Question Number 195612 by Mastermind last updated on 05/Aug/23 Answered by a.lgnaoui last updated on 05/Aug/23 $$\mathrm{r}−\mathrm{73}=\pm\mathrm{16} \\ $$$$\begin{cases}{\mathrm{r}−\mathrm{73}=\mathrm{16}\:\:\:\:\:\:\:\:\Rightarrow\:\:\boldsymbol{\mathrm{r}}=\mathrm{89}}\\{\boldsymbol{\mathrm{r}}−\mathrm{73}=−\mathrm{16}\:\:\:\Rightarrow\:\:\boldsymbol{\mathrm{r}}=\mathrm{57}}\end{cases} \\ $$$$\:\:\:\:\boldsymbol{\mathrm{r}}=\left\{\mathrm{57},\mathrm{89}\right\} \\ $$ Terms of…
Question Number 195608 by Rodier97 last updated on 05/Aug/23 $$ \\ $$$$ \\ $$$$ \\ $$$$\:\:\:{solve}\::\:\:\:\int_{\mathrm{0}} ^{\:\pi} \:\left(\mathrm{sin}\:{x}\right)^{\mathrm{cos}\:{x}} \:{dx} \\ $$$$ \\ $$$$ \\ $$$$…
Question Number 195611 by Mingma last updated on 05/Aug/23 Answered by mr W last updated on 06/Aug/23 $${a}={side}\:{length}\:{of}\:{small}\:{pentagon} \\ $$$${b}={side}\:{length}\:{of}\:{big}\:{pentagon} \\ $$$${b}=\mathrm{2}{a}\:\mathrm{sin}\:\mathrm{54}° \\ $$$${a}=\mathrm{2}{r}\:\mathrm{sin}\:\mathrm{36}°\:\Rightarrow{r}=\frac{{a}}{\mathrm{2}\:\mathrm{sin}\:\mathrm{36}°} \\…
Question Number 195578 by sonukgindia last updated on 05/Aug/23 Answered by Frix last updated on 05/Aug/23 $$\mathrm{sin}\:\alpha\:+\mathrm{cos}\:\alpha\:=\frac{\sqrt{\mathrm{3}}}{\mathrm{3}} \\ $$$${t}=\mathrm{tan}\:\alpha \\ $$$$\frac{{t}+\mathrm{1}}{\:\sqrt{{t}^{\mathrm{2}} +\mathrm{1}}}=\frac{\sqrt{\mathrm{3}}}{\mathrm{3}} \\ $$$${t}=−\frac{\mathrm{3}−\sqrt{\mathrm{5}}}{\mathrm{2}}\:\Rightarrow \\…
Question Number 195606 by Mastermind last updated on 05/Aug/23 Commented by mr W last updated on 08/Aug/23 $${do}\:{you}\:{have}\:{the}\:{solution}\:{of}\:{the} \\ $$$${question}? \\ $$ Terms of Service…
Question Number 195569 by York12 last updated on 05/Aug/23 $${a}_{{i}} ,{b}_{{i}} ,{x}_{{i}} {be}\:{reals}\:{for}\:{i}=\mathrm{1},\mathrm{2},\mathrm{3},…,{n},\:{such}\:{that} \\ $$$$\sum_{{i}=\mathrm{1}} ^{{n}} \left[{a}_{{i}} {x}_{{i}} \right]=\mathrm{0}.\:{Prove}\:{that} \\ $$$$\left(\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}\left[{x}_{{i}} ^{\mathrm{2}} \right]\right)\left(\underset{{i}=\mathrm{1}}…
Question Number 195571 by York12 last updated on 05/Aug/23 $${let}\:{f}\left({x}+{y}\right)+{f}\left({x}−{y}\right)=\mathrm{2}{f}\left({x}\right){f}\left({y}\right)\wedge{f}\left(\frac{\mathrm{1}}{\mathrm{2}}\right)=−\mathrm{1} \\ $$$${compute}\:\underset{{k}=\mathrm{1}} {\overset{\mathrm{20}} {\sum}}\left[\frac{\mathrm{1}}{\mathrm{sin}\:\left({k}\right)\mathrm{sin}\:\left({k}+{f}\left({k}\right)\right)}\right] \\ $$ Answered by mahdipoor last updated on 05/Aug/23 $${x}=\mathrm{1}/\mathrm{2}\:\:\:{y}=\mathrm{0}\:\Rightarrow\:\mathrm{2}{f}\left(\mathrm{1}/\mathrm{2}\right)=\mathrm{2}{f}\left(\mathrm{1}/\mathrm{2}\right){f}\left(\mathrm{0}\right)\:\Rightarrow{f}\left(\mathrm{0}\right)=\mathrm{1} \\…
Question Number 195602 by mokys last updated on 05/Aug/23 $${solve}\:\int\:\frac{{dx}}{{sin}^{\mathrm{10}} \left({x}\right)+{cos}^{\mathrm{10}} \left({x}\right)} \\ $$ Answered by Frix last updated on 06/Aug/23 $$\int\frac{{dx}}{\mathrm{sin}^{\mathrm{10}} \:{x}\:+\mathrm{cos}^{\mathrm{10}} \:{x}}= \\…
Question Number 195570 by York12 last updated on 05/Aug/23 $$\mathrm{Given}\:\mathrm{three}\:\mathrm{Real}\:\mathrm{numbers}\:\left({x},{y},{z}\right),{such}\:{that} \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} =\mathrm{1} \\ $$$${maximize} \\ $$$${x}^{\mathrm{4}} +{y}^{\mathrm{4}} −\mathrm{2}{z}^{\mathrm{4}} −\mathrm{3}\sqrt{\mathrm{2}}{xyz} \\ $$ Commented…
Question Number 195597 by sonukgindia last updated on 05/Aug/23 Terms of Service Privacy Policy Contact: info@tinkutara.com