Question Number 108420 by mathdave last updated on 16/Aug/20 Answered by prakash jain last updated on 18/Sep/20 $$−−−−−−−−−−−−−−−− \\ $$$$\mathrm{12}+\mathrm{3}=\mathrm{15}\:\mathrm{dashes} \\ $$$$\mathrm{select}\:\mathrm{3}\:\mathrm{dashes}\:\mathrm{and}\:\mathrm{change}\:\mathrm{them}\:\mathrm{to} \\ $$$$\mathrm{bar}\:\mathrm{it}\:\mathrm{will}\:\mathrm{create}\:\mathrm{four}\:\mathrm{partions} \\…
Question Number 108417 by mathdave last updated on 16/Aug/20 Answered by Aziztisffola last updated on 16/Aug/20 $$\mathrm{t}=\mathrm{2x}\:\Rightarrow\mathrm{dt}=\mathrm{2dx} \\ $$$$\int_{\mathrm{0}} ^{\:\infty} \frac{\mathrm{2x}}{\mathrm{e}^{\mathrm{2x}} −\mathrm{1}}\:\mathrm{dx}=\frac{\mathrm{1}}{\mathrm{2}}\int_{\mathrm{0}} ^{\:\infty} \frac{\mathrm{t}}{\mathrm{e}^{\mathrm{t}} −\mathrm{1}}\:\mathrm{dt}…
Question Number 108416 by mathdave last updated on 16/Aug/20 Answered by mathmax by abdo last updated on 16/Aug/20 $$\mathrm{I}\:=\int\:\mathrm{ln}\left(\sqrt{\mathrm{1}+\mathrm{x}}+\sqrt{\mathrm{1}−\mathrm{x}}\right)\mathrm{dx}\:\mathrm{we}\:\mathrm{do}\:\mathrm{the}\:\mathrm{changement}\:\mathrm{x}\:=\mathrm{cos}\left(\mathrm{2t}\right)\:\Rightarrow \\ $$$$\mathrm{I}\:=\int\:\mathrm{ln}\left(\sqrt{\mathrm{2cos}^{\mathrm{2}} \mathrm{t}}\:+\sqrt{\mathrm{2sin}^{\mathrm{2}} \mathrm{t}}\right)\left(−\mathrm{2sin}\left(\mathrm{2t}\right)\:\mathrm{dt}\right. \\ $$$$=−\mathrm{2}\:\int\:\mathrm{ln}\left(\sqrt{\mathrm{2}}\left(\mathrm{cost}\:+\mathrm{sint}\right)\mathrm{sin}\left(\mathrm{2t}\right)\mathrm{dt}\right.…
Question Number 108415 by mathdave last updated on 16/Aug/20 Commented by bobhans last updated on 17/Aug/20 $$\frac{\mathrm{1}}{{n}\left({n}+\mathrm{2}\right)\left({n}+\mathrm{4}\right)}\:=\:\frac{{p}}{{n}}+\frac{{q}}{{n}+\mathrm{2}}+\frac{{r}}{{n}+\mathrm{4}} \\ $$$$\mathrm{1}={p}\left({n}+\mathrm{2}\right)\left({n}+\mathrm{4}\right)+{qn}\left({n}+\mathrm{4}\right)+{rn}\left({n}+\mathrm{2}\right) \\ $$$${n}=\mathrm{0}\Rightarrow\mathrm{1}=\mathrm{8}{p}\rightarrow{p}=\frac{\mathrm{1}}{\mathrm{8}} \\ $$$${n}=−\mathrm{2}\Rightarrow\mathrm{1}=−\mathrm{4}{q}\rightarrow{q}=−\frac{\mathrm{1}}{\mathrm{4}} \\ $$$${n}=−\mathrm{4}\Rightarrow\mathrm{1}=\mathrm{8}{r}\rightarrow{r}=\frac{\mathrm{1}}{\mathrm{8}}…
Question Number 108413 by Yusufa last updated on 16/Aug/20 $$\mathrm{228}{x}=\mathrm{87}\:{find}\:{x} \\ $$ Answered by Aziztisffola last updated on 16/Aug/20 $${x}=\frac{\mathrm{87}}{\mathrm{288}} \\ $$ Commented by Sarah85…
Question Number 42861 by mondodotto@gmail.com last updated on 03/Sep/18 $$\mathrm{14}\boldsymbol{\div}\mathrm{2}\left(\mathrm{3}+\mathrm{4}\right)=? \\ $$ Answered by MJS last updated on 03/Sep/18 $$\mathrm{brackets}\:\mathrm{first} \\ $$$$×/\:\mathrm{before}\:+− \\ $$$$\mathrm{14}/\mathrm{2}×\left(\mathrm{3}+\mathrm{4}\right)=\mathrm{14}/\mathrm{2}×\mathrm{7}=\mathrm{49} \\…
Question Number 108389 by mathdave last updated on 16/Aug/20 Answered by mbertrand658 last updated on 19/Aug/20 $$\left({a}\right) \\ $$$$\mathrm{V}\:=\:\frac{\mathrm{1}}{\mathrm{3}}\pi{r}^{\mathrm{2}} {h} \\ $$$${h}\:=\:\mathrm{8}.\mathrm{1}\:\Rightarrow\:{r}\:=\:\frac{\mathrm{2}}{\mathrm{3}}\left(\mathrm{8}.\mathrm{1}\right)\:=\:\mathrm{5}.\mathrm{4} \\ $$$$\mathrm{V}\:=\:\frac{\mathrm{1}}{\mathrm{3}}\pi\left(\mathrm{5}.\mathrm{4}\right)^{\mathrm{2}} \left(\mathrm{8}.\mathrm{1}\right)…
Question Number 108370 by mathdave last updated on 16/Aug/20 Commented by som(math1967) last updated on 16/Aug/20 $$\angle\mathrm{XZY}=\frac{\mathrm{130}}{\mathrm{2}}=\mathrm{65}° \\ $$$$\angle\mathrm{OZX}=\angle\mathrm{OXZ}=\mathrm{38}° \\ $$$$\therefore\angle\mathrm{OYZ}=\angle\mathrm{OZY}=\mathrm{65}−\mathrm{38}=\mathrm{27}° \\ $$$$\angle\mathrm{ZOY}=\mathrm{180}−\mathrm{27}−\mathrm{27}=\mathrm{126}° \\ $$…
Question Number 108371 by Skabetix last updated on 16/Aug/20 $${prove}\:{by}\:{reccurence}\: \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{4}}+\frac{\mathrm{1}}{\mathrm{6}}+…+\frac{\mathrm{1}}{\mathrm{2}{n}}<{or}\:=\frac{{n}}{\mathrm{2}} \\ $$$${thanks} \\ $$ Answered by Aziztisffola last updated on 16/Aug/20 $$\:\mathrm{for}\:\mathrm{n}=\mathrm{1}\:\Rightarrow\frac{\mathrm{1}}{\mathrm{2}}\leqslant\frac{\mathrm{1}}{\mathrm{2}}\:\:\mathrm{true} \\…
Question Number 108366 by mathdave last updated on 16/Aug/20 Commented by som(math1967) last updated on 16/Aug/20 $$\angle\mathrm{QRU}=\angle\mathrm{STU}=\mathrm{124}° \\ $$$$\therefore\angle\mathrm{RQU}=\mathrm{180}−\mathrm{124}−\mathrm{31} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{25}° \\ $$ Terms of…