Question Number 139544 by melanie last updated on 28/Apr/21 Answered by bemath last updated on 28/Apr/21 $$\:\mathrm{Tanzalin}\:\mathrm{formula} \\ $$$$\:\begin{array}{|c|c|c|c|}{\mathrm{u}\left(\mathrm{diff}\right)}&\hline{\mathrm{dv}\:\left(\mathrm{integrate}\right)}\\{\mathrm{4x}}&\hline{\mathrm{cos}\:\left(\mathrm{2}−\mathrm{3x}\right)}\\{\mathrm{4}}&\hline{−\frac{\mathrm{1}}{\mathrm{3}}\mathrm{sin}\:\left(\mathrm{2}−\mathrm{3x}\right)}\\{\mathrm{0}}&\hline{−\frac{\mathrm{1}}{\mathrm{9}}\mathrm{cos}\:\left(\mathrm{2}−\mathrm{3x}\right)}\\\hline\end{array} \\ $$$$\mathrm{I}=\:−\frac{\mathrm{4x}\:\mathrm{sin}\:\left(\mathrm{2}−\mathrm{3x}\right)}{\mathrm{3}}\:+\frac{\mathrm{4}\:\mathrm{cos}\:\left(\mathrm{2}−\mathrm{3x}\right)}{\mathrm{9}}\:+\:\mathrm{c}\: \\ $$ Answered by…
Question Number 74006 by necxxx last updated on 17/Nov/19 $${If}\:\mathrm{3}{x}^{\mathrm{2}} {e}^{\mathrm{log}\:_{{x}} \mathrm{27}} =\mathrm{27000}\:{then}\:{find}\:{x} \\ $$ Commented by necxxx last updated on 17/Nov/19 $${please}\:{how}\:{can}\:{this}\:{be}\:{solved}\:{analytically} \\ $$$${or}\:{even}\:{by}\:{numerical}\:{methods}=…
Question Number 8468 by FilupSmith last updated on 12/Oct/16 $$\mathrm{Prove}\:\mathrm{or}\:\mathrm{disprove}\:\mathrm{that}: \\ $$$$\left(\mathrm{2}{k}+\mathrm{1}\right)^{{n}} \in\mathbb{O}\:\:\:\:\:\:\forall{k},{n}\in\mathbb{Z} \\ $$ Answered by Rasheed Soomro last updated on 12/Oct/16 $$\left(\mathrm{2k}+\mathrm{1}\right)^{\mathrm{n}} =\begin{pmatrix}{\mathrm{n}}\\{\mathrm{0}}\end{pmatrix}\left(\mathrm{2k}\right)^{\mathrm{n}}…
Question Number 8466 by FilupSmith last updated on 12/Oct/16 $${t}={n}^{\mathrm{3}} −{n}^{\mathrm{2}} \\ $$$${t}\in\mathbb{E} \\ $$$$\mathrm{Give}\:\mathrm{a}\:\mathrm{general}\:\mathrm{form}\:\mathrm{solving}\:\mathrm{for}\:{n} \\ $$$${i}.{e} \\ $$$${n}^{\mathrm{3}} −{n}^{\mathrm{2}} =\mathrm{2}{k} \\ $$$${n}=? \\ $$…
Question Number 139532 by mathdanisur last updated on 28/Apr/21 $$\frac{\mathrm{1}}{\mathrm{3}}\:−\:\frac{{x}−\mathrm{3}}{\mathrm{9}}\:+\:\frac{\left({x}−\mathrm{3}\right)^{\mathrm{2}} }{\mathrm{27}}\:+\:…\:=? \\ $$ Commented by mr W last updated on 28/Apr/21 $$=\frac{\mathrm{1}}{{x}} \\ $$ Commented…
Question Number 139505 by bemath last updated on 28/Apr/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{greatest}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x}^{\mathrm{2}} \mathrm{y}^{\mathrm{3}} \: \\ $$$$\mathrm{when}\:\mathrm{3x}+\mathrm{4y}=\mathrm{5} \\ $$ Commented by mr W last updated on 28/Apr/21 $$\mathrm{3}{x}+\mathrm{4}{y}=\mathrm{5}\:\Rightarrow{y}\in\left(−\infty,\infty\right)…
Question Number 139502 by bemath last updated on 28/Apr/21 $$\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{8x}}\:\leqslant\:\mathrm{24}−\left(\mathrm{x}+\mathrm{2}\right)\left(\mathrm{x}+\mathrm{6}\right) \\ $$$$ \\ $$ Answered by TheSupreme last updated on 28/Apr/21 $${domain}:\:{x}<−\mathrm{8}\:\vee\:{x}>\mathrm{0} \\ $$$$\begin{cases}{\mathrm{24}−\left({x}+\mathrm{2}\right)\left({x}+\mathrm{6}\right)>\mathrm{0}\rightarrow\mathrm{12}−{x}^{\mathrm{2}}…
Question Number 139490 by EnterUsername last updated on 27/Apr/21 $$\mathrm{If}\:{w}\neq\mathrm{1}\:\mathrm{is}\:\mathrm{a}\:\mathrm{cube}\:\mathrm{root}\:\mathrm{of}\:\mathrm{unity},\:\mathrm{x}={a}+{b},\:\mathrm{y}={aw}+{bw}^{\mathrm{2}} \\ $$$$\mathrm{and}\:{z}={aw}^{\mathrm{2}} +{bw},\:\mathrm{then}\:\mathrm{x}^{\mathrm{3}} +\mathrm{y}^{\mathrm{3}} +{z}^{\mathrm{3}} =? \\ $$ Answered by Rasheed.Sindhi last updated on 27/Apr/21…
Question Number 139474 by mathdanisur last updated on 27/Apr/21 $${let}:\:\:\Omega_{\boldsymbol{{n}}} =\underset{\:\mathrm{0}} {\overset{\:\mathrm{2}\pi} {\int}}{cos}\left({x}\right)\centerdot{cos}\left(\mathrm{2}{x}\right)\centerdot…\centerdot{cos}\left({nx}\right)\:{dx} \\ $$$${for}\:{which}\:{integers}\:{n},\:\mathrm{1}\leqslant{n}\leqslant\mathrm{10},\:{is}\:\Omega_{\boldsymbol{{n}}} \neq\mathrm{0}? \\ $$ Answered by mathmax by abdo last updated…
Question Number 139468 by mathdanisur last updated on 27/Apr/21 $${prove}:\:\:\sqrt{\mathrm{3}+\sqrt{\mathrm{2}}−\sqrt{\mathrm{9}+\mathrm{4}\sqrt{\mathrm{2}}}}\:=\:\sqrt{\mathrm{2}−\sqrt{\mathrm{2}}} \\ $$ Answered by OlafThorendsen last updated on 27/Apr/21 $${x}\:=\:\:\sqrt{\mathrm{3}+\sqrt{\mathrm{2}}−\sqrt{\mathrm{9}+\mathrm{4}\sqrt{\mathrm{2}}}} \\ $$$${x}\:=\:\:\sqrt{\mathrm{3}+\sqrt{\mathrm{2}}−\sqrt{\left(\mathrm{1}+\mathrm{2}\sqrt{\mathrm{2}}\right)^{\mathrm{2}} }} \\ $$$${x}\:=\:\:\sqrt{\mathrm{3}+\sqrt{\mathrm{2}}−\left(\mathrm{1}+\mathrm{2}\sqrt{\mathrm{2}}\right)}…