Question Number 118011 by mmmmmm1 last updated on 14/Oct/20 Answered by mr W last updated on 14/Oct/20 $$\left({x}−{h}\right)^{\mathrm{2}} +\left({y}−{k}\right)^{\mathrm{2}} ={R}^{\mathrm{2}} \\ $$$$ \\ $$$$\left(\mathrm{0}−{h}\right)^{\mathrm{2}} +\left(\mathrm{0}−{k}\right)^{\mathrm{2}}…
Question Number 118002 by mmmmmm1 last updated on 14/Oct/20 Answered by TANMAY PANACEA last updated on 14/Oct/20 $${x}^{\mathrm{3}} +\frac{\mathrm{1}}{{x}^{\mathrm{3}} }+{x}+\frac{\mathrm{1}}{{x}} \\ $$$$\left({x}+\frac{\mathrm{1}}{{x}}\right)^{\mathrm{3}} −\mathrm{3}\left({x}+\frac{\mathrm{1}}{{x}}\right)+\left({x}+\frac{\mathrm{1}}{{x}}\right) \\ $$$${now}\:{x}+\frac{\mathrm{1}}{{x}}=\mathrm{3}+\mathrm{2}\sqrt{\mathrm{2}}\:+\frac{\mathrm{1}}{\mathrm{3}+\mathrm{2}\sqrt{\mathrm{2}}}=\mathrm{3}+\mathrm{2}\sqrt{\mathrm{2}}\:+\mathrm{3}−\mathrm{2}\sqrt{\mathrm{2}}\:=\mathrm{6}…
Question Number 52450 by maxmathsup by imad last updated on 07/Jan/19 $${let}\:{P}\left({x}\right)=\left(\mathrm{1}+{ix}\:−{x}^{\mathrm{2}} \right)^{{n}} −\mathrm{1} \\ $$$${find}\:{roots}\:{of}\:\:{P}\left({x}\right)\:{and}\:{factorize}\:{P}\left({x}\right){inside}\:{C}\left({x}\right). \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 52449 by maxmathsup by imad last updated on 07/Jan/19 $${let}\:{j}={e}^{\frac{{i}\mathrm{2}\pi}{\mathrm{3}}} \:\:\:{and}\:{P}\left({x}\right)=\left(\mathrm{1}+{jx}\right)^{{n}} −\left(\mathrm{1}−{jx}\right)^{{n}} \:\:{with}\:{n}\:{integr}\:{natural} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{roots}\:{of}\:{P}\left({x}\right) \\ $$$$\left.\mathrm{2}\right){factorize}\:{P}\left({x}\right)\:{inside}\:{C}\left[{x}\right] \\ $$$$\left.\mathrm{3}\right)\:\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} {P}\left({x}\right){dx}. \\ $$$$\left.\mathrm{4}\right)\:{decompose}\:{inside}\:{C}\left({x}\right)\:{the}\:{fraction}\:{F}\left({x}\right)=\frac{\mathrm{1}}{{P}\left({x}\right)}…
Question Number 117984 by Ar Brandon last updated on 14/Oct/20 $$\mathrm{If}\:{f}\left({x}\right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{polynomial}\:\mathrm{function}\:\mathrm{satisfying}\:\mathrm{the}\:\mathrm{relation} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{f}\left({x}\right)+{f}\left(\frac{\mathrm{1}}{{x}}\right)={f}\left({x}\right){f}\left(\frac{\mathrm{1}}{{x}}\right) \\ $$$$\mathrm{for}\:\mathrm{all}\:\mathrm{0}\neq{x}\in\mathbb{R}\:\mathrm{and}\:\mathrm{if}\:{f}\left(\mathrm{2}\right)=\mathrm{9},\:\mathrm{then}\:\mathrm{f}\left(\mathrm{6}\right)\:\mathrm{is} \\ $$$$\left(\mathrm{A}\right)\:\mathrm{216}\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{B}\right)\:\mathrm{217}\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{C}\right)\:\mathrm{126}\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{D}\right)\:\mathrm{127} \\ $$ Answered by Ar Brandon last updated…
Question Number 117972 by Ar Brandon last updated on 14/Oct/20 $$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{surjections}\:\mathrm{of}\:\left\{\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4}\right\}\:\mathrm{onto}\:\left\{\mathrm{x},\mathrm{y}\right\}\:\mathrm{is} \\ $$$$\left(\mathrm{A}\right)\:\mathrm{16}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{B}\right)\:\mathrm{8}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{C}\right)\:\mathrm{14}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{D}\right)\:\mathrm{6} \\ $$ Answered by Lordose last updated on 14/Oct/20 $$\mathrm{N}=\:\mathrm{2}^{\mathrm{n}\left(\mathrm{A}\right)−\mathrm{1}} =\:\mathrm{2}^{\mathrm{3}} =\mathrm{8}…
Question Number 52421 by ahmetcu07@hotmail.com last updated on 07/Jan/19 Commented by ahmetcu07@hotmail.com last updated on 07/Jan/19 $${help}\:{me}\:{please} \\ $$ Commented by MJS last updated on…
Question Number 52412 by Tawa1 last updated on 07/Jan/19 Commented by tanmay.chaudhury50@gmail.com last updated on 08/Jan/19 Commented by tanmay.chaudhury50@gmail.com last updated on 08/Jan/19 Commented by…
Question Number 52406 by Tawa1 last updated on 07/Jan/19 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{cube}\:\mathrm{root}\:\mathrm{of}\:\:\:\:\:\mathrm{26}\:+\:\mathrm{5}\sqrt{\mathrm{3}} \\ $$ Answered by MJS last updated on 07/Jan/19 $$\mathrm{no}\:\mathrm{exact}\:\mathrm{solution} \\ $$$$\mathrm{I}\:\mathrm{think}\:\mathrm{it}\:\mathrm{should}\:\mathrm{be}\:\mathrm{26}+\mathrm{15}\sqrt{\mathrm{3}} \\ $$$$\left({a}+{b}\sqrt{\mathrm{3}}\right)^{\mathrm{3}} =\mathrm{26}+\mathrm{15}\sqrt{\mathrm{3}}…
Question Number 117934 by Ar Brandon last updated on 14/Oct/20 $$\mathrm{Let}\:{f}\::\:\left[\mathrm{1},\infty\right)\rightarrow\left[\mathrm{2},\infty\right)\:\mathrm{be}\:\mathrm{the}\:\mathrm{function}\:\mathrm{defined}\:\mathrm{by} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{f}\left({x}\right)={x}+\frac{\mathrm{1}}{{x}} \\ $$$$\mathrm{If}\:\mathrm{g}\::\:\left[\mathrm{2},\infty\right)\rightarrow\left[\mathrm{1},\infty\right),\:\mathrm{is}\:\mathrm{a}\:\mathrm{function}\:\mathrm{such}\:\mathrm{that}\:\left(\mathrm{g}\circ{f}\right)\left({x}\right)={x} \\ $$$$\mathrm{for}\:\mathrm{all}\:{x}\geqslant\mathrm{1}.\:\mathrm{Show}\:\mathrm{that}\:\mathrm{g}\left({t}\right)=\frac{{t}+\sqrt{{t}^{\mathrm{2}} −\mathrm{4}}}{\mathrm{2}} \\ $$ Answered by Lordose last updated…