Question Number 62176 by Tawa1 last updated on 16/Jun/19 Answered by MJS last updated on 17/Jun/19 $$\mathrm{to}\:\mathrm{make}\:\mathrm{it}\:\mathrm{clear}\:\mathrm{let}:\:{a},\:{b},\:{c},\:{d}\:\in\mathbb{R} \\ $$$${a}+{b}+{c}+{d}=\mathrm{1} \\ $$$${F}={ab}+{bc}+{cd} \\ $$$$ \\ $$$${d}=\mathrm{1}−{a}−{b}−{c}…
Question Number 127708 by ajfour last updated on 01/Jan/21 Commented by ajfour last updated on 01/Jan/21 $${A}\:{ball}\:{is}\:{dropped}\:{from}\:{a}\:{tall} \\ $$$${tower},\:{height}\:{h},\:{at}\:{the}\:{equator}. \\ $$$${Find}\:{how}\:{far}\:{from}\:{the}\:{foot}\:{of} \\ $$$${the}\:{building},\:{does}\:{the}\:{ball}\:{land}. \\ $$…
Question Number 127706 by arash sharifi last updated on 01/Jan/21 $${dx}+{ydy}={x}^{\mathrm{2}} {ydy} \\ $$ Answered by liberty last updated on 01/Jan/21 $$\:\mathrm{dx}\:=\:\mathrm{y}\left(\mathrm{x}^{\mathrm{2}} −\mathrm{1}\right)\mathrm{dy} \\ $$$$\:\frac{\mathrm{dx}}{\mathrm{x}^{\mathrm{2}}…
Question Number 127704 by NATTAPONG4359 last updated on 01/Jan/21 $$ \\ $$$${if}\:{f}\left({x}\right)=\begin{cases}{{x}−{n}\:;\:\mathrm{2}{n}\:\leqslant\:{x}\:\leqslant\mathrm{2}{n}+\mathrm{1}}\\{{n}+\mathrm{1}\:;\:\mathrm{2}{n}+\mathrm{1}\leqslant{x}\leqslant\mathrm{2}{n}+\mathrm{2}\:}\end{cases}\:{where}\:\:{n}\:=\mathrm{0},\mathrm{1},\mathrm{2},\mathrm{3},..,\mathrm{9} \\ $$$${find}\:\int_{\mathrm{0}} ^{\mathrm{20}} {f}\left({x}\right){dx} \\ $$ Answered by mahdipoor last updated on 01/Jan/21…
Question Number 62169 by Tawa1 last updated on 16/Jun/19 $$\mathrm{Prove}\:\mathrm{without}\:\mathrm{induction}\:\mathrm{that}:\:\:\left(\mathrm{1}\:+\:\sqrt{\mathrm{2}}\right)^{\mathrm{2n}} \:+\:\left(\mathrm{1}\:−\:\sqrt{\mathrm{2}}\right)^{\mathrm{2n}} \:\:\mathrm{is}\:\mathrm{even}\:\mathrm{for}\:\mathrm{every} \\ $$$$\mathrm{natural}\:\mathrm{number}\:\mathrm{n}.\:\:\: \\ $$ Answered by ajfour last updated on 16/Jun/19 $$\left(\mathrm{1}+\sqrt{\mathrm{2}}\right)^{\mathrm{2}{n}} +\left(\mathrm{1}−\sqrt{\mathrm{2}}\right)^{\mathrm{2}{n}}…
Question Number 127698 by MathSh last updated on 01/Jan/21 $$−\mathrm{1}!+\mathrm{2}!−\mathrm{3}!−\mathrm{5}!+\mathrm{6}!−\mathrm{4}!!+\mathrm{7}!!+\mathrm{8}!!+\mathrm{9}!!=\mathrm{2021} \\ $$$${Happy}\:{New}\:{Year}! \\ $$ Commented by talminator2856791 last updated on 04/Jan/21 $$\:\mathrm{are}\:\mathrm{you}\:\mathrm{sure}\:\mathrm{this}\:\mathrm{is}\:\mathrm{true}? \\ $$$$\:\mathrm{9}!!\:\mathrm{seems}\:\mathrm{much}\:\mathrm{larger}\:\mathrm{than}\:\mathrm{any}\:\mathrm{of}\:\mathrm{the}\:\mathrm{other}\:\mathrm{numbers}. \\…
Question Number 127684 by liberty last updated on 01/Jan/21 $$\mathrm{P}\:=\:\mathrm{cos}\:\left(\frac{\pi}{\mathrm{15}}\right)\mathrm{cos}\:\left(\frac{\mathrm{2}\pi}{\mathrm{15}}\right)\mathrm{cos}\:\left(\frac{\mathrm{3}\pi}{\mathrm{15}}\right)\mathrm{cos}\:\left(\frac{\mathrm{4}\pi}{\mathrm{15}}\right)\mathrm{cos}\:\left(\frac{\mathrm{5}\pi}{\mathrm{15}}\right)\mathrm{cos}\:\left(\frac{\mathrm{6}\pi}{\mathrm{15}}\right)\mathrm{cos}\:\left(\frac{\mathrm{7}\pi}{\mathrm{15}}\right) \\ $$$$\mathrm{P}=?\: \\ $$ Answered by bramlexs22 last updated on 01/Jan/21 Commented by bobhans last…
Question Number 127682 by Dwaipayan Shikari last updated on 31/Dec/20 $$\frac{\pi^{\mathrm{2}} }{\mathrm{1}+\frac{\pi^{\mathrm{2}} }{\mathrm{3}−\pi^{\mathrm{2}} +\frac{\mathrm{9}\pi^{\mathrm{2}} }{\mathrm{5}−\mathrm{3}\pi^{\mathrm{2}} +\frac{\mathrm{25}\pi^{\mathrm{2}} }{\mathrm{7}−\mathrm{5}\pi^{\mathrm{2}} +\frac{\mathrm{49}\pi^{\:\mathrm{2}} }{\mathrm{9}−\mathrm{7}\pi^{\mathrm{2}} +\frac{\mathrm{81}\pi^{\mathrm{2}} }{\mathrm{11}−\mathrm{9}\pi^{\mathrm{2}} +\frac{\mathrm{121}\pi^{\mathrm{2}} }{…..}}}}}}} \\ $$…
Question Number 62147 by Tawa1 last updated on 16/Jun/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 62146 by maxmathsup by imad last updated on 16/Jun/19 $${calculate}\:\int\:\sqrt{\frac{{x}−\mathrm{1}}{{x}^{\mathrm{2}} \:+\mathrm{3}}}{dx}\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com