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Q-In-AB-C-cos-A-cos-B-2cos-C-2-show-that-a-b-2c-

Question Number 212552 by mnjuly1970 last updated on 17/Oct/24 $$ \\ $$$$\:\overset{\mathrm{Q}:} {\:}\:\mathrm{In}\:\mathrm{A}\overset{\Delta} {\mathrm{B}C}\::\:\:\:{cos}\left(\mathrm{A}\right)\:+{cos}\left(\mathrm{B}\:\right)+\:\mathrm{2}{cos}\left(\mathrm{C}\:\right)=\:\mathrm{2} \\ $$$$\:\:\: \\ $$$$\:\:\:\:\:\:\mathrm{show}\:\mathrm{that}\::\:\:\:{a}\:+\:{b}\:=\:\mathrm{2}{c}\:\:\:\:\:\:\:\:\:\:\:\blacksquare\: \\ $$$$ \\ $$ Answered by Ghisom…

lim-n-2-1-n-1-2n-1-1-n-1-1-2n-e-y-2-dy-2n-1-2n-e-y-2-dy-

Question Number 212553 by MrGaster last updated on 17/Oct/24 $$ \\ $$$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\frac{\sqrt[{{n}}]{\mathrm{2}}−\mathrm{1}}{\:\sqrt[{{n}}]{\mathrm{2}{n}+\mathrm{1}}}\mid\int_{\mathrm{1}} ^{\frac{\mathrm{1}}{\mathrm{2}{n}}} {e}^{−{y}^{\mathrm{2}} } {dy}+\ldots+\int^{\frac{\mathrm{2}{n}+\mathrm{1}}{\mathrm{2}{n}}} {e}^{−{y}^{\mathrm{2}} } {dy}\mid=? \\ $$$$ \\ $$ Terms…

the-following-equation-has-no-root-find-the-relationship-between-a-b-c-1-c-2-2-c-gt-2-3-c-gt-ab-4-c-ab-eq-n-x-1-b-2-x-b-x-1-a-2-

Question Number 212550 by mnjuly1970 last updated on 17/Oct/24 $$ \\ $$$$\:\:\:\:{the}\:{following}\:{equation}\:{has} \\ $$$$\:\:\:\:\:{no}\:{root}\:.\:{find}\:{the}\:{relationship} \\ $$$$\:\:\:{between}\:{a}\:,\:{b}\:,\:{c}\:: \\ $$$$\:\:\:\:\mathrm{1}:\:\:{c}\leqslant\mathrm{2} \\ $$$$\:\:\:\:\mathrm{2}:\:{c}\:>\mathrm{2} \\ $$$$\:\:\:\:\mathrm{3}:\:{c}\:>{ab} \\ $$$$\:\:\:\:\mathrm{4}:\:{c}\leqslant\:{ab} \\…

If-x-2-yz-a-2-bc-y-2-zx-b-2-ca-z-2-xy-c-2-ab-then-prove-that-x-a-y-b-z-c-

Question Number 212576 by MATHEMATICSAM last updated on 17/Oct/24 $$\mathrm{If}\:\frac{{x}^{\mathrm{2}} \:−\:{yz}}{{a}^{\mathrm{2}} \:−\:{bc}}\:=\:\frac{{y}^{\mathrm{2}} \:−\:{zx}}{{b}^{\mathrm{2}} \:−\:{ca}}\:=\:\frac{{z}^{\mathrm{2}} \:−\:{xy}}{{c}^{\mathrm{2}} \:−\:{ab}}\:\mathrm{then}\: \\ $$$$\mathrm{prove}\:\mathrm{that}\:\frac{{x}}{{a}}\:=\:\frac{{y}}{{b}}\:=\:\frac{{z}}{{c}}\:. \\ $$ Terms of Service Privacy Policy…

lim-n-n-2-1-1-n-1-n-1-1-1-n-n-

Question Number 212544 by MrGaster last updated on 17/Oct/24 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}{n}^{\mathrm{2}} \left[\left(\mathrm{1}+\frac{\mathrm{1}}{{n}+\mathrm{1}}\right)^{{n}+\mathrm{1}} −\left(\mathrm{1}+\frac{\mathrm{1}}{{n}}\right)^{{n}} \right]=? \\ $$ Answered by lepuissantcedricjunior last updated on 17/Oct/24 $$\underset{\boldsymbol{{n}}\rightarrow+\infty} {\mathrm{lim}}\boldsymbol{{n}}^{\mathrm{2}}…

llim-n-i-1-n-1-i-n-3-1-

Question Number 212545 by MrGaster last updated on 17/Oct/24 $$\underset{{n}\rightarrow\infty} {\mathrm{llim}}\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}\left(\sqrt{\mathrm{1}+\frac{{i}}{{n}^{\mathrm{3}} }}−\mathrm{1}\right)=? \\ $$ Answered by lepuissantcedricjunior last updated on 17/Oct/24 $$\underset{\boldsymbol{{n}}\rightarrow+\infty} {\mathrm{lim}}\underset{\boldsymbol{{i}}=\mathrm{1}}…

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}}…