Question Number 19262 by djatmiko last updated on 08/Aug/17 $$\mathrm{Let}\:\boldsymbol{\mathrm{p}},\:\boldsymbol{\mathrm{q}},\:\boldsymbol{\mathrm{r}}\:\mathrm{be}\:\mathrm{three}\:\mathrm{mutually}\:\mathrm{perpendicular} \\ $$$$\mathrm{vectors}\:\mathrm{of}\:\mathrm{the}\:\mathrm{same}\:\mathrm{magnitude}.\:\mathrm{If}\:\mathrm{a}\:\mathrm{vector} \\ $$$$\boldsymbol{\mathrm{x}}\:\:\mathrm{satisfies}\:\mathrm{the}\:\mathrm{equation}\: \\ $$$$\left.\boldsymbol{\mathrm{p}}\left.\:×\left\{\boldsymbol{\mathrm{x}}−\boldsymbol{\mathrm{q}}\right)×\boldsymbol{\mathrm{p}}\right\}+\boldsymbol{\mathrm{q}}×\left\{\boldsymbol{\mathrm{x}}−\boldsymbol{\mathrm{r}}\right)×\boldsymbol{\mathrm{q}}\right\} \\ $$$$\left.\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:+\:\:\boldsymbol{\mathrm{r}}×\left\{\boldsymbol{\mathrm{x}}−\boldsymbol{\mathrm{p}}\right)×\boldsymbol{\mathrm{r}}\right\}=\mathrm{0},\:\mathrm{then}\:\boldsymbol{\mathrm{x}}\:\mathrm{is} \\ $$$$\mathrm{given}\:\mathrm{by} \\ $$ Answered by ajfour…
Question Number 19148 by khamizan833@yahoo.com last updated on 06/Aug/17 $$\mathrm{If} \\ $$$${f}\left({x}\right)=\begin{vmatrix}{\mathrm{sin}\:{x}+\mathrm{sin2}{x}+\mathrm{sin}\:\mathrm{3}{x}}&{\mathrm{sin}\:\mathrm{2}{x}}&{\mathrm{sin}\:\mathrm{3}{x}}\\{\:\:\:\:\:\:\:\:\mathrm{3}+\mathrm{4}\:\mathrm{sin}\:{x}}&{\:\:\:\:\mathrm{3}}&{\mathrm{4}\:\mathrm{sin}\:{x}}\\{\:\:\:\:\:\:\:\:\:\:\mathrm{1}+\mathrm{sin}\:{x}}&{\:\mathrm{sin}\:{x}}&{\:\:\:\:\mathrm{1}}\end{vmatrix} \\ $$$$\mathrm{then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\underset{\:\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\:{f}\left({x}\right)\:{dx}\:\:\:\mathrm{is} \\ $$ Answered by ajfour last updated on 06/Aug/17…
Question Number 19134 by chernoaguero@gmail.com last updated on 05/Aug/17 $$\mathrm{If}\:\frac{\mathrm{1}}{\left(\mathrm{243}\right)^{{x}} }\:=\:\left(\mathrm{729}\right)^{{y}} =\:\mathrm{3}^{\mathrm{3}} ,\:\mathrm{then}\:\mathrm{find}\:\mathrm{the}\: \\ $$$$\mathrm{value}\:\mathrm{of}\:\:\mathrm{5}{x}\:+\:\mathrm{6}{y}. \\ $$ Answered by Tinkutara last updated on 05/Aug/17 $$\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{5}{x}}…
Question Number 18969 by chernoaguero@gmail.com last updated on 02/Aug/17 $$\mathrm{If}\:\left(\frac{{a}}{{b}}\right)+\left(\frac{{b}}{{a}}\right)=\mathrm{2},\:\mathrm{then}\:\mathrm{find}\:\left(\frac{{a}}{{b}}\right)^{\mathrm{10}} −\:\left(\frac{{b}}{{a}}\right)^{\mathrm{10}} . \\ $$ Answered by Joel577 last updated on 02/Aug/17 $$\:\:{a}^{\mathrm{2}} \:+\:{b}^{\mathrm{2}} \:=\:\mathrm{2}{ab} \\…
Question Number 18881 by Anowar last updated on 31/Jul/17 $$\mathrm{If}\:\left(\mathrm{6}\:\sqrt{\mathrm{6}}\:+\mathrm{14}\right)^{\mathrm{2}{n}+\mathrm{1}} =\:{m}\:\mathrm{and}\:\mathrm{if}\:{f}\:\:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{fractional}\:\mathrm{part}\:\mathrm{of}\:{m},\:\mathrm{then}\:{f}\:{m}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 18762 by 786786AM last updated on 29/Jul/17 $$\mathrm{If}\:\left(\mathrm{1}+{x}\right)^{{n}} ={C}_{\mathrm{0}} +{C}_{\mathrm{1}} {x}+{C}_{\mathrm{2}} {x}^{\mathrm{2}} +…+{C}_{{n}} {x}^{{n}} , \\ $$$$\mathrm{then}\:{C}_{\mathrm{1}} \:^{\mathrm{2}} +{C}_{\mathrm{2}} \:^{\mathrm{2}} +….+{C}_{{n}} \:^{\mathrm{2}} \:\mathrm{is}\:\mathrm{equal}\:\mathrm{to}…
Question Number 18761 by 786786AM last updated on 29/Jul/17 $$\mathrm{If}\:\:{x}\:\in\:{R},\:\:\:\mathrm{then}\:\mathrm{the}\:\mathrm{expression}\:\mathrm{9}^{{x}} −\mathrm{3}^{{x}} +\mathrm{1} \\ $$$$\mathrm{assumes}\: \\ $$ Commented by Tinkutara last updated on 29/Jul/17 $$\mathrm{What}\:\mathrm{are}\:\mathrm{the}\:\mathrm{options}? \\…
Question Number 18759 by 786786AM last updated on 29/Jul/17 $$\mathrm{The}\:\mathrm{coefficient}\:\mathrm{of}\:\mathrm{the}\:\mathrm{middle}\:\mathrm{term}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{expansion}\:\mathrm{of}\:\left(\mathrm{1}+{x}\right)^{\mathrm{2}{n}} \:\mathrm{is} \\ $$ Answered by anuragbhandari123@gmail.com last updated on 29/Jul/17 $$\frac{\mathrm{2}{nC}\left({n}+\mathrm{1}\right){xofpower}\left({n}+\mathrm{1}\right)}{} \\ $$…
Question Number 18760 by 786786AM last updated on 29/Jul/17 $$\mathrm{If}\:\mathrm{the}\:\mathrm{coefficient}\:\mathrm{of}\:{x}^{\mathrm{7}} \mathrm{and}\:{x}^{\mathrm{8}} \:\mathrm{in}\:\left(\mathrm{2}+\frac{{x}}{\mathrm{3}}\right)^{{n}} \\ $$$$\mathrm{are}\:\mathrm{equal}\:\mathrm{then}\:{r}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$ Commented by Tinkutara last updated on 29/Jul/17 $$\mathrm{There}\:\mathrm{is}\:\mathrm{an}\:\mathrm{error}\:\mathrm{in}\:\mathrm{the}\:\mathrm{question}.\:{r}\:\mathrm{comes} \\…
Question Number 18757 by 786786AM last updated on 29/Jul/17 $$\mathrm{If}\:{a}_{\mathrm{1}} ,\:{a}_{\mathrm{2}} ,\:{a}_{\mathrm{3}} ,\:{a}_{\mathrm{4}} \:\mathrm{are}\:\mathrm{the}\:\mathrm{coefficient}\:\mathrm{of}\:\mathrm{any} \\ $$$$\mathrm{four}\:\mathrm{four}\:\mathrm{consecutive}\:\mathrm{terms}\:\mathrm{in}\:\mathrm{the}\:\mathrm{expansion} \\ $$$$\mathrm{of}\:\left(\mathrm{1}+{x}\right)^{{n}} ,\:\mathrm{then}\:\frac{{a}_{\mathrm{1}} }{{a}_{\mathrm{1}} +{a}_{\mathrm{2}} }\:+\:\frac{{a}_{\mathrm{3}} }{{a}_{\mathrm{3}} +{a}_{\mathrm{4}} }\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to}…