\:\:{x}=\frac{−{b}\pm\sqrt{{b}^{\mathrm{2}} −\mathrm{4}{ac}}}{\mathrm{2}{a}} \\…
Question Number 16918 by rustylee last updated on 28/Jun/17 $$\mathrm{2}{x}\mathrm{2}+\mathrm{9}{x}=\mathrm{10} \\ $$ Answered by Joel577 last updated on 28/Jun/17 $$\mathrm{2}{x}^{\mathrm{2}} \:+\:\mathrm{9}{x}\:−\:\mathrm{10}\:=\:\mathrm{0} \\ $$$${x}_{\mathrm{1},\mathrm{2}} \:=\:\frac{−\mathrm{9}\:\pm\:\sqrt{\mathrm{81}\:+\:\mathrm{80}}}{\mathrm{4}} \\…
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Question Number 147762 by DomaPeti last updated on 23/Jul/21 $${how}\:{to}\:{minimalize}\:{t}? \\ $$$$\underset{{x}_{\mathrm{2}} } {\overset{{x}_{\mathrm{1}} } {\int}}\frac{\sqrt{\mathrm{1}+\left({y}\left({x}\right)'\right)^{\mathrm{2}} }}{\:\sqrt{{x}^{\mathrm{2}} +{y}\left({x}\right)^{\mathrm{2}} }\centerdot{c}_{\mathrm{1}} +{c}_{\mathrm{0}} }\Delta{x}={t} \\ $$$$ \\ $$…
Question Number 16547 by Sai dadon. last updated on 23/Jun/17 $${solve} \\ $$$${dy}/{dx}\:+\:{xy}={y}^{\mathrm{2}} {e}^{\mathrm{1}/\mathrm{2}{x}^{\mathrm{2}} } {logx} \\ $$ Commented by Sai dadon. last updated on…
Question Number 16546 by Sai dadon. last updated on 23/Jun/17 $${dv}/{dt}=−\left({kv}+{bt}\right)\:{where}\:{k}\:{and}\:{b}\:{are}\:{constants} \\ $$$${solve}\:{the}\:{equation}\:{of}\:{v}\:{given} \\ $$$${v}={u}\:{when}\:{t}=\mathrm{0} \\ $$ Answered by mrW1 last updated on 23/Jun/17 $$\frac{\mathrm{dv}}{\mathrm{dt}}+\mathrm{kv}=−\mathrm{bt}…
Question Number 16514 by Sai dadon. last updated on 23/Jun/17 $${Help}\:{plz} \\ $$$${Given}\:\mathrm{2}{d}^{\mathrm{2}} {x}/{dt}^{\mathrm{2}} +\mathrm{2}{dx}/{dt}+{x}={ksint} \\ $$$${where}\:{k}\:{is}\:{constant}\:{show}\:{that}\:{if}\:{x}={n} \\ $$$${and}\:{dx}/{dt}=\mathrm{0}\:{when}\:{t}=\mathrm{0}\:{then}\: \\ $$$$\left.{x}={e}^{−\mathrm{1}/\mathrm{2}{t}} \left\{\left({n}+\mathrm{2}/\mathrm{5}{k}\right){cos}\left({t}/\mathrm{2}\right)+\right)+\left({n}+\mathrm{4}/\mathrm{5}{k}\right){sin}\left({t}/\mathrm{2}\right)\right\} \\ $$$$−\mathrm{1}/\mathrm{5}{ksint}−\mathrm{2}/\mathrm{5}{kcost}. \\…
Question Number 16493 by Sai dadon. last updated on 23/Jun/17 $${Find}\:{L}\left\{{tcosh}\mathrm{2}{t}\right\} \\ $$ Commented by prakash jain last updated on 23/Jun/17 $$\int_{\mathrm{0}} ^{\infty} {t}\mathrm{cosh}\:\mathrm{2}{te}^{−{st}} {dt}…
Question Number 16492 by Sai dadon. last updated on 23/Jun/17 $${solve} \\ $$$${Mdc}/{dt}={P}+{km}−{Cm}\:{where}\:{M}.{P}.{m}\:{and} \\ $$$${k}\:{are}\:{constant} \\ $$$${solve}\:{the}\:{equation}\:{given}\:{C}={a}\:{when}\:{t}={o} \\ $$ Answered by mrW1 last updated on…