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Category: Mensuration

Question-53907

Question Number 53907 by peter frank last updated on 27/Jan/19 Answered by ajfour last updated on 27/Jan/19 $${y}={ax}^{\mathrm{2}} \\ $$$$\mathrm{0}.\mathrm{1}=\left(\frac{\mathrm{5}}{\mathrm{2}}\right)^{\mathrm{2}} {a}\:\:\:\Rightarrow\:\:{a}=\frac{\mathrm{2}}{\mathrm{125}} \\ $$$${y}=\frac{\mathrm{2}}{\mathrm{125}}{x}^{\mathrm{2}} \\ $$$${No}\:{need}\:{of}\:{above}\:{calculations}…

Question-53867

Question Number 53867 by byaw last updated on 26/Jan/19 Answered by tanmay.chaudhury50@gmail.com last updated on 27/Jan/19 $${Removed}\:{sector}\:{area}=\frac{\pi{r}^{\mathrm{2}} }{\mathrm{360}}×\mathrm{120}=\frac{\pi{r}^{\mathrm{2}} }{\mathrm{3}} \\ $$$${Remaining}\:{sector}\:{area}=\pi{r}^{\mathrm{2}} −\frac{\pi{r}^{\mathrm{2}} }{\mathrm{3}}=\frac{\mathrm{2}\pi{r}^{\mathrm{2}} }{\mathrm{3}} \\…

Question-184387

Question Number 184387 by ajfour last updated on 05/Jan/23 Commented by ajfour last updated on 05/Jan/23 $${If}\:{all}\:{three}\:{coloured}\:{areas}\:{are} \\ $$$${equal}\:{then}\:{find}\:{parameters}\: \\ $$$${h}\:{and}\:{k}\:{of}\:{parabola}\:{y}=\left({x}−{h}\right)^{\mathrm{2}} +{k}. \\ $$ Answered…

Let-a-b-gt-0-and-x-0-pi-2-Prove-a-sinx-1-b-cosx-1-1-2ab-2-

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. \\…

Let-ABC-be-a-triangle-such-as-2cosA-3sinB-4-and-3cosB-2sinA-3-Prove-that-the-angle-C-is-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…

what-is-the-centre-of-the-circle-with-radius-4-2-that-can-be-inscribed-in-the-parabola-y-x-2-16x-128-

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…