Question Number 153553 by mnjuly1970 last updated on 08/Sep/21 $$ \\ $$$$\:{sin}\left(\mathrm{9}\right)\:+\:{sin}\left(\mathrm{21}\right)+{sin}\left(\mathrm{39}\right)\overset{?} {=}\frac{\varphi}{\:\sqrt{\mathrm{2}}} \\ $$$$\:\:\:\varphi:=\:{golden}\:{ratio} \\ $$$$\:{m}.{n} \\ $$ Answered by bramlexs22 last updated on…
Question Number 88015 by M±th+et£s last updated on 07/Apr/20 $${if}\:{u}={f}\left({x},{y}\right)\:{where}\:{x}={rcos}\left(\theta\right)\:\:,\:{y}={r}\:{sin}\left(\theta\right) \\ $$$${prove}\: \\ $$$$\left(\frac{\partial{u}}{\partial{x}}\right)^{\mathrm{2}} +\left(\frac{\partial{u}}{\partial{y}}\right)^{\mathrm{2}} =\left(\frac{\partial{u}}{\partial{r}}\right)^{\mathrm{2}} +\frac{\mathrm{1}}{{r}}\left(\frac{\partial{u}}{\partial\theta}\right)^{\mathrm{2}} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 87989 by john santu last updated on 07/Apr/20 $$\mathrm{find}\:\mathrm{maximum}\:\mathrm{value} \\ $$$$\mathrm{2x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} \:\mathrm{with}\:\mathrm{constraint} \\ $$$$\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} −\mathrm{4x}+\mathrm{2y}+\mathrm{1}=\mathrm{0}\: \\ $$$$ \\ $$ Answered by…
Question Number 22332 by A1B1C1D1 last updated on 15/Oct/17 Answered by ajfour last updated on 15/Oct/17 $$\frac{{d}\left[{f}\left({x}\right)\right]}{{dx}}=\mathrm{1}+\mathrm{2cos}\:{x}=\mathrm{0} \\ $$$$\Rightarrow\:\mathrm{cos}\:{x}=−\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\:\:\:\:\:{x}=\mathrm{2}{n}\pi\pm\frac{\mathrm{2}\pi}{\mathrm{3}}\:\:{where}\:{n}\in\mathbb{Z}\:. \\ $$$$\:\:\:\:{which}\:{is}\:{equivalent}\:{to} \\ $$$$\:\:\:\:{x}=\left(\mathrm{2}{n}+\mathrm{1}\right)\pi\pm\frac{\pi}{\mathrm{3}}\:.…
Question Number 153340 by mnjuly1970 last updated on 06/Sep/21 $$ \\ $$$$\:\:\:\:\:\mathrm{Solve}\:.. \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{x}\:,\:\mathrm{y}\:,\:\mathrm{z}\:\in\:\mathbb{R}^{\:+} \:\&\:\:\mathrm{x}+\:\mathrm{y}=\:\mathrm{z} \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{K}\::=\:\mathrm{Min}_{\:} \:\left(\frac{\:\mathrm{x}^{\:\mathrm{4}} \:+\:\mathrm{y}^{\:\mathrm{4}} +\:\mathrm{z}^{\:\mathrm{4}} }{\mathrm{x}^{\:\mathrm{2}} \mathrm{y}^{\:\mathrm{2}} }\:\right)\:=\:?\:\:\:\:\:\:\:\:\:\:\blacksquare\:\:\:\:\:\:\:\:\:…
Question Number 153252 by liberty last updated on 06/Sep/21 Answered by MJS_new last updated on 06/Sep/21 $${y}''=\mathrm{0} \\ $$$$\frac{\mathrm{2}{ax}\left({x}^{\mathrm{2}} −\mathrm{3}{b}\right)}{\left({x}^{\mathrm{2}} +{b}\right)^{\mathrm{3}} }=\mathrm{0} \\ $$$$\Rightarrow\:{x}=\mathrm{0}\vee{x}=\pm\sqrt{\mathrm{3}{b}}\vee{a}=\mathrm{0}\:\left(\mathrm{rejected}\right) \\…
Question Number 87687 by ~blr237~ last updated on 05/Apr/20 $${Let}\:\:{w}=\left[\mathrm{1};\frac{\pi}{{n}}\right]\:,{n}\in\mathbb{N}^{\ast} \: \\ $$$$\:{a}_{{n}} =\underset{{p}=\mathrm{0}} {\overset{{n}−\mathrm{1}} {\sum}}\:\frac{\mathrm{2}{p}+\mathrm{1}}{\mathrm{1}−{w}^{\mathrm{2}{p}+\mathrm{1}} }\:\:\:\:{and}\:\:\:{b}_{{n}} =\underset{{p}=\mathrm{0}} {\overset{{n}−\mathrm{1}} {\sum}}\:\frac{{n}}{\mathrm{1}+{w}^{{p}} }\: \\ $$$${Find}\:\:{all}\:{integer}\:{n}\:{such}\:{as}\:\:{a}_{{n}} ={b}_{{n}} \:…
Question Number 153212 by mnjuly1970 last updated on 05/Sep/21 $$ \\ $$$$\:\:\int_{−\infty} ^{\:\infty} \frac{\:{tan}\left({x}\right).{Arctanh}\left({cos}\left({x}\right)\right)}{{x}}{dx}=? \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 153189 by liberty last updated on 05/Sep/21 Answered by EDWIN88 last updated on 05/Sep/21 $$\:{eq}\:{of}\:{circle}\:\mathrm{16}{x}^{\mathrm{2}} +\mathrm{16}{y}^{\mathrm{2}} +\mathrm{48}{x}−\mathrm{8}{y}−\mathrm{43}= \\ $$$${with}\:{center}\:{point}\:\begin{cases}{{x}=−\frac{\mathrm{48}}{\mathrm{32}}=−\frac{\mathrm{3}}{\mathrm{2}}}\\{{y}=\frac{\mathrm{8}}{\mathrm{32}}=\frac{\mathrm{1}}{\mathrm{4}}}\end{cases} \\ $$$${with}\:{radius}\:=\sqrt{\frac{\mathrm{9}}{\mathrm{4}}+\frac{\mathrm{1}}{\mathrm{6}}−\left(\frac{−\mathrm{43}}{\mathrm{16}}\right)} \\ $$$$\Rightarrow{r}=\sqrt{\frac{\mathrm{36}+\mathrm{1}+\mathrm{43}}{\mathrm{16}}}\:=\frac{\mathrm{4}\sqrt{\mathrm{5}}}{\mathrm{4}}=\sqrt{\mathrm{5}}\:…
Question Number 22105 by j.masanja06@gmail.com last updated on 11/Oct/17 $${use}\:{the}\:{first}\:{principle}\:{to}\:{find} \\ $$$${value}\:{of} \\ $$$${f}\left({x}\right)=\left({x}\right)^{\frac{\mathrm{1}}{\mathrm{3}}} \\ $$ Answered by $@ty@m last updated on 11/Oct/17 $$\frac{{dy}}{{dx}}=\underset{\delta{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{f}\left({x}+\delta{x}\right)−{f}\left({x}\right)}{\delta{x}}…