Question Number 53161 by peter frank last updated on 18/Jan/19 Answered by peter frank last updated on 18/Jan/19 $${from} \\ $$$${x}_{{n}+\mathrm{1}\:} =\frac{\mathrm{1}}{{r}}\left[\left({r}−\mathrm{1}\right){x}_{{n}} +{Ax}_{{n}\:} ^{\mathrm{1}−{r}} \right]…
Question Number 52506 by ajfour last updated on 09/Jan/19 Commented by ajfour last updated on 09/Jan/19 $${Find}\:{radii}\:{of}\:{both}\:{circles}\:{in}\:{terms} \\ $$$${of}\:{a}\:{and}\:{b}. \\ $$ Answered by mr W…
Question Number 117832 by snipers237 last updated on 13/Oct/20 $$\left.{Let}\:{a},{b}>\mathrm{0}\:\:{and}\:{x}\in\right]\mathrm{0};\frac{\pi}{\mathrm{2}}\left[\:\right. \\ $$$$\:\:{Prove}\:\:\:\left(\frac{{a}}{{sinx}}+\mathrm{1}\right)\left(\frac{{b}}{{cosx}}+\mathrm{1}\right)\geqslant\left(\mathrm{1}+\sqrt{\mathrm{2}{ab}}\right)^{\mathrm{2}} \\ $$$$ \\ $$ Answered by 1549442205PVT last updated on 14/Oct/20 $$\left.\mathrm{From}\:\mathrm{the}\:\mathrm{hypothesis}\:{a},{b}>\mathrm{0}\:\:{and}\:{x}\in\right]\mathrm{0};\frac{\pi}{\mathrm{2}}\left[\:\right. \\…
Question Number 117825 by snipers237 last updated on 13/Oct/20 $${Let}\:{ABC}\:{be}\:{a}\:{triangle}\:{such}\:{as}\: \\ $$$$\:\mathrm{2}{cosA}+\mathrm{3}{sinB}=\mathrm{4}\:{and}\:\:\mathrm{3}{cosB}+\mathrm{2}{sinA}=\mathrm{3} \\ $$$${Prove}\:{that}\:{the}\:{angle}\:{C}\:{is}\:{right}. \\ $$$$\: \\ $$ Answered by john santu last updated on…
Question Number 117739 by bemath last updated on 13/Oct/20 $$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{centre}\:\mathrm{of}\:\mathrm{the}\:\mathrm{circle} \\ $$$$\mathrm{with}\:\mathrm{radius}\:\mathrm{4}\sqrt{\mathrm{2}}\:\mathrm{that}\:\mathrm{can}\:\mathrm{be}\: \\ $$$$\mathrm{inscribed}\:\mathrm{in}\:\mathrm{the}\:\mathrm{parabola}\: \\ $$$$\mathrm{y}=\mathrm{x}^{\mathrm{2}} −\mathrm{16x}+\mathrm{128}? \\ $$ Answered by bobhans last updated on…
Question Number 52034 by somil last updated on 02/Jan/19 Commented by afachri last updated on 02/Jan/19 $$\mathrm{Number}\:\mathrm{of}\:\mathrm{discs}\:\mathrm{can}\:\mathrm{be}\:\mathrm{calculated}\:\mathrm{by} \\ $$$$\mathrm{dividing}\:\mathrm{area}\:\mathrm{of}\:\mathrm{sheet}\:\mathrm{and}\:\mathrm{area}\:\mathrm{of}\:\mathrm{a}\:\mathrm{disc}.\: \\ $$ Answered by tanmay.chaudhury50@gmail.com last…
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Question Number 51774 by ajfour last updated on 30/Dec/18 Commented by ajfour last updated on 30/Dec/18 $${Find}\:{maximum}\:{area}\:{A}\:{in}\:{light}\:{blue}. \\ $$$$\left({source}\::\:{ajfour}\right) \\ $$ Commented by tanmay.chaudhury50@gmail.com last…
Question Number 182437 by akolade last updated on 09/Dec/22 Answered by qaz last updated on 09/Dec/22 $$\begin{pmatrix}{{n}+\mathrm{2}}\\{\:\:\:\:{r}}\end{pmatrix}=\left[{x}^{{r}} \right]\left(\mathrm{1}+{x}\right)^{{n}+\mathrm{2}} =\left[{x}^{{r}} \right]\left(\left(\mathrm{1}+{x}\right)^{{n}} +\mathrm{2}{x}\left(\mathrm{1}+{x}\right)^{{n}} +{x}^{\mathrm{2}} \left(\mathrm{1}+{x}\right)^{{n}} \right) \\…
Question Number 182109 by amin96 last updated on 04/Dec/22 $$\boldsymbol{{f}}\left(\boldsymbol{{x}}\right)=\mathrm{3}\boldsymbol{{x}}^{\mathrm{2}} −\mathrm{2}\boldsymbol{{x}}\sqrt{\mathrm{3}}−\mathrm{8}\:\:\:\:\:\boldsymbol{{g}}\left(\boldsymbol{{x}}\right)=\boldsymbol{{x}}^{\mathrm{2}} −\frac{\mathrm{1}}{\mathrm{3}} \\ $$$$\boldsymbol{{gof}}^{−\mathrm{1}} \left(\mathrm{18}\right)=? \\ $$ Answered by FelipeLz last updated on 04/Dec/22 $${f}\left({x}\right)\:=\:\mathrm{3}{x}^{\mathrm{2}}…