Question Number 145975 by mathdanisur last updated on 09/Jul/21 $$\underset{\:\mathrm{0}} {\overset{\:\mathrm{6}} {\int}}\:\left[\:\sqrt{\mathrm{36}−{x}^{\mathrm{2}} }−\left(\mathrm{6}−{x}\right)\right]{dx}=? \\ $$ Answered by puissant last updated on 09/Jul/21 $$\mathrm{x}=\mathrm{6sin}\left(\mathrm{t}\right)\Rightarrow\mathrm{dx}=\mathrm{6cos}\left(\mathrm{t}\right)\mathrm{dt} \\ $$$$\mathrm{I}=\mathrm{6}\int_{\mathrm{0}}…
Question Number 80433 by jagoll last updated on 03/Feb/20 $${find}\:{the}\:{solution}\:{of} \\ $$$$\sqrt{\mathrm{4}−{x}}−\mathrm{2}\leqslant{x}\mid{x}−\mathrm{3}\mid+\mathrm{4}{x} \\ $$ Commented by john santu last updated on 03/Feb/20 $$\left(\mathrm{1}\right)\:\mathrm{4}−{x}\geqslant\mathrm{0}\:\Rightarrow{x}\leqslant\mathrm{4} \\ $$$$\left(\mathrm{2}\right)\sqrt{\mathrm{4}−{x}\:}\leqslant{x}\mid{x}−\mathrm{3}\mid+\mathrm{4}{x}+\mathrm{2}…
Question Number 145953 by mathdanisur last updated on 09/Jul/21 Commented by mathdanisur last updated on 09/Jul/21 $${Solve}\:{the}\:{trigonometric}\:{equation} \\ $$ Commented by puissant last updated on…
Question Number 145954 by mathdanisur last updated on 09/Jul/21 $$\mathrm{1}+{i}+{i}^{\mathrm{2}} +{i}^{\mathrm{3}} +…+{i}^{\mathrm{99}} =? \\ $$ Answered by mr W last updated on 09/Jul/21 $$=\frac{\mathrm{1}−{i}^{\mathrm{100}} }{\mathrm{1}−{i}}=\frac{\mathrm{1}−\left(−\mathrm{1}\right)^{\mathrm{50}}…
Question Number 145947 by Khalmohmmad last updated on 09/Jul/21 Commented by hknkrc46 last updated on 09/Jul/21 $$\:\left.\begin{matrix}{\int\boldsymbol{{f}}\left(\boldsymbol{{x}}\right)\boldsymbol{{dx}}\:=\:\boldsymbol{{F}}\left(\boldsymbol{{x}}\right)\:+\:\boldsymbol{{c}}}\\{\int\boldsymbol{{g}}\left(\boldsymbol{{x}}\right)\boldsymbol{{dx}}\:=\:\boldsymbol{{G}}\left(\boldsymbol{{x}}\right)\:+\:\boldsymbol{{c}}}\end{matrix}\right\}\:\begin{matrix}{\boldsymbol{{G}}\left(\mathrm{2}\right)\:=\:\mathrm{3}}\\{\boldsymbol{{f}}\left(\mathrm{5}\right)\:=\:\mathrm{1}}\end{matrix} \\ $$$$ \\ $$$$\:\:\:\bullet\:\boldsymbol{{f}}\left(\boldsymbol{{x}}\right)\:=\:\boldsymbol{{F}}\:'\left(\boldsymbol{{x}}\right)\:\wedge\:\boldsymbol{{g}}\left(\boldsymbol{{x}}\right)\:=\:\boldsymbol{{G}}\:'\left(\boldsymbol{{x}}\right) \\ $$$$\:\:\:\bullet\:\frac{\boldsymbol{{d}}\left[\left(\boldsymbol{{x}}^{\mathrm{2}} \:+\:\mathrm{2}\right)\boldsymbol{{G}}\left(\boldsymbol{{x}}\right)\right]}{\boldsymbol{{dx}}}\:=\:\frac{\boldsymbol{{d}}\left[\boldsymbol{{F}}\left(\mathrm{3}\boldsymbol{{x}}\:−\:\mathrm{1}\right)\right]}{\boldsymbol{{dx}}} \\…
Question Number 80404 by peter frank last updated on 02/Feb/20 Answered by MJS last updated on 02/Feb/20 $${f}\left({x}\right):\:{y}=\frac{{x}^{\mathrm{2}} }{\mathrm{5}}\:\Rightarrow\:{f}^{−\mathrm{1}} \left({y}\right):\:{x}=\sqrt{\mathrm{5}{y}} \\ $$$${x}'=\frac{\sqrt{\mathrm{5}}}{\mathrm{2}\sqrt{{y}}} \\ $$$$\mathrm{surface}=\mathrm{2}\pi\underset{{a}} {\overset{{b}}…
Question Number 80405 by TawaTawa last updated on 02/Feb/20 $$\mathrm{Solve}: \\ $$$$\left(\mathrm{a}\right)\:\:\:\:\:\:\:\:\:\left(\mathrm{x}\:−\:\mathrm{3}\right)^{\mathrm{2}} \:\:>\:\:−\:\mathrm{5} \\ $$$$\left(\mathrm{b}\right)\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{3x}^{\mathrm{2}} \:\:>\:\:−\:\mathrm{12} \\ $$ Commented by MJS last updated on 02/Feb/20…
Question Number 145918 by mathdanisur last updated on 09/Jul/21 Answered by Olaf_Thorendsen last updated on 09/Jul/21 $${l}\:=\:\mathrm{3}+\sqrt{\mathrm{3}^{\mathrm{2}} +\sqrt{\mathrm{3}^{\mathrm{4}} +\sqrt{\mathrm{3}^{\mathrm{8}} +\sqrt{…}}}} \\ $$$$\left({l}−\mathrm{3}\right)^{\mathrm{2}} \:=\:\mathrm{3}^{\mathrm{2}} +\sqrt{\mathrm{3}^{\mathrm{4}} +\sqrt{\mathrm{3}^{\mathrm{8}}…
Question Number 80362 by Power last updated on 02/Feb/20 Answered by key of knowledge last updated on 02/Feb/20 $$\frac{\mathrm{1}}{\mathrm{1}+\mathrm{2}+…+\mathrm{i}}−\frac{\mathrm{1}}{\mathrm{1}+\mathrm{2}+…+\mathrm{i}+\left(\mathrm{i}+\mathrm{1}\right)}=\frac{\left(\mathrm{1}+…+\mathrm{i}+\left(\mathrm{i}+\mathrm{1}\right)\right)−\left(\mathrm{1}+…+\mathrm{i}\right)}{\left(\mathrm{1}+\mathrm{2}+…+\mathrm{i}\right)\left(\mathrm{1}+\mathrm{2}+…+\mathrm{i}+\left(\mathrm{i}+\mathrm{1}\right)\right)}= \\ $$$$\frac{\left(\mathrm{i}+\mathrm{1}\right)}{\left(\mathrm{1}+\mathrm{2}+…+\mathrm{i}\right)\left(\mathrm{1}+\mathrm{2}+…+\mathrm{i}+\left(\mathrm{i}+\mathrm{1}\right)\right)} \\ $$$$\Rightarrow\mathrm{1}−\left[\left(\frac{\mathrm{1}}{\mathrm{1}}−\frac{\mathrm{1}}{\mathrm{1}+\mathrm{2}}\right)+\left(\frac{\mathrm{1}}{\mathrm{1}+\mathrm{2}}−\frac{\mathrm{1}}{\mathrm{1}+\mathrm{2}+\mathrm{3}}\right)+…+\left(\frac{\mathrm{1}}{\mathrm{1}+…+\mathrm{99}}−\frac{\mathrm{1}}{\mathrm{1}+…+\mathrm{100}}\right)\right]= \\ $$$$\mathrm{1}−\left[\mathrm{1}−\frac{\mathrm{1}}{\mathrm{1}+…+\mathrm{100}}\right]=\frac{\mathrm{1}}{\mathrm{5050}}…
Question Number 145886 by bramlexs22 last updated on 09/Jul/21 $$\frac{\mathrm{x}\sqrt{\frac{\mathrm{129934}}{\mathrm{14348057}}}}{\pi^{\mathrm{2}} }\:=\:\mathrm{e}^{\pi} \:\mathrm{then}\: \\ $$$$\:\frac{\sqrt{\mathrm{x}−\mathrm{96}}}{\mathrm{4}}\:=?\: \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com