Question Number 4889 by 123456 last updated on 19/Mar/16 $${f}\left({x}\right)={x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{3} \\ $$$${g}\left({x}\right)=\mathrm{2}{x}^{\mathrm{2}} +\mathrm{7}{x}−\mathrm{1} \\ $$$${h}\left({x}\right)={x}^{\mathrm{2}} +\mathrm{10}{x}−\mathrm{7} \\ $$$${f}\left({g}\left({h}\left({x}\right)\right)\right)=\mathrm{0},{x}=? \\ $$ Answered by Yozzii last…
Question Number 70425 by ahmadshahhimat775@gmail.com last updated on 04/Oct/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 135957 by mathmax by abdo last updated on 17/Mar/21 $$\left.\mathrm{1}\right)\:\mathrm{find}\:\int\:\:\frac{\mathrm{dx}}{\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} \left(\mathrm{x}−\mathrm{3}\right)^{\mathrm{4}} } \\ $$$$\left.\mathrm{2}\right)\:\mathrm{deduce}\:\mathrm{the}\:\mathrm{decomposition}\:\mathrm{of}\:\mathrm{F}\left(\mathrm{x}\right)=\frac{\mathrm{1}}{\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} \left(\mathrm{x}−\mathrm{3}\right)^{\mathrm{4}} } \\ $$ Answered by Dwaipayan Shikari last…
Question Number 70423 by ajfour last updated on 04/Oct/19 Commented by ajfour last updated on 04/Oct/19 $${Within}\:{a}\:{hollow}\:{sphere},\:{mass} \\ $$$${M}_{\mathrm{0}} \:,\:{radius}\:{R},\:{rests}\:{two}\:{smaller} \\ $$$${spheres}\:{masses},\:{M}\:{and}\:{m},\:{radii} \\ $$$${b},\:{a}\:,\:{respectively}.\:{Find}\:{equilibrium} \\…
Question Number 135958 by benjo_mathlover last updated on 17/Mar/21 $${Find}\:{the}\:{value}\:{of}\:{n}\:{such}\:{that} \\ $$$$\:\frac{{n}\left({n}+\mathrm{1}\right)}{\mathrm{2}}\:=\:{k}\:\left({mod}\:\mathrm{10}\right)\:{for} \\ $$$${n}\:{is}\:{integer}\:{number}\: \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 70418 by oyemi kemewari last updated on 04/Oct/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 4883 by 123456 last updated on 19/Mar/16 $${f}\left({x}\right)=\begin{cases}{{x}}&{{x}<\mathrm{0}}\\{{xf}\left({x}−\mathrm{1}\right)+\mathrm{1}}&{{x}\geqslant\mathrm{0}}\end{cases} \\ $$$$\underset{−\mathrm{5}} {\overset{\mathrm{5}} {\int}}{f}\left({x}\right){dx}=? \\ $$ Commented by prakash jain last updated on 19/Mar/16 $$\mathrm{0}\leqslant{x}<\mathrm{1}\:\Rightarrow\left({x}−\mathrm{1}\right)<\mathrm{0}…
Question Number 135952 by Dwaipayan Shikari last updated on 17/Mar/21 Commented by Dwaipayan Shikari last updated on 17/Mar/21 $${It}\:{isArchimedes}'{s}\:{Nothing}\:{Grinder}.\:{We}\:{can}\:{move}\:{this}\:{back} \\ $$$${and}\:{forth}\:{and}\:{sideways}\:.{Prove}\:{that}\:{the}\:{tip}\:{on}\:{various} \\ $$$${positions}\:{on}\:{that}\:{hand}\:{of}\:{the}\:{wodden}\:{grinder}\:{creates}\: \\ $$$${various}\:{shapes}\:{of}\:{ellipses}…
Question Number 70417 by aliesam last updated on 04/Oct/19 Answered by MJS last updated on 04/Oct/19 $$\mathrm{just}\:\mathrm{use}\:\mathrm{formulas} \\ $$$$\mathrm{sphere}:\:{V}=\frac{\mathrm{4}\pi}{\mathrm{3}}{r}^{\mathrm{3}} ;\:{S}=\mathrm{4}\pi{r}^{\mathrm{2}} \\ $$$$\mathrm{cylinder}:\:{V}=\pi{r}^{\mathrm{2}} {h} \\ $$$$\:\:\:\:\:{S}=\mathrm{2}×\mathrm{circle}+\mathrm{lateral}=\mathrm{2}\pi{r}^{\mathrm{2}}…
Question Number 135944 by mnjuly1970 last updated on 17/Mar/21 $$\:\:\:\:\:\:\:\:\:\:\:…..{nice}\:\:{calculus}… \\ $$$$\:\:\:{prove}\:{that}: \\ $$$$\:\:\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(\sqrt{\mathrm{2}}\:−\mathrm{1}\right)^{{n}} }{\left(\mathrm{2}{n}+\mathrm{1}\right)^{\mathrm{2}} }=\frac{\pi^{\mathrm{2}} }{\mathrm{8}}−\frac{\mathrm{1}}{\mathrm{2}}{ln}^{\mathrm{2}} \left(\mathrm{1}+\sqrt{\mathrm{2}}\:\right)… \\ $$$$\:\:\:\:…………….\checkmark \\ $$ Answered…