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Question Number 202170 by sonukgindia last updated on 22/Dec/23 Answered by AST last updated on 22/Dec/23 $$\mathrm{112}={a}\mathrm{2}^{{m}} \Rightarrow{a}\mathrm{2}^{{m}−\mathrm{4}} =\mathrm{7}\Rightarrow\mathrm{2}^{{m}−\mathrm{4}} =\mathrm{1}\Rightarrow{m}=\mathrm{4};{a}=\mathrm{7} \\ $$$$\mathrm{11392}={b}\mathrm{2}^{{n}} =\mathrm{2}^{\mathrm{7}} ×\mathrm{89}\Rightarrow{n}=\mathrm{7};{b}=\mathrm{89} \\…

Question Number 202153 by sonukgindia last updated on 22/Dec/23 Answered by witcher3 last updated on 22/Dec/23 $$\mathrm{ln}\left(\mathrm{x}\right)\mathrm{y}'+\frac{\mathrm{y}}{\mathrm{x}}=\left(\mathrm{ln}\left(\mathrm{x}\right)\right)\mathrm{y}'+\left(\mathrm{ln}\left(\mathrm{x}\right)\right)'\mathrm{y} \\ $$$$=\frac{\mathrm{d}}{\mathrm{dx}}\left(\mathrm{ln}\left(\mathrm{x}\right)\mathrm{y}\right) \\ $$$$\Leftrightarrow\begin{cases}{\frac{\mathrm{d}}{\mathrm{dx}}\left(\mathrm{y}.\left(\mathrm{ln}\left(\mathrm{x}\right)\right)=\mathrm{x}^{\mathrm{2}} \mathrm{sin}\left(\mathrm{x}\right)\right.}\\{\mathrm{y}\left(\pi\right)=\frac{\pi^{\mathrm{2}} }{\mathrm{ln}\left(\pi\right)}}\end{cases} \\ $$$$\Rightarrow\int_{\pi}…

Question Number 202143 by otchereabdullai@gmail.com last updated on 21/Dec/23 $$\:{find}\:{x}\:{in}\:{the}\:{interval}\:\:\mathrm{0}°<{x}<\mathrm{360}°\:{if} \\ $$$$\:\:{f}\left({x}\right)=\:\mathrm{6}{sinx}\:{is}\:−\mathrm{12} \\ $$ Commented by otchereabdullai@gmail.com last updated on 22/Dec/23 $${answer}\:{in}\:{the}\:{book}\:{is}\:\mathrm{210}°\:{and}\:\mathrm{330}°\: \\ $$$${but}\:{i}\:{dont}\:{know}\:{how}\:\:{he}\:{come}\:{about}\: \\…

Question Number 202100 by sonukgindia last updated on 20/Dec/23 Answered by mr W last updated on 21/Dec/23 $${f}'={g} \\ $$$${f}''={g}'={f} \\ $$$${f}''−{f}=\mathrm{0} \\ $$$${r}^{\mathrm{2}} −\mathrm{1}=\mathrm{0}\:\Rightarrow{r}=\pm\mathrm{1}…

Question Number 202093 by sonukgindia last updated on 20/Dec/23 Commented by a.lgnaoui last updated on 22/Dec/23 Commented by a.lgnaoui last updated on 22/Dec/23 $$\Delta\mathrm{AMN}\:\:\measuredangle\:\mathrm{MNA}=\frac{\mathrm{3}\pi}{\mathrm{4}}−\alpha \\…