Question Number 26769 by julli deswal last updated on 29/Dec/17 $$\underset{\:\mathrm{0}} {\overset{\infty} {\int}}\:\:\frac{{dx}}{\left[{x}+\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}\:\right]^{\mathrm{3}} }\:=\: \\ $$ Commented by prakash jain last updated on 29/Dec/17…
Question Number 26712 by julli deswal last updated on 28/Dec/17 $$\mathrm{If}\:\:\mid{x}\mid\:<\:\mathrm{1},\:\mathrm{then}\:\mathrm{the}\:\mathrm{coefficient}\:\mathrm{of}\:{x}^{{n}} \:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{expansion}\:\mathrm{of}\:\left(\mathrm{1}+{x}+{x}^{\mathrm{2}} +{x}^{\mathrm{3}} +{x}^{\mathrm{4}} +…\right)^{\mathrm{2}} \:\mathrm{is} \\ $$ Answered by mrW1 last updated…
Question Number 26703 by julli deswal last updated on 28/Dec/17 $$\mathrm{The}\:\mathrm{total}\:\mathrm{number}\:\mathrm{of}\:\mathrm{dissimilar}\:\mathrm{terms}\:\mathrm{in} \\ $$$$\mathrm{the}\:\mathrm{expansion}\:\mathrm{of}\:\left({x}_{\mathrm{1}} +{x}_{\mathrm{2}} +…+{x}_{{n}} \right)^{\mathrm{3}} \:\mathrm{is} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 26523 by nishant@123 last updated on 26/Dec/17 $$\mathrm{The}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{regular}\:\mathrm{polygon}\:\mathrm{of} \\ $$$${n}\:\mathrm{sides}\:\mathrm{is}\:\left(\mathrm{where}\:{R}\:\mathrm{is}\:\mathrm{the}\:\mathrm{radius}\:\mathrm{of}\:\mathrm{the}\right. \\ $$$$\left.\mathrm{circumpolygon}\right), \\ $$ Commented by mrW1 last updated on 26/Dec/17 Terms of…
Question Number 26521 by Samar khan last updated on 26/Dec/17 $$\mathrm{If}\:\:\frac{\mathrm{1}}{\mathrm{1}^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{2}} }\:+\:…\mathrm{to}\:\infty\:=\:\frac{\pi^{\mathrm{2}} }{\mathrm{6}},\:\mathrm{then} \\ $$$$\frac{\mathrm{1}}{\mathrm{1}^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{\mathrm{5}^{\mathrm{2}} }\:+\:…\:\mathrm{equals} \\ $$ Commented by abdo…
Question Number 26498 by keshabthagunna3@gmail.com last updated on 26/Dec/17 $$\mathrm{If}\:\left(\mathrm{5}{x}+\mathrm{7}{y}\right)\::\:\left(\mathrm{3}{x}+\mathrm{11}{y}\right)=\:\mathrm{2}\::\:\mathrm{3},\:\mathrm{then}\: \\ $$$${x}\::\:{y}\:=\:\_\_\_\_. \\ $$ Answered by Rasheed.Sindhi last updated on 26/Dec/17 $$\frac{\mathrm{5x}+\mathrm{7y}}{\mathrm{3x}+\mathrm{11y}}=\frac{\mathrm{2}}{\mathrm{3}} \\ $$$$\frac{\left(\mathrm{5x}+\mathrm{7y}\right)/\mathrm{y}}{\left(\mathrm{3x}+\mathrm{11y}\right)/\mathrm{y}}=\frac{\mathrm{2}}{\mathrm{3}} \\…
Question Number 92003 by zainal tanjung last updated on 04/May/20 $$\mathrm{The}\:\mathrm{sum}\:\mathrm{to}\:{n}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{the}\:\mathrm{series} \\ $$$$\frac{\mathrm{3}}{\mathrm{1}^{\mathrm{2}} }\:+\:\frac{\mathrm{5}}{\mathrm{1}^{\mathrm{2}} +\mathrm{2}^{\mathrm{2}} }\:+\:\frac{\mathrm{7}}{\mathrm{1}^{\mathrm{2}} +\mathrm{2}^{\mathrm{2}} +\mathrm{3}^{\mathrm{2}} }\:+\:….\:\mathrm{is} \\ $$ Commented by Prithwish Sen…
Question Number 91919 by zainal tanjung last updated on 03/May/20 $$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\:\mathrm{sin}\:\mathrm{12}°\:\mathrm{sin}\:\mathrm{48}°\:\mathrm{sin}\:\mathrm{54}°\:\:\mathrm{is} \\ $$ Commented by Tony Lin last updated on 03/May/20 $${sin}\mathrm{12}{sin}\mathrm{48}{sin}\mathrm{54}\:\:\:\:\left({in}\:{deg}\right) \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}}\left[{cos}\left(\mathrm{36}\right)−{cos}\left(\mathrm{60}\right)\right]{sin}\mathrm{54} \\…
A-rectangular-hall-12m-long-and-10m-broad-is-surrounded-by-a-path-2m-wide-Find-the-area-of-the-path-
Question Number 26316 by jenna.superable last updated on 24/Dec/17 $$\mathrm{A}\:\mathrm{rectangular}\:\mathrm{hall}\:\mathrm{12m}\:\mathrm{long}\:\mathrm{and}\:\mathrm{10m} \\ $$$$\mathrm{broad},\:\mathrm{is}\:\mathrm{surrounded}\:\mathrm{by}\:\mathrm{a}\:\mathrm{path}\:\mathrm{2m} \\ $$$$\mathrm{wide}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{path}. \\ $$ Answered by rita1608 last updated on 24/Dec/17 $${area}\:{of}\:{rectangular}\:{hall}={l}×{b} \\…
Question Number 26281 by kkr1729 last updated on 23/Dec/17 $$\mathrm{If}\:{f}\left({x}\right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{function}\:\mathrm{satisfying} \\ $$$$\:{f}\left({x}+{y}\right)={f}\left({x}\right)\:{f}\left({y}\right)\:\mathrm{for}\:\mathrm{all}\:{x},\:{y}\:\in\:{N}\:\:\mathrm{such} \\ $$$$\mathrm{that}\:{f}\left(\mathrm{1}\right)=\mathrm{3}\:\mathrm{and}\:\underset{{x}=\mathrm{1}} {\overset{{n}} {\sum}}\:{f}\left({x}\right)=\mathrm{120}.\:\mathrm{Then} \\ $$$$\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{n}\:\mathrm{is} \\ $$ Answered by mrW1 last updated…