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…
Question Number 26249 by Gabriel Wendell Celestino Roch last updated on 23/Dec/17 $$\mathrm{If}\:\:\:{x},\:{y},\:{z}\:\mathrm{are}\:\mathrm{in}\:\mathrm{GP}\:\mathrm{and}\:{a}^{{x}} =\:{b}^{{y}} =\:{c}^{{z}} ,\:\mathrm{then} \\ $$ Commented by Rasheed.Sindhi last updated on 23/Dec/17…
Question Number 26036 by chand908 last updated on 18/Dec/17 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{a}\:\mathrm{square}\:\mathrm{if}\:\mathrm{the}\:\mathrm{sum} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{diagonals}\:\mathrm{is}\:\mathrm{100}\:\mathrm{cm}. \\ $$ Answered by mrW1 last updated on 18/Dec/17 $$\mathrm{2}{d}=\mathrm{100} \\ $$$$\Rightarrow{d}=\mathrm{50}\:{cm} \\…
Question Number 25985 by Vignesh vkj last updated on 17/Dec/17 $$\mathrm{In}\:\mathrm{a}\:\bigtriangleup{ABC},\:{a}\:\mathrm{cot}\:{A}+\:{b}\:\mathrm{cot}\:{B}+{c}\:\mathrm{cot}\:{C}\:= \\ $$ Answered by ajfour last updated on 17/Dec/17 $$\Sigma{a}\mathrm{cot}\:{A}\:=\Sigma\sqrt{\mathrm{4}{R}^{\mathrm{2}} −{a}^{\mathrm{2}} } \\ $$$${R}\:{is}\:{the}\:{circumradius}\:.…
Question Number 91508 by Zainal Arifin last updated on 01/May/20 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{greatest}\:\mathrm{number}\:\mathrm{that}\:\mathrm{divides} \\ $$$$\mathrm{59}\:\mathrm{and}\:\mathrm{54}\:\mathrm{leaving}\:\mathrm{remainders}\:\mathrm{3}\:\mathrm{and} \\ $$$$\mathrm{5}\:\mathrm{respectively}. \\ $$ Commented by som(math1967) last updated on 01/May/20 $${H}.{C}.{F}\:{of}\:\left(\mathrm{59}−\mathrm{3}\right),\left(\mathrm{54}−\mathrm{5}\right)\:{is}\mathrm{7}…
Question Number 91507 by Zainal Arifin last updated on 01/May/20 $$\sqrt[{\mathrm{3}}]{\frac{−{a}^{\mathrm{6}} ×{b}^{\mathrm{3}} ×{c}^{\mathrm{21}} }{{c}^{\mathrm{9}} ×{a}^{\mathrm{12}} }}\:=\: \\ $$ Commented by jagoll last updated on 01/May/20…