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…
Question Number 25773 by Ali Makhzoum last updated on 14/Dec/17 $$\mathrm{The}\:\mathrm{least}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{function} \\ $$$$\:\:\:\phi\left({x}\right)\:=\:\underset{\mathrm{5}\pi/\mathrm{4}} {\overset{{x}} {\int}}\:\left(\mathrm{3}\:\mathrm{sin}\:{t}+\mathrm{4}\:\mathrm{cos}\:{t}\right)\:{dt} \\ $$$$\mathrm{on}\:\mathrm{the}\:\mathrm{interval}\:\left[\:\frac{\mathrm{5}\pi}{\mathrm{4}},\:\frac{\mathrm{4}\pi}{\mathrm{3}}\:\right]\:\mathrm{is} \\ $$ Answered by ajfour last updated on…
Question Number 25741 by gugalesweta@gmail.com last updated on 13/Dec/17 $$\mathrm{If}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:{n}\:\mathrm{terms}\:\mathrm{f}\:\mathrm{a}\:\mathrm{series}\:\mathrm{is}\: \\ $$$${A}\:{n}^{\mathrm{2}} +{B}\:{n}\:,\:\mathrm{where}\:{A},\:{B}\:\mathrm{are}\:\mathrm{constants}, \\ $$$$\mathrm{then}\:\mathrm{it}\:\mathrm{is}\:\mathrm{an}\:\mathrm{AP}. \\ $$ Commented by math solver last updated on 13/Dec/17…