Question Number 204645 by cortano12 last updated on 24/Feb/24 $$\:\:\mathrm{Let}\:{f}\::\:\left[\:\bar {\mathrm{1}}\infty\right)\:\rightarrow\mathrm{R}\:\mathrm{be}\:\mathrm{a}\:\mathrm{differentiable}\: \\ $$$$\:\mathrm{function}\:\mathrm{such}\:\mathrm{that}\:{f}\left(\mathrm{1}\right)=\:\frac{\mathrm{1}}{\mathrm{3}}\:\mathrm{and}\: \\ $$$$\:\mathrm{3}\underset{\mathrm{1}} {\overset{\mathrm{x}} {\int}}\:{f}\left({t}\right)\:{dt}\:=\:{x}\:{f}\left({x}\right)−\frac{{x}^{\mathrm{3}} }{\mathrm{3}}\:,\mathrm{x}\in\left[\mathrm{1},\infty\right)\: \\ $$$$\:\mathrm{find}\:\mathrm{tbe}\:\mathrm{value}\:\mathrm{of}\:{f}\left({e}\right)\: \\ $$ Commented by universe…
Question Number 204663 by LuisTony last updated on 24/Feb/24 Answered by TonyCWX08 last updated on 25/Feb/24 $$\mathrm{sin}\left(\mathrm{52}°\mathrm{20}'\right)=\frac{{h}}{\mathrm{1200}} \\ $$$${h}=\mathrm{1200sin}\left(\mathrm{52}°\mathrm{20}'\right) \\ $$$${h}\approx\mathrm{949}.\mathrm{9}{m} \\ $$ Terms of…
Question Number 204647 by Engr_Jidda last updated on 24/Feb/24 Answered by Rasheed.Sindhi last updated on 24/Feb/24 $$\left(\frac{{x}}{\mathrm{2}}\right)^{\frac{{x}}{\mathrm{2}}−\mathrm{1}} =\mathrm{3}^{\mathrm{2}} \\ $$$$\Leftarrow\frac{{x}}{\mathrm{2}}=\mathrm{3}\:\wedge\:\frac{{x}}{\mathrm{2}}−\mathrm{1}=\mathrm{2}\Rightarrow{x}=\mathrm{6} \\ $$ Commented by Engr_Jidda…
Question Number 204640 by liuxinnan last updated on 24/Feb/24 $${f}\left({x}\right)=\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+{x}}}+\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+{a}}}+\sqrt{\frac{{ax}}{{ax}+\mathrm{8}}} \\ $$$${a}>\mathrm{0}\:{x}>\mathrm{0} \\ $$$${prove}\:\mathrm{1}<{f}\left({x}\right)<\mathrm{2} \\ $$ Answered by lepuissantcedricjunior last updated on 26/Feb/24 $$\boldsymbol{{x}}>\mathrm{0}\:\boldsymbol{{a}}>\mathrm{0} \\…
Question Number 204657 by es last updated on 24/Feb/24 $${Consider}\:{point}\:{A}\:{inside}\:{a}\:{triangle} \\ $$$${with}\:{sides}\:\mathrm{3},\mathrm{4}\:{and}\:\mathrm{5}.\:{if}\:{d}\:\:{is}\:{the}\:{sum} \\ $$$$\:{of}\:{the}\:{distances}\:\:{of}\:{this}\:{point}\:{from} \\ $$$${the}\:{sides}.{what}\:{is}\:{the}\:{smallest} \\ $$$${value}\:{of}\:{d}? \\ $$$$ \\ $$ Answered by mr…
Question Number 204658 by hardmath last updated on 24/Feb/24 $$\mathrm{If}\:\:\:\mathrm{a}\:=\:\sqrt[{\mathrm{3}}]{\mathrm{9}}\:−\:\sqrt[{\mathrm{3}}]{\mathrm{3}}\:+\:\mathrm{1} \\ $$$$\mathrm{Find}\:\:\:\left(\frac{\mathrm{4}\:−\:\mathrm{a}}{\mathrm{a}}\right)^{\mathrm{6}} =\:? \\ $$ Answered by Rasheed.Sindhi last updated on 24/Feb/24 $$\:\mathrm{a}\:=\:\sqrt[{\mathrm{3}}]{\mathrm{9}}\:−\:\sqrt[{\mathrm{3}}]{\mathrm{3}}\:+\:\mathrm{1};\:\left(\frac{\mathrm{4}\:−\:\mathrm{a}}{\mathrm{a}}\right)^{\mathrm{6}} =\:? \\…
Question Number 204642 by BaliramKumar last updated on 24/Feb/24 $$\mathrm{If}\:\:\frac{\mathrm{1}}{\mathrm{1}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{2}} }+\:\frac{\mathrm{1}}{\mathrm{4}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{5}^{\mathrm{2}} }\:+\:………….\:=\:\frac{\pi^{\mathrm{2}} }{\mathrm{6}} \\ $$$$\mathrm{then}\:\:\frac{\mathrm{1}}{\mathrm{1}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{5}^{\mathrm{2}} }\:+\:………….\:=\:? \\ $$$$ \\ $$…
Question Number 204632 by mr W last updated on 23/Feb/24 Answered by witcher3 last updated on 23/Feb/24 $$\left.\mathrm{x}>\mathrm{1};\mathrm{x}=\frac{\mathrm{1}}{\mathrm{sin}\left(\mathrm{t}\right)};\mathrm{t}\in\right]\mathrm{0},\frac{\pi}{\mathrm{2}}\left[\right. \\ $$$$\Rightarrow\frac{\mathrm{1}}{\mathrm{sin}\left(\mathrm{t}\right)}+\frac{\frac{\mathrm{1}}{\mathrm{sin}\left(\mathrm{t}\right)}}{\:\sqrt{\frac{\mathrm{1}}{\mathrm{sin}^{\mathrm{2}} \left(\mathrm{t}\right)}−\mathrm{1}}}=\frac{\mathrm{1}}{\mathrm{sin}\left(\mathrm{t}\right)}+\frac{\mathrm{1}}{\mathrm{cos}\left(\mathrm{t}\right)}=\mathrm{2}\sqrt{\mathrm{2}} \\ $$$$\mathrm{cauchy}\:\mathrm{shwartz}\:\left(\left(\frac{\mathrm{1}}{\:\sqrt{\mathrm{sin}\left(\mathrm{t}\right)}}\right)^{\mathrm{2}} +\left(\frac{\mathrm{1}}{\:\sqrt{\mathrm{cos}\left(\mathrm{t}\right)}}\right)^{\mathrm{2}} \right)\left(\left(\sqrt{\mathrm{sin}\left(\mathrm{t}\right)}\right)^{\mathrm{2}}…
Question Number 204603 by liuxinnan last updated on 23/Feb/24 Commented by TonyCWX08 last updated on 23/Feb/24 $${Please}\:{use}\:{the}\:{latex}\:{form}. \\ $$$${I}\:{don}'{t}\:{understand}\:{what}\:{you}'{re}\:{trying}\:{to}\:{express}… \\ $$ Commented by liuxinnan last…
Question Number 204628 by MM42 last updated on 23/Feb/24 $$ \\ $$ Answered by MM42 last updated on 23/Feb/24 Answered by A5T last updated on…