Question Number 8230 by 314159 last updated on 03/Oct/16 $$\mathrm{If}\:\frac{{x}+{y}}{{x}+{y}+{z}}\:=\:\frac{{y}+{z}}{{x}+{y}+{z}}\:=\:\frac{{x}+{z}}{{x}+{y}+{z}}\:={p},\:\mathrm{then}\:\mathrm{which}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{following}\:\mathrm{can}\:\mathrm{be}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{p}? \\ $$ Answered by Rasheed Soomro last updated on 03/Oct/16 $$\frac{\mathrm{a}}{\mathrm{A}}=\frac{\mathrm{b}}{\mathrm{B}}=\frac{\mathrm{c}}{\mathrm{C}}=\frac{\mathrm{a}+\mathrm{b}+\mathrm{c}}{\mathrm{A}+\mathrm{B}+\mathrm{C}} \\ $$$$\:\mathrm{p}=\frac{{x}+{y}}{{x}+{y}+{z}}\:=\:\frac{{y}+{z}}{{x}+{y}+{z}}\:=\:\frac{{x}+{z}}{{x}+{y}+{z}}…
Question Number 73706 by Faradtimmy last updated on 15/Nov/19 $$\mathrm{If}\:\:\frac{\mathrm{tan}\:\mathrm{3}{A}}{\mathrm{tan}\:{A}}\:=\:{k},\:\mathrm{then}\:\frac{\mathrm{sin}\:\mathrm{3}{A}}{\mathrm{sin}\:{A}}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$ Answered by Tanmay chaudhury last updated on 15/Nov/19 $${tanA}={t} \\ $$$$\frac{\mathrm{3}{t}−{t}^{\mathrm{3}} }{{t}\left(\mathrm{1}−\mathrm{3}{t}^{\mathrm{2}} \right)}={k}\rightarrow{k}−\mathrm{3}{kt}^{\mathrm{2}}…
Question Number 8156 by 314159 last updated on 02/Oct/16 $$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{series} \\ $$$$\left.\mathrm{3}\:^{{n}} {C}_{\mathrm{0}} −\:\mathrm{8}\:^{{n}} {C}_{\mathrm{1}} +\mathrm{13}\:^{{n}} {C}_{\mathrm{2}} −\mathrm{18}\:^{{n}} {C}_{\mathrm{3}} +…+\left(−\mathrm{1}\right)^{{n}} \:\left(\mathrm{3}+\mathrm{5}{n}\right)\:^{{n}} {C}_{{n}} \right] \\ $$…
Question Number 8155 by 314159 last updated on 02/Oct/16 $$\mathrm{If}\:{f}\left({x}\right)={x}^{{n}} ,\:\mathrm{then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$${f}\left(\mathrm{1}\right)\:+\:\frac{{f}^{\mathrm{1}} \left(\mathrm{1}\right)}{\mathrm{1}}\:+\:\frac{{f}^{\mathrm{2}} \left(\mathrm{1}\right)}{\mathrm{2}!}\:+\:…\:+\:\frac{{f}^{\:{n}} \left(\mathrm{1}\right)}{{n}!}\:,\:\mathrm{where} \\ $$$${f}^{\:{r}} \left({x}\right)\:\mathrm{denotes}\:\mathrm{the}\:{r}\mathrm{th}\:\mathrm{order}\:\mathrm{derivative}\:\mathrm{of} \\ $$$${f}\left({x}\right)\:\mathrm{with}\:\mathrm{respect}\:\mathrm{to}\:{x}\:,\:\mathrm{is} \\ $$ Commented by…
Question Number 8132 by 314159 last updated on 01/Oct/16 $$\mathrm{The}\:\:\mathrm{coefficient}\:\mathrm{of}\:{x}^{{n}−\mathrm{2}} \:\mathrm{in}\:\mathrm{the}\:\mathrm{polynomial} \\ $$$$\left({x}−\mathrm{1}\right)\left({x}−\mathrm{2}\right)….\left({x}−{n}\right)\:\:\mathrm{is} \\ $$ Commented by Yozzia last updated on 01/Oct/16 $${coefficient}\left({x}^{{n}−\mathrm{2}} \right)=\underset{\forall\alpha,\beta\in\left[\mathrm{1},{n}\right]} {\sum}\alpha\beta…
Question Number 8107 by Nadium last updated on 30/Sep/16 $$\mathrm{The}\:\mathrm{general}\:\mathrm{term}\:\mathrm{in}\:\mathrm{the}\:\mathrm{expansion}\:\mathrm{of} \\ $$$$\left(\mathrm{1}−\mathrm{2}{x}\right)^{\mathrm{3}/\mathrm{4}} \:\:\mathrm{is} \\ $$ Answered by prakash jain last updated on 30/Sep/16 $$\mathrm{If}\:\mid{x}\mid<\mathrm{1} \\…
Question Number 8061 by Chantria last updated on 29/Sep/16 $$\mathrm{If}\:\:\mathrm{5}\:=\:{a}^{{x}} \:,\:\mathrm{then}\:\frac{\mathrm{5}}{{a}}\:= \\ $$ Commented by 123456 last updated on 29/Sep/16 $$\mathrm{5}={a}^{{x}} \Rightarrow{a}=\mathrm{5}^{\mathrm{1}/{x}} \\ $$$$\frac{\mathrm{5}}{{a}}=\frac{{a}^{{x}} }{{a}}={a}^{{x}−\mathrm{1}}…
Question Number 8050 by Chantria last updated on 28/Sep/16 $$\mathrm{The}\:\mathrm{value}\:\mathrm{of} \\ $$$$\frac{\mathrm{18}^{\mathrm{3}} +\mathrm{7}^{\mathrm{3}} +\mathrm{3}\:\centerdot\:\mathrm{18}\:\centerdot\:\mathrm{7}\:\centerdot\:\mathrm{25}}{\mathrm{3}^{\mathrm{6}} +\mathrm{6}\centerdot\mathrm{243}\centerdot\mathrm{2}+\mathrm{15}\centerdot\mathrm{181}\centerdot\mathrm{4}+\mathrm{20}\centerdot\mathrm{27}\centerdot\mathrm{8}+\mathrm{15}\centerdot\mathrm{9}\centerdot\mathrm{16}+\mathrm{6}\centerdot\mathrm{3}\centerdot\mathrm{32}+\mathrm{64}} \\ $$$$\mathrm{is} \\ $$ Answered by sandy_suhendra last updated on…
Question Number 7911 by ashis786 last updated on 24/Sep/16 $$\mathrm{If}\:{a}>\mathrm{0},\:{b}>\mathrm{0},\:{c}>\mathrm{0}\:\mathrm{are}\:\mathrm{respectively}\:\mathrm{the} \\ $$$${p}^{\mathrm{th}} ,\:{q}^{\mathrm{th}} ,\:{r}^{\mathrm{th}} \:\mathrm{terms}\:\mathrm{of}\:\mathrm{a}\:\mathrm{GP},\:\mathrm{then}\:\mathrm{the}\:\mathrm{value} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{determinant}\:\begin{vmatrix}{\mathrm{log}\:{a}}&{{p}}&{\mathrm{1}}\\{\mathrm{log}\:{b}}&{{q}}&{\mathrm{1}}\\{\mathrm{log}\:{c}}&{{r}}&{\mathrm{1}}\end{vmatrix}\:\mathrm{is} \\ $$ Answered by prakash jain last updated…
Question Number 7710 by abdel19599@yahoo.com last updated on 11/Sep/16 $$\mathrm{If}\:{n}\left(\mathrm{A}\cup\mathrm{B}\right)=\mathrm{32},\:{n}\left(\mathrm{B}\right)=\mathrm{12}\:\mathrm{and}\:{n}\left(\mathrm{A}\cap\mathrm{B}\right)=\mathrm{5} \\ $$$$\mathrm{then}\:{n}\left(\mathrm{A}\right)=? \\ $$ Answered by Rasheed Soomro last updated on 11/Sep/16 $$\:{n}\left(\mathrm{A}\cup\mathrm{B}\right)={n}\left({A}\right)+{n}\left({B}\right)−{n}\left(\mathrm{A}\cap\mathrm{B}\right) \\ $$$$\mathrm{32}={n}\left({A}\right)+\mathrm{12}−\mathrm{5}…