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Category: Mensuration

Question-52034

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…

Question-182437

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) \\…

f-x-3x-2-2x-3-8-g-x-x-2-1-3-gof-1-18-

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}}…

Question-50936

Question Number 50936 by Rio Michael last updated on 22/Dec/18 Commented by Rio Michael last updated on 22/Dec/18 $${the}\:{figure}\:{above}\:{is}\:{a}\:{solid}\:{with}\:{trapezium}\:{PQRS}\:{as}\:{its}\:{uniform} \\ $$$${cross}−{section}. \\ $$$$\left.{a}\right)\:{Find}\:{the}\:{area}\:{of}\:{the}\:{trapezuim}\:{PQRS} \\ $$$$\left.{b}\right)\:{calculate}\:{the}\:{volume}\:{of}\:{the}\:{solid}\:{figure}.…

If-a-right-angled-triangle-has-same-area-and-double-perimeter-as-that-of-a-circle-of-unit-radius-find-the-mutually-perpendicular-sides-of-the-triangle-

Question Number 50818 by ajfour last updated on 20/Dec/18 $${If}\:{a}\:{right}\:{angled}\:{triangle}\:{has} \\ $$$${same}\:{area}\:{and}\:{double}\:{perimeter} \\ $$$${as}\:{that}\:{of}\:{a}\:{circle}\:{of}\:{unit}\:{radius}, \\ $$$${find}\:{the}\:{mutually}\:{perpendicular} \\ $$$${sides}\:{of}\:{the}\:{triangle}. \\ $$ Answered by mr W last…

Question-50640

Question Number 50640 by ajfour last updated on 18/Dec/18 Commented by mr W last updated on 18/Dec/18 $${when}\:{the}\:{angle}\:{between}\:{k}\:{and}\:{h}\:{is} \\ $$$${fixed},\:{then}\:{the}\:{shape}\:{and}\:{therefore} \\ $$$${also}\:{the}\:{area}\:{of}\:{the}\:{quadrilateral}\:{is} \\ $$$${fixed}.\:{the}\:{area}\:{is}\:{a}\:{constant}. \\…

Question-50630

Question Number 50630 by peter frank last updated on 18/Dec/18 Answered by ajfour last updated on 18/Dec/18 $$\alpha+\beta\:=\:\mathrm{0}\:\:,\:\gamma+\delta\:=\:−{b}\:\:\:\:…\left({i}\right) \\ $$$$\alpha\beta+\left(\alpha+\beta\right)\gamma+\gamma\delta+\left(\alpha+\beta\right)\delta\:=\:{c} \\ $$$$\Rightarrow\:\:\alpha\beta+\gamma\delta\:=\:{c}\:\:\:\:\:\:\:\:\:\:\:….\left({ii}\right) \\ $$$$\alpha\beta.\gamma\delta\:=\:{e}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:….\left({iii}\right) \\…

Solve-the-differential-equation-a-x-x-y-dy-dx-x-2-xy-3y-2-b-y-xy-2-x-dy-dx-0-c-x-2-d-2-y-dx-2-2x-dy-dx-2-2x-2-1-y-24x-3-given-that-dy-dx-6-d-2-y-dx-2-0-

Question Number 50140 by peter frank last updated on 14/Dec/18 $${Solve}\:{the}\:{differential} \\ $$$${equation} \\ $$$$\left.{a}\right){x}\left({x}+{y}\right)\frac{{dy}}{{dx}}={x}^{\mathrm{2}} +{xy}−\mathrm{3}{y}^{\mathrm{2}} \\ $$$$\left.{b}\right){y}+{xy}^{\mathrm{2}} −{x}\frac{{dy}}{{dx}}=\mathrm{0} \\ $$$${c}\:\left[\:\:{x}^{\mathrm{2}} \frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}\:} }−\mathrm{2}{x}\frac{{dy}}{{dx}}+\mathrm{2}\left(\mathrm{2}{x}^{\mathrm{2}} +\mathrm{1}\right){y}=\mathrm{24}{x}^{\mathrm{3}}…