Question Number 169497 by Huy last updated on 01/May/22 $$\mathrm{Determine}\:\mathrm{all}\:\mathrm{functions}\:{f}:\mathbb{R}\rightarrow\mathbb{R}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{a}{f}\left(\mathrm{b}\right)+\mathrm{b}{f}\left(\mathrm{a}\right)=\left(\mathrm{a}+\mathrm{b}\right){f}\left(\sqrt{\mathrm{ab}}\right)\:\forall\mathrm{ab}>\mathrm{0} \\ $$ Answered by aleks041103 last updated on 02/May/22 $${let}\:{a}={x},\:{b}={x}+\mathrm{2}{dx} \\ $$$$\sqrt{{ab}}=\sqrt{{x}\left({x}+\mathrm{2}{dx}\right)}={x}\left(\mathrm{1}+\mathrm{2}\frac{{dx}}{{x}}\right)^{\mathrm{1}/\mathrm{2}} ={x}+{dx}…
Question Number 169466 by BHOOPENDRA last updated on 30/Apr/22 Answered by mr W last updated on 01/May/22 $${deflection}\:{at}\:{center}\:{of}\:{simple}\:{beam}\: \\ $$$${under}\:{uniform}\:{load}\:{is} \\ $$$$\delta=\frac{\mathrm{5}{wl}^{\mathrm{4}} }{\mathrm{384}{EI}} \\ $$$$\Rightarrow{EI}=\frac{\mathrm{5}{wl}^{\mathrm{4}}…
Question Number 169436 by mathocean1 last updated on 30/Apr/22 Commented by mathocean1 last updated on 30/Apr/22 $${with}\:\mathrm{0}<\alpha<\mathrm{1} \\ $$ Answered by Mathspace last updated on…
Question Number 169438 by mokys last updated on 30/Apr/22 Commented by mkam last updated on 30/Apr/22 $$????? \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 103894 by Study last updated on 18/Jul/20 $$\frac{{d}}{{d}\left(\frac{{d}}{{dx}}{sinx}\right)}\centerdot{sinx}=? \\ $$ Answered by 1549442205 last updated on 18/Jul/20 $$\mathrm{Denote}\:\mathrm{I}=\frac{\mathrm{d}}{\mathrm{d}\frac{\mathrm{d}}{\mathrm{dx}}\mathrm{sinx}}\mathrm{sinx}=\frac{\mathrm{d}}{\mathrm{dcosx}}\mathrm{sinx}. \\ $$$$\mathrm{Putting}\:\:\mathrm{cos}\:\mathrm{x}=\mathrm{t}.\mathrm{Then} \\ $$$$\mathrm{we}\:\mathrm{have}\:\mathrm{I}=\frac{\mathrm{d}}{\mathrm{dt}}\sqrt{\mathrm{1}−\mathrm{t}^{\mathrm{2}} }=\frac{−\mathrm{t}}{\:\sqrt{\mathrm{1}−\mathrm{t}^{\mathrm{2}}…
Question Number 103879 by abony1303 last updated on 18/Jul/20 Commented by abony1303 last updated on 18/Jul/20 $$\mathrm{Please},\:\mathrm{help} \\ $$ Commented by myear last updated on…
Question Number 103869 by mohammad17 last updated on 17/Jul/20 $${by}\:{using}\:{the}\:{Frobinus}\:{method}\:{solve}\:{the}\:{deffrentional}\:{equation} \\ $$$${xy}^{''} −\mathrm{2}{pxy}^{'} +\left({p}\left({p}+\mathrm{1}\right)+{b}^{\mathrm{2}} {x}^{\mathrm{2}} \right){y}=\mathrm{0} \\ $$$$ \\ $$$${and}\:{give}\:{for}\:{example}\:{for}\:{this}\:{when}\:{p}=\mathrm{1},{b}=\mathrm{2}\: \\ $$$${such}\:{that}\:\left({p},{b}\right)\:{be}\:{areal}\:{number}\:? \\ $$ Terms…
Question Number 169397 by mokys last updated on 29/Apr/22 Answered by mr W last updated on 30/Apr/22 $${AC}\leqslant{AB}+{BC} \\ $$$$\sqrt{\left({x}+{y}\right)^{\mathrm{2}} +\left(\mathrm{3}+\mathrm{1}\right)^{\mathrm{2}} }\leqslant\sqrt{{x}^{\mathrm{2}} +\mathrm{3}^{\mathrm{2}} }+\sqrt{{y}^{\mathrm{2}} +\mathrm{1}^{\mathrm{2}}…
Question Number 38286 by mondodotto@gmail.com last updated on 23/Jun/18 $$\left(\boldsymbol{{i}}\right)\:\mathrm{given}\:\mathrm{the}\:\mathrm{function}\:\boldsymbol{{f}}\left(\boldsymbol{{t}}\right)=\boldsymbol{\mathrm{e}}^{\boldsymbol{{t}}} \:\:\boldsymbol{\mathrm{and}}\:\boldsymbol{{g}}\left(\boldsymbol{{t}}\right)=\boldsymbol{\mathrm{ln}{t}} \\ $$$$\boldsymbol{\mathrm{show}}\:\boldsymbol{\mathrm{that}}\:\boldsymbol{{f}}\circ\boldsymbol{{g}}\left(\boldsymbol{{t}}\right)=\boldsymbol{{g}}\circ\boldsymbol{{f}}\left(\boldsymbol{{t}}\right) \\ $$$$\left(\boldsymbol{{ii}}\right)\mathrm{if}\:\boldsymbol{{f}}\left(\boldsymbol{{t}}\right)=\boldsymbol{{at}}\:,\:\boldsymbol{{g}}\left(\boldsymbol{{t}}\right)=\boldsymbol{{bt}}^{\mathrm{2}} +\mathrm{3} \\ $$$$\left(\boldsymbol{{fog}}\right)\left(\mathrm{2}\right)=\mathrm{35}\:\boldsymbol{\mathrm{and}}\:\left(\boldsymbol{{fog}}\right)\left(\mathrm{3}\right)=\mathrm{75} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\boldsymbol{{a}}\:\mathrm{and}\:\boldsymbol{{b}} \\ $$ Commented by math…
Question Number 169340 by leicianocosta last updated on 29/Apr/22 Terms of Service Privacy Policy Contact: info@tinkutara.com