Question Number 8817 by sÁê< last updated on 30/Oct/16 $$\mathrm{If}\:{I}_{\mathrm{1}} =\underset{\:\mathrm{0}} {\overset{\mathrm{3}\pi} {\int}}\:{f}\:\left(\mathrm{cos}^{\mathrm{2}} {x}\right){dx}\:\mathrm{and}\:\:{I}_{\mathrm{2}} =\underset{\:\mathrm{0}} {\overset{\pi} {\int}}\:{f}\:\left(\mathrm{cos}^{\mathrm{2}} {x}\right){dx} \\ $$$$\mathrm{then} \\ $$ Commented by ridwan…
Question Number 8803 by desniati@rocketmail.com last updated on 28/Oct/16 $$\mathrm{The}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{a}\:\mathrm{leap}\:\mathrm{year}\:\mathrm{selected} \\ $$$$\mathrm{at}\:\mathrm{random}\:\mathrm{contains}\:\mathrm{either}\:\mathrm{53}\:\mathrm{Sundays}\:\mathrm{or} \\ $$$$\mathrm{53}\:\mathrm{Mondays},\:\mathrm{is} \\ $$ Answered by myintkhaing last updated on 02/Nov/16 $${number}\:{of}\:{days}\:{in}\:{leap}\:{year}=\mathrm{366} \\…
Question Number 8662 by tttttyyyyuuuuuu77 last updated on 20/Oct/16 $$\mathrm{If}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{2}{x}^{\mathrm{2}} +\mathrm{7}{x}+\mathrm{5}=\mathrm{0}\:\mathrm{are}\:\mathrm{the}\: \\ $$$$\mathrm{reciprocal}\:\mathrm{roots}\:\mathrm{of}\:{ax}^{\mathrm{2}} +{bx}+{c}=\mathrm{0}, \\ $$$$\mathrm{then}\:{a}−{c}\:=\:\_\_\_\_\_\_. \\ $$ Answered by sandy_suhendra last updated on 20/Oct/16…
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}}…