Question Number 199753 by sonukgindia last updated on 08/Nov/23 Answered by MM42 last updated on 09/Nov/23 $${let}\:\::\:\:{f}={xsinx}+{cosx}\:\:\&\:\:{g}={xcosx}+{sinx} \\ $$$${f}={g}\:\:\overset{\mathrm{0}\leqslant{x}\leqslant\mathrm{1}} {\Rightarrow}\:{x}=\mathrm{1}\:,\frac{\pi}{\mathrm{4}} \\ $$$$\Rightarrow{s}=\mid\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \left({f}−{g}\right){dx}\mid+\mid\int_{\frac{\pi}{\mathrm{4}}} ^{\mathrm{1}}…
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Question Number 199723 by cortano12 last updated on 08/Nov/23 Answered by AST last updated on 08/Nov/23 $${Suppose}\:{ABCD}\:{is}\:{a}\:{square} \\ $$$${Through}\:{P},{let}\:{the}\:{line}\:{parallel}\:{to}\:{BC}\:{meet}\:{AB} \\ $$$${at}\:{F};{then}\:{PF}=\mathrm{8}\Rightarrow\frac{{sin}\left(\mathrm{2}\alpha\right)}{\mathrm{1}}=\frac{\mathrm{4}}{\mathrm{5}} \\ $$$$\Rightarrow{cos}\left(\mathrm{2}\alpha\right)=\frac{\mathrm{3}}{\mathrm{5}}=\frac{{AF}}{\mathrm{10}}\Rightarrow{AF}=\mathrm{6}\Rightarrow{PC}=\mathrm{2} \\ $$…
Question Number 199718 by cortano12 last updated on 08/Nov/23 $$\:\begin{cases}{\mathrm{cos}\:\mathrm{x}+\mathrm{cos}\:\mathrm{y}=\frac{\mathrm{1}}{\mathrm{2}}}\\{\mathrm{sin}\:\mathrm{x}+\mathrm{sin}\:\mathrm{y}=\frac{\mathrm{1}}{\mathrm{4}}}\\{\mathrm{sin}\:\mathrm{2x}\:+\:\mathrm{sin}\:\mathrm{2y}=−\frac{\mathrm{27}}{\mathrm{20}}}\end{cases} \\ $$$$\:\:\:\mathrm{sin}\:\left(\mathrm{x}+\mathrm{y}\right)\:=\:… \\ $$ Answered by Sutrisno last updated on 08/Nov/23 $$\left({cosx}+{cosy}\right)\left({sinx}+{siny}\right)=\frac{\mathrm{1}}{\mathrm{8}} \\ $$$${cosxsinx}+{cosxsiny}+{cosysinx}+{cosysiny}=\frac{\mathrm{1}}{\mathrm{8}} \\…
Question Number 199719 by sonukgindia last updated on 08/Nov/23 Answered by witcher3 last updated on 08/Nov/23 $$\mathrm{I}_{\mathrm{a}} =\mathrm{I}_{\mathrm{b}} \\ $$$$\mathrm{I}_{\mathrm{a}} =\int_{\mathrm{0}} ^{\pi} \mathrm{e}^{\mathrm{sin}\left(\mathrm{x}\right)} \mathrm{cos}\left(\mathrm{cos}\left(\mathrm{x}\right)\right)\mathrm{dx}+\int_{\pi} ^{\mathrm{2}\pi}…
Question Number 199714 by dimentri last updated on 08/Nov/23 $$\:{Statement}\: \\ $$$$\:{Does}\:{the}\:{number}\:{of}\:{data}\:{have} \\ $$$$\:{to}\:{be}\:{more}\:{than}\:\mathrm{100}\:{in}\:{order}\: \\ $$$$\:{to}\:{have}\:{a}\:{percentile}\:{value}\:? \\ $$ Commented by mr W last updated on…
Question Number 199672 by Mingma last updated on 07/Nov/23 Answered by mr W last updated on 07/Nov/23 Commented by mr W last updated on 07/Nov/23…
Question Number 199705 by jlewis last updated on 11/Nov/23 $$\mathrm{Calculate}\:\mathrm{the}\:\mathrm{first}\:\mathrm{order}\:\mathrm{energy}\:\mathrm{correction}\: \\ $$$$\mathrm{for}\:\mathrm{the}\:\mathrm{one}\:\mathrm{dimentional}\:\mathrm{non}-\mathrm{degenerate} \\ $$$$\mathrm{an}\:\mathrm{harmonic}\:\mathrm{oscillator}\:\mathrm{whose}\:\mathrm{harmiltonian} \\ $$$$\mathrm{id}\:\mathrm{written}\:\mathrm{as}; \\ $$$$\hat {\mathrm{H}}=−\frac{\mathrm{h}^{\mathrm{2}} }{\mathrm{2}{m}}\:\frac{\mathrm{d}^{\mathrm{2}} }{\mathrm{dx}^{\mathrm{2}} }\:+\frac{\mathrm{1}}{\mathrm{2}}\mathrm{kx}^{\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{5}}\Upsilon\mathrm{x}^{\mathrm{3}} \:+\frac{\mathrm{1}}{\mathrm{12}}\beta\mathrm{x}^{\mathrm{4}} \\…
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Question Number 199671 by Mingma last updated on 07/Nov/23 Answered by mr W last updated on 07/Nov/23 $${a}_{\mathrm{1}} =\mathrm{3},\:{a}_{\mathrm{2}} =\mathrm{9}\:\Rightarrow{a}_{\mathrm{0}} =−\mathrm{1} \\ $$$${a}_{{n}} =\frac{{a}_{{n}−\mathrm{1}} +{a}_{{n}+\mathrm{1}}…