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Author: Tinku Tara

Have-you-ever-wondered-why-the-sum-ofd-igits-in-decimal-system-is-a-multiple-of-3a-nd-the-sum-of-digits-in-decimal-system-isa-multiple-of-9-Prove-the-abovei-propertes-

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…

Find-x-sin-88pi-2-x-1-cos-3x-

Question Number 212541 by hardmath last updated on 16/Oct/24 $$\mathrm{Find}:\:\:\boldsymbol{\mathrm{x}}\:=\:? \\ $$$$\mathrm{sin}\left(\frac{\mathrm{88}\pi^{\mathrm{2}} }{\mathrm{x}}\right)\:=\:\frac{\mathrm{1}}{\mathrm{cos}\left(\mathrm{3x}\right)} \\ $$ Answered by Frix last updated on 17/Oct/24 $$\mathrm{sin}\:\frac{\mathrm{88}\pi^{\mathrm{2}} }{{x}}\:\in\left[−\mathrm{1},\:\mathrm{1}\right] \\…

given-isoscele-triangle-with-sides-10-and-inradius-3-how-find-base-

Question Number 212533 by emilagazade last updated on 16/Oct/24 $${given}\:{isoscele}\:{triangle}\:{with}\:{sides}\:\mathrm{10}\:{and}\:{inradius}\:\mathrm{3}.\:{how}\:{find}\:{base}? \\ $$ Answered by A5T last updated on 16/Oct/24 $${Let}\:{base}={b}\:;{angle}\:{between}\:{non}-{equal}\:{sides}=\theta \\ $$$$\left[\bigtriangleup\right]=\frac{\mathrm{10}×\mathrm{10}{sin}\left(\mathrm{180}−\mathrm{2}\theta\right)}{\mathrm{2}}=\frac{{b}×\mathrm{10}×{sin}\theta}{\mathrm{2}} \\ $$$$\Rightarrow\mathrm{50}×\mathrm{2}{cos}\theta=\mathrm{5}{b}\Rightarrow{cos}\theta=\frac{{b}}{\mathrm{20}}\Rightarrow{sin}\theta=\frac{\sqrt{\mathrm{400}−{b}^{\mathrm{2}} }}{\mathrm{20}}…

Question-212531

Question Number 212531 by RojaTaniya last updated on 16/Oct/24 Answered by a.lgnaoui last updated on 17/Oct/24 $$\boldsymbol{\mathrm{x}}=\mathrm{1}+^{\mathrm{7}} \sqrt{\mathrm{2}}\:+\left(^{\mathrm{7}} \sqrt{\mathrm{2}}\:\right)^{\mathrm{2}} +\left(^{\mathrm{7}} \sqrt{\mathrm{2}}\:\right)^{\mathrm{3}} +\left(^{\mathrm{7}} \sqrt{\mathrm{2}\:}\:\right)^{\mathrm{4}} +\left(^{\mathrm{7}} \sqrt{\mathrm{2}}\:\right)^{\mathrm{5}}…

in-how-many-ways-we-can-distribute-6-distinct-balls-in-3-identical-boxes-

Question Number 212522 by Nadirhashim last updated on 16/Oct/24 $$\:\:\boldsymbol{{in}}\:\boldsymbol{{how}}\:\boldsymbol{{many}}\:\boldsymbol{{ways}}\:\boldsymbol{{we}} \\ $$$$\boldsymbol{{can}}\:\boldsymbol{{distribute}}\:\mathrm{6}\:\boldsymbol{{distinct}} \\ $$$$\boldsymbol{{balls}}\:\boldsymbol{{in}}\:\mathrm{3}\:\boldsymbol{{identical}}\:\boldsymbol{{boxes}} \\ $$ Answered by mehdee7396 last updated on 16/Oct/24 $$\:\mathrm{6}/\mathrm{0}/\mathrm{0}\:{or}\:\mathrm{5}/\mathrm{1}/\mathrm{0}\:{or}\:\mathrm{4}/\mathrm{2}/\mathrm{0}\:\:{or}\:\mathrm{4}/\mathrm{1}/\mathrm{1}\:{or}\:\mathrm{3}/\mathrm{3}/\mathrm{0}/\:{or}\:\mathrm{3}/\mathrm{2}/\mathrm{1}\:{or}\:\mathrm{2}/\mathrm{2}/\mathrm{2} \\…

Question-212518

Question Number 212518 by efronzo1 last updated on 16/Oct/24 $$\:\:\:\cancel{\underbrace{\downharpoonleft}\underline{}\:} \\ $$ Answered by golsendro last updated on 16/Oct/24 $$\:\:\:\cancel{\underline{\underbrace{\pm}} }=\:\left(\mathrm{x}−\mathrm{a}\right)^{\mathrm{2}} +\mathrm{a}\: \\ $$$$\:\:\mathrm{f}^{−\mathrm{1}} \left(\mathrm{x}\right)=\:\sqrt{\mathrm{x}−\mathrm{a}}\:+\mathrm{a}\:…

certificate-x-1-x-2n-1-1-and-x-1-x-2n-1-1-All-established-2024-10-16-

Question Number 212519 by MrGaster last updated on 16/Oct/24 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{certificate}: \\ $$$$\:\:\:\:\:\left({x}−\mathrm{1}\right)\mid\left({x}^{\mathrm{2}{n}+\mathrm{1}} −\mathrm{1}\right)\mathrm{and}\left({x}+\mathrm{1}\right)\mid\left({x}^{\mathrm{2}{n}+\mathrm{1}} +\mathrm{1}\right) \\ $$$$\mathrm{All}\:\mathrm{established} \\ $$$$\left[\mathrm{2024}.\mathrm{10}.\mathrm{16}\right] \\ $$ Answered by mathmax last updated…

certificate-x-2n-1-Can-always-be-x-1-be-divisible-

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}}…