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…
Question Number 108369 by mathdave last updated on 16/Aug/20 Answered by Rasheed.Sindhi last updated on 16/Aug/20 $${Fractions}:\:\frac{{x}}{\mathrm{8}},\frac{{y}}{\mathrm{8}} \\ $$$$ \\ $$$$\frac{{x}}{\mathrm{8}}+\frac{{y}}{\mathrm{8}}=\frac{\mathrm{1}}{\mathrm{2}}\Rightarrow{x}+{y}=\frac{\mathrm{8}}{\mathrm{2}}=\mathrm{4}…..\left({i}\right) \\ $$$$\frac{{x}}{\mathrm{8}}+\frac{\mathrm{5}{y}}{\mathrm{8}}=\mathrm{2}\Rightarrow{x}+\mathrm{5}{y}=\mathrm{16}……..\left({ii}\right) \\ $$$$\left({ii}\right)−\left({i}\right):…
Question Number 108365 by mathdave last updated on 16/Aug/20 Answered by JDamian last updated on 16/Aug/20 $${S}\:=\underset{{n}=\mathrm{1}} {\overset{\mathrm{2019}} {\sum}}\frac{\mathrm{1}+\mathrm{2}+\mathrm{3}+\:\centerdot\centerdot\centerdot\:+\:{n}}{\mathrm{1}^{\mathrm{3}} +\mathrm{2}^{\mathrm{3}} +\mathrm{3}^{\mathrm{3}} +\:\centerdot\centerdot\centerdot\:+\mathrm{2019}^{\mathrm{3}} }\:= \\ $$$$=\frac{\underset{{n}=\mathrm{1}}…
Question Number 173874 by akolade last updated on 20/Jul/22 Answered by a.lgnaoui last updated on 21/Jul/22 $$\mathrm{I}=\int_{\pi/\mathrm{4}} ^{\mathrm{15}\pi/\mathrm{4}} \left(\mathrm{sin}\:{x}\mathrm{cos}\:^{\mathrm{2}} {x}+\mathrm{3sin}^{\mathrm{2}} {x}\mathrm{cos}^{\mathrm{2}} {x}+\mathrm{4sin}^{\mathrm{5}} {x}\mathrm{cos}^{\mathrm{2}} {x}+\mathrm{2sin}^{\mathrm{3}} {x}\right){dx}=…
Question Number 108326 by abony1303 last updated on 16/Aug/20 Commented by abony1303 last updated on 16/Aug/20 $$\mathrm{pls}\:\mathrm{help} \\ $$ Answered by mr W last updated…
Question Number 108320 by Khalmohmmad last updated on 16/Aug/20 Answered by Dwaipayan Shikari last updated on 16/Aug/20 $${T}_{{n}} ={n}.\mathrm{2}{n}.\mathrm{4}{n}=\mathrm{8}{n}^{\mathrm{3}} \\ $$$${And} \\ $$$${T}_{{n}} ^{'} ={n}.\mathrm{3}{n}.\mathrm{9}{n}=\mathrm{27}{n}^{\mathrm{3}}…
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