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}} }}\:=\: \\ $$ Commented by jagoll last updated on 01/May/20…
Question Number 91496 by Zainal Arifin last updated on 01/May/20 $$\mathrm{The}\:\mathrm{vector}\:\boldsymbol{\mathrm{a}}=\mathrm{3}\boldsymbol{\mathrm{i}}−\mathrm{2}\boldsymbol{\mathrm{j}}+\mathrm{2}\boldsymbol{\mathrm{k}}\:\:\mathrm{and}\:\boldsymbol{\mathrm{b}}=−\boldsymbol{\mathrm{i}}−\mathrm{2}\boldsymbol{\mathrm{k}} \\ $$$$\mathrm{are}\:\mathrm{the}\:\mathrm{adjacent}\:\mathrm{sides}\:\mathrm{of}\:\mathrm{a}\:\mathrm{parallelogram}. \\ $$$$\mathrm{Then}\:\mathrm{angle}\:\mathrm{between}\:\mathrm{its}\:\mathrm{diagonal}\:\mathrm{is} \\ $$ Commented by jagoll last updated on 01/May/20 $$\overset{\rightarrow}…
Question Number 91494 by Zainal Arifin last updated on 01/May/20 $$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{integral}\:\underset{\:\mathrm{1}} {\overset{\mathrm{3}} {\int}}\:\sqrt{\mathrm{3}+{x}^{\mathrm{3}} }\:{dx} \\ $$$$\mathrm{lies}\:\mathrm{in}\:\mathrm{the}\:\mathrm{interval}…. \\ $$ Answered by Joel578 last updated on 01/May/20…
Question Number 91493 by Zainal Arifin last updated on 01/May/20 $$\underset{\:\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\:\mathrm{log}\:\left(\frac{\mathrm{4}+\mathrm{3}\:\mathrm{sin}\:{x}}{\mathrm{4}+\mathrm{3}\:\mathrm{cos}\:{x}}\right){dx}\:= \\ $$ Commented by mathmax by abdo last updated on 01/May/20 $${I}\:=\int_{\mathrm{0}}…
Question Number 25948 by 272; 2; 2 last updated on 16/Dec/17 $$\mathrm{Factorise}:\:\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} −{z}^{\mathrm{2}} −\mathrm{2}{xy} \\ $$ Commented by tawa tawa last updated on 16/Dec/17…
Question Number 25786 by gugalesweta@gmail.com last updated on 14/Dec/17 $$\mathrm{If}\:{C}_{\mathrm{0}} +\:{C}_{\mathrm{1}} +\:{C}_{\mathrm{2}} +…+\:{C}_{{n}} \:=\:\mathrm{256},\:\mathrm{then} \\ $$$$\:^{\mathrm{2}{n}} {C}_{\mathrm{2}} \:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$ Answered by mrW1 last updated…