Question Number 155488 by SANOGO last updated on 01/Oct/21 Answered by puissant last updated on 01/Oct/21 $${Q}=\int_{{a}} ^{{b}} \frac{{f}\left({x}\right)}{{f}\left({x}\right)+{f}\left({a}+{b}−{x}\right)}{dx}\:\:\left(\mathrm{1}\right) \\ $$$${u}={a}+{b}−{x}\:\rightarrow\:{x}={a}+{b}−{u}\:\rightarrow\:{dx}=−{du} \\ $$$$\Rightarrow\:{Q}=\int_{{b}} ^{{a}} \frac{{f}\left({a}+{b}−{u}\right)}{{f}\left({a}+{b}−{u}\right)+{f}\left({u}\right)}\left(−{du}\right)…
Question Number 89955 by swizanjere@gmail.com last updated on 20/Apr/20 $$\mathrm{9}^{\mathrm{x}+\mathrm{1}} \nmid\mathrm{28}\left(\mathrm{3}^{\mathrm{x}} \right)+\mathrm{3}=\mathrm{0} \\ $$ Commented by jagoll last updated on 20/Apr/20 $$\mathrm{what}\:\mathrm{do}\:\mathrm{you}\:\mathrm{mean}\:\mathrm{notation} \\ $$$$\nmid\:? \\…
Question Number 89953 by swizanjere@gmail.com last updated on 20/Apr/20 $$\mathrm{solvethefollowingequation} \\ $$$$\mathrm{5}^{\mathrm{2x}+\mathrm{y}} =\mathrm{625and2}^{\mathrm{4x}\nmid\mathrm{2y}} =\frac{\mathrm{1}}{\mathrm{6}} \\ $$ Commented by jagoll last updated on 20/Apr/20 $$\mathrm{2x}+\mathrm{y}\:=\:\mathrm{4} \\…
Question Number 89950 by student work last updated on 20/Apr/20 Commented by Tony Lin last updated on 20/Apr/20 $${a}=\mathrm{10},{b}=\mathrm{6},{c}=\sqrt{\mathrm{10}^{\mathrm{2}} −\mathrm{6}^{\mathrm{2}} }=\mathrm{8} \\ $$$${AA}^{'} =\mathrm{2}{a}=\mathrm{20} \\…
Question Number 89951 by john santu last updated on 20/Apr/20 $$\mathrm{log}\:_{\mathrm{2}} \:\left(\mathrm{sin}\:\left({x}+\frac{\mathrm{5}\pi}{\mathrm{12}}\right)\right)\:+\:\mathrm{log}\:_{\mathrm{2}} \left(\mathrm{sin}\:\left({x}+\frac{\pi}{\mathrm{12}}\right)\right)=−\mathrm{1} \\ $$ Commented by jagoll last updated on 20/Apr/20 $$\Rightarrow\mathrm{sin}\:\left(\mathrm{x}+\frac{\mathrm{5}\pi}{\mathrm{12}}\right)\:\mathrm{sin}\:\left(\mathrm{x}+\frac{\pi}{\mathrm{12}}\right)\:=\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\mathrm{cos}\:\left(\frac{\mathrm{4}\pi}{\mathrm{12}}\right)−\mathrm{cos}\:\left(\mathrm{2x}+\frac{\mathrm{6}\pi}{\mathrm{12}}\right)\:=\:\mathrm{1}…
Question Number 155481 by mathdanisur last updated on 01/Oct/21 $$\mathrm{if}\:\:\mathrm{a};\mathrm{b};\mathrm{c}\in\left[\mathrm{1};\infty\right) \\ $$$$\mathrm{then}\:\mathrm{prove}\:\mathrm{that}\:\:\mathrm{a}^{\frac{\mathrm{1}}{\boldsymbol{\mathrm{a}}}} \:;\:\mathrm{b}^{\frac{\mathrm{1}}{\boldsymbol{\mathrm{b}}}} \:;\:\mathrm{c}^{\frac{\mathrm{1}}{\boldsymbol{\mathrm{c}}}} \\ $$$$\mathrm{are}\:\mathrm{the}\:\mathrm{sides}\:\mathrm{of}\:\mathrm{a}\:\mathrm{triangle}. \\ $$ Answered by mr W last updated on…
Question Number 89946 by jagoll last updated on 20/Apr/20 $$\int\underset{−\frac{\pi}{\mathrm{2}}} {\overset{\frac{\pi}{\mathrm{2}}} {\:}}\:\frac{\mathrm{dx}}{\mathrm{1}+\mathrm{e}^{\mathrm{sin}\:\mathrm{x}} } \\ $$ Answered by john santu last updated on 20/Apr/20 $${I}\:=\:\underset{\frac{−\pi}{\mathrm{2}}} {\overset{\frac{\pi}{\mathrm{2}}}…
Question Number 24411 by A1B1C1D1 last updated on 17/Nov/17 Answered by mrW1 last updated on 17/Nov/17 $$\int_{\frac{\pi}{\mathrm{2}}} ^{\:\mathrm{0}} \int_{\mathrm{2}} ^{\:\mathrm{0}} {r}^{\mathrm{4}} \mathrm{cos}\:\left(\mathrm{2}\theta\right)\:{dr}\:{d}\theta \\ $$$$=\int_{\frac{\pi}{\mathrm{2}}} ^{\:\mathrm{0}}…
Question Number 155480 by mathdanisur last updated on 01/Oct/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{positive}\:\mathrm{integer}\:\mathrm{solution} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{equation}: \\ $$$$\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{y}^{\mathrm{3}} \:=\:\mathrm{911}\left(\mathrm{xy}\:+\:\mathrm{49}\right) \\ $$ Answered by Rasheed.Sindhi last updated on 01/Oct/21…
Question Number 155477 by alcohol last updated on 01/Oct/21 Answered by puissant last updated on 01/Oct/21 $$\left.{a}\right)\:\forall{n}\in\mathbb{N},\:{f}\left({n}\right)={nf}\left(\mathrm{1}\right) \\ $$$$ \\ $$$${f}\left(\mathrm{2}\right)={f}\left(\mathrm{1}+\mathrm{1}\right)={f}\left(\mathrm{1}\right)+{f}\left(\mathrm{1}\right)=\mathrm{2}{f}\left(\mathrm{1}\right) \\ $$$${alors},\:{on}\:{montre}\:{par}\:{recurrence}\:{que} \\ $$$${f}\left({n}\right)={nf}\left(\mathrm{1}\right)..…