Question Number 212579 by MrGaster last updated on 18/Oct/24 $$\mathrm{Have}\:\mathrm{you}\:\mathrm{ever}\:\mathrm{wondered}\:\mathrm{why}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{ofd} \\ $$$$\mathrm{igits}\:\mathrm{in}\:\mathrm{decimal}\:\mathrm{system}\:\mathrm{is}\:\mathrm{a}\:\mathrm{multiple}\:\mathrm{of}\:\mathrm{3a} \\ $$$$\mathrm{nd}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{digits}\:\mathrm{in}\:\mathrm{decimal}\:\mathrm{system}\: \\ $$$$\mathrm{isa}\:\mathrm{multiple}\:\mathrm{of}\:\mathrm{9}\:\mathrm{Prove}\:\mathrm{the}\:\mathrm{abovei} \\ $$$$\mathrm{propertes}. \\ $$ Terms of Service Privacy Policy…
Question Number 212513 by MrGaster last updated on 16/Oct/24 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{certificate}: \\ $$$$\:\:\:\:\:\:\:\:\:{x}^{\mathrm{2}{n}} −\mathrm{1} \\ $$$$\mathrm{Can}\:\mathrm{always}\:\mathrm{be}\:{x}+\mathrm{1}\:\mathrm{be}\:\mathrm{divisible}\:\:\:\:\:\:\:\:\: \\ $$ Answered by A5T last updated on 16/Oct/24 $${x}\equiv−\mathrm{1}\left({mod}\:{x}+\mathrm{1}\right)\Rightarrow{x}^{\mathrm{2}{n}}…
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Question Number 212492 by MrGaster last updated on 15/Oct/24 $$\mathrm{Given}\:\mathrm{that}\:{x}\:\in\:\mathbb{R}\left(\right. \\ $$$$\:\left(\mathrm{the}\:\mathrm{set}\:\mathrm{of}\:\mathrm{real}\:\mathrm{numbers}\right)\mathrm{d} \\ $$$$\mathrm{an}\:{n}\:\in\:\mathbb{N}^{\ast} \\ $$$$\left(\mathrm{the}\:\mathrm{set}\:\mathrm{of}\:\mathrm{positive}\:\mathrm{naturalu}\right. \\ $$$$\left.\mathrm{nmbers}\right)\:\mathrm{prove}\:\mathrm{that}\:: \\ $$$$\mid\mathrm{cos}\:{x}\mid+\mid\mathrm{cos}\:\mathrm{2}{x}\mid+\mid\mathrm{cos}\:\mathrm{3}{x}\mid+\ldots+\mid\mathrm{cos}\left({n}+\mathrm{1}\right){x}\mid\geq\frac{{n}}{\mathrm{2}} \\ $$ Terms of Service…
Question Number 212464 by liuxinnan last updated on 14/Oct/24 Commented by liuxinnan last updated on 14/Oct/24 $${is}\:{it}\:{right} \\ $$ Answered by MrGaster last updated on…
Question Number 212467 by Hanuda354 last updated on 14/Oct/24 $$\mathrm{Use}\:\:\mathrm{the}\:\:\mathrm{integration}\:\:\mathrm{by}\:\:\mathrm{parts}. \\ $$$$ \\ $$$$\int\:\frac{\mathrm{2}}{\:\sqrt{{r}^{\mathrm{2}} −\mathrm{4}}}\:{dr}\: \\ $$ Answered by mehdee7396 last updated on 14/Oct/24 $${r}=\mathrm{2}{coshx}\Rightarrow{dr}=\mathrm{2}{sinhxdx}…
Question Number 212462 by MrGaster last updated on 14/Oct/24 $$\mathrm{1}.\:\mathrm{In}\:\mathrm{a}\:\mathrm{plane}\:\mathrm{there}\:\mathrm{are}\:\mathrm{nt} \\ $$$$\mathrm{poins}\:\mathrm{arranged}\:\mathrm{such}\:\mathrm{that}\: \\ $$$$\mathrm{nostraight}\:\mathrm{line}\:\mathrm{passesg} \\ $$$$\mathrm{throuh}\:\mathrm{more}\:\mathrm{than}\:\mathrm{3}\:\mathrm{points}.\mathrm{h} \\ $$$$\mathrm{Wat}\:\mathrm{is}\:\mathrm{the}\:\mathrm{maximume} \\ $$$$\mathrm{numbr}\:\mathrm{of}\:\mathrm{straight}\:\mathrm{lines}\: \\ $$$$\mathrm{thatcan}\:\mathrm{pass}\:\mathrm{throughy} \\ $$$$\mathrm{exactl}\:\mathrm{3}\:\mathrm{points2}.\:\mathrm{If}\:\mathrm{thee} \\…
Question Number 212456 by Hanuda354 last updated on 14/Oct/24 $$\int\:\:\frac{\sqrt{\mathrm{9}{x}^{\mathrm{2}} −\mathrm{49}}}{{x}^{\mathrm{3}} }\:\:{dx}\:=\:? \\ $$ Answered by Sutrisno last updated on 14/Oct/24 $$\int\frac{\sqrt{\left(\mathrm{3}{x}\right)^{\mathrm{2}} −\mathrm{7}^{\mathrm{2}} }}{{x}^{\mathrm{3}} }{dx}…
Question Number 212415 by MrGaster last updated on 13/Oct/24 $$\:\:\:\:\:\:\:\:\:\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{2}^{\frac{{k}}{{n}}} }{{n}+\frac{\mathrm{1}}{{k}}} \\ $$$$ \\ $$ Answered by Frix last updated on 13/Oct/24…
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