Question Number 87382 by mathocean1 last updated on 04/Apr/20 $$\mathrm{Show}\:\mathrm{that}\:\mathrm{tan}\frac{\mathrm{5}\pi}{\mathrm{12}}\:\:\mathrm{is}\:\mathrm{a}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{this}\: \\ $$$$\mathrm{equation}:\:{x}^{\mathrm{3}} −\mathrm{3}{x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{1}=\mathrm{0} \\ $$ Answered by ajfour last updated on 04/Apr/20 $${x}^{\mathrm{3}} +\mathrm{1}=\mathrm{3}{x}\left({x}+\mathrm{1}\right)…
Question Number 152918 by ZiYangLee last updated on 03/Sep/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{first}\:\mathrm{derivative}\:\mathrm{of}\: \\ $$$${y}={x}\sqrt{\mathrm{16}−{x}^{\mathrm{2}} }+\mathrm{16sin}^{−\mathrm{1}} \frac{{x}}{\mathrm{4}} \\ $$ Answered by puissant last updated on 03/Sep/21 $${y}={x}\sqrt{\mathrm{16}−{x}^{\mathrm{2}} }+\mathrm{16}{arcsin}\left(\frac{{x}}{\mathrm{4}}\right)…
Question Number 87378 by jagoll last updated on 04/Apr/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{tan}\:\mathrm{3x}−\mathrm{3tan}\:\mathrm{x}}{\mathrm{x}^{\mathrm{3}} } \\ $$ Commented by john santu last updated on 04/Apr/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left(\mathrm{3x}+\frac{\mathrm{1}}{\mathrm{3}}\left(\mathrm{3x}\right)^{\mathrm{3}} +\mathrm{o}\left(\left(\mathrm{3x}\right)^{\mathrm{3}}…
Question Number 152912 by mathdanisur last updated on 03/Sep/21 Answered by ghimisi last updated on 03/Sep/21 $$\Sigma\frac{{a}}{\mathrm{2}{b}+\mathrm{3}{c}}=\Sigma\frac{{a}^{\mathrm{2}} }{\mathrm{2}{ab}+\mathrm{3}{ac}}\geqslant\frac{\left({a}+{b}+{c}\right)^{\mathrm{2}} }{\mathrm{5}\left({ab}+{bc}+{ac}\right)}\geqslant\frac{\mathrm{3}\left({ab}+{bc}+{ca}\right)}{\mathrm{5}\left({ab}+{bc}+{ac}\right)}=\frac{\mathrm{3}}{\mathrm{5}} \\ $$ Commented by ghimisi last…
Question Number 87379 by john santu last updated on 04/Apr/20 $$\underset{\mathrm{k}\:=\:\mathrm{2}} {\overset{\mathrm{2010}} {\prod}}\:\frac{\mathrm{k}^{\mathrm{2}} −\mathrm{1}}{\mathrm{k}^{\mathrm{2}} }\:=\:? \\ $$ Commented by jagoll last updated on 04/Apr/20 $$\underset{\mathrm{k}\:=\:\mathrm{2}}…
Question Number 87376 by naka3546 last updated on 04/Apr/20 Answered by john santu last updated on 04/Apr/20 $$\mathrm{A}^{\mathrm{3}} \:=\:\begin{pmatrix}{\mathrm{3}\:\:\:\:−\mathrm{2}}\\{\:\mathrm{3}\:\:\:\:−\mathrm{4}}\end{pmatrix}\:−\:\begin{pmatrix}{\mathrm{2}\:\:\:\:\:−\mathrm{1}}\\{\mathrm{1}\:\:\:\:\:\:\:\:\:\mathrm{1}}\end{pmatrix} \\ $$$$\mathrm{A}^{\mathrm{3}} \:=\:\begin{pmatrix}{\mathrm{1}\:\:\:\:−\mathrm{1}}\\{\mathrm{2}\:\:\:\:−\mathrm{3}}\end{pmatrix} \\ $$$$\mathrm{det}\:\left(\mathrm{A}\right)\:=\:\sqrt[{\mathrm{3}\:\:}]{−\mathrm{3}+\mathrm{2}}\:=\:−\mathrm{1} \\…
Question Number 21840 by Joel577 last updated on 05/Oct/17 $$\mathrm{A}\:\mathrm{cone}\:\mathrm{is}\:\mathrm{placed}\:\mathrm{inside}\:\mathrm{a}\:\mathrm{sphere}. \\ $$$$\mathrm{If}\:\mathrm{volume}\:\mathrm{of}\:\mathrm{the}\:\mathrm{cone}\:\mathrm{is}\:\mathrm{maximum}, \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{ratio}\:\mathrm{of}\:\mathrm{radius}\:\mathrm{from}\:\mathrm{the}\:\mathrm{cone}\:\mathrm{and}\:\mathrm{sphere} \\ $$ Answered by mrW1 last updated on 05/Oct/17 $$\mathrm{R}=\mathrm{radius}\:\mathrm{of}\:\mathrm{sphere} \\…
Question Number 21837 by math solver last updated on 05/Oct/17 Commented by math solver last updated on 05/Oct/17 $${anyone}?? \\ $$$${will}\:{anyone}\:{answer}\:{my}\:{question}???\:\:\:\:\:\:\:\: \\ $$$$;\left(\right. \\ $$…
Question Number 152910 by 281981 last updated on 03/Sep/21 $$\int^{} {x}^{{x}^{{x}} } {dx}= \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 152904 by DELETED last updated on 03/Sep/21 Answered by DELETED last updated on 03/Sep/21 $$\left.\mathrm{1}\right).\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{4cos}\:\mathrm{x}+\mathrm{5sin}\:\mathrm{x} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{dy}}{\mathrm{dx}}\:\:\:=−\mathrm{4}\:\mathrm{sin}\:\mathrm{x}+\mathrm{5}\:\mathrm{cos}\:× \\ $$$$\left.\mathrm{2}\right).\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{3}\:\mathrm{sin}\:\mathrm{2x}\:−\:\mathrm{5}\:\mathrm{cos}\:\mathrm{x} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{dy}}{\mathrm{dx}}\:\:=\mathrm{3}×\mathrm{2}\:\mathrm{cos}\:\mathrm{2x}\:+\mathrm{5}\:\mathrm{sin}\:\mathrm{x} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{6}\:\mathrm{cos}\:\mathrm{2x}\:+\:\mathrm{5}\:\mathrm{sin}\:\mathrm{x}//…