Question Number 175250 by Shrinava last updated on 24/Aug/22 $$\mathrm{If}\:\mathrm{in}\:\:\bigtriangleup\mathrm{ABC}\:\:\mathrm{and}\:\:\mathrm{A}\:=\:\frac{\mathrm{2}\pi}{\mathrm{3}}\:\:\mathrm{then}: \\ $$$$\left(\sqrt{\frac{\mathrm{1}}{\mathrm{sinB}}}\right)^{\mathrm{3}} +\:\left(\sqrt{\frac{\mathrm{1}}{\mathrm{sinC}}}\right)^{\mathrm{3}} \geqslant\:\mathrm{4}\:\sqrt{\mathrm{2}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 109699 by bemath last updated on 25/Aug/20 $$\:\:\:\:\:{x}\left({x}−\mathrm{1}\right)^{\mathrm{2}} \:\geqslant\:\mathrm{12}\left({x}−\mathrm{1}\right) \\ $$ Answered by bemath last updated on 25/Aug/20 $$\Leftrightarrow\:\left({x}−\mathrm{1}\right)\left({x}\left({x}−\mathrm{1}\right)−\mathrm{12}\right)\geqslant\mathrm{0} \\ $$$$\Leftrightarrow\left({x}−\mathrm{1}\right)\left({x}−\mathrm{4}\right)\left({x}+\mathrm{3}\right)\geqslant\mathrm{0} \\ $$$$\Leftrightarrow\:−\mathrm{3}\leqslant{x}\leqslant\mathrm{1}\:\cup\:{x}\geqslant\mathrm{4}…
Question Number 175230 by infinityaction last updated on 24/Aug/22 Answered by Ar Brandon last updated on 24/Aug/22 $${S}=\underset{{n}=\mathrm{3}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{\overset{{n}} {\:}{C}_{\mathrm{3}} }=\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{{n}!×\mathrm{3}!}{\left({n}+\mathrm{3}\right)!} \\…
Question Number 175218 by mnjuly1970 last updated on 23/Aug/22 $$ \\ $$$$\:\:\lfloor\:\:\left(\:\mathrm{1}\:+\:\sqrt{\mathrm{5}}\:\right)^{\:\mathrm{8}} \:\rfloor\:=\:? \\ $$$$\:\:\: \\ $$ Answered by behi834171 last updated on 23/Aug/22 $$\varphi^{\mathrm{2}}…
Question Number 175180 by Rasheed.Sindhi last updated on 22/Aug/22 $${a}_{{n}} \:{is}\:{an}\:{AP}\:{and}\:{S}_{{n}} \:{is}\:{sum}\:{of}\:{n}\:{terms} \\ $$$${of}\:{this}\:{AP}. \\ $$$${Given}\:{that}\:{S}_{\mathrm{11}} −{S}_{\mathrm{7}} =\mathrm{72},\:{determine} \\ $$$${a}_{\mathrm{6}} +{a}_{\mathrm{13}} . \\ $$ Answered…
Question Number 175173 by Shrinava last updated on 21/Aug/22 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 175175 by Shrinava last updated on 21/Aug/22 Answered by TheHoneyCat last updated on 23/Aug/22 $$\mathrm{Let}\:\mathrm{me}\:\mathrm{proove}\:\mathrm{a}\:\mathrm{slightly}\:\mathrm{more}\:\mathrm{general}\:\mathrm{statement}: \\ $$$$\mathrm{let}\:{x}=\frac{{a}}{\mathrm{2}}\:\leqslant\:{y}=\frac{{c}}{\mathrm{2}}\: \\ $$$$\mathrm{let}\:{t}\in\left[\mathrm{0},\mathrm{1}\right]\::\:{t}.{x}+\left(\mathrm{1}−{t}\right).{y}={b} \\ $$$$\mathrm{and}\:\mathrm{let}\:\mathrm{us}\:\mathrm{proove}\:\mathrm{that} \\ $$$$\mathrm{e}^{{x}}…
Question Number 175174 by Shrinava last updated on 21/Aug/22 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 44095 by peter frank last updated on 21/Sep/18 Answered by tanmay.chaudhury50@gmail.com last updated on 22/Sep/18 $${ax}^{\mathrm{3}} +{bx}^{\mathrm{2}} +{cx}+{d}=\mathrm{0} \\ $$$$\alpha+\beta+\gamma=\frac{−{b}}{{a}} \\ $$$$\alpha\beta+\beta\gamma\alpha\gamma=\frac{{c}}{{a}} \\…
Question Number 109626 by qwerty111 last updated on 24/Aug/20 Commented by kaivan.ahmadi last updated on 24/Aug/20 $${log}_{\mathrm{20}} \mathrm{2}×\mathrm{5}^{\mathrm{3}} ={log}_{\mathrm{20}} \mathrm{2}+\mathrm{3}{log}_{\mathrm{20}} \mathrm{5}=\frac{\mathrm{1}}{{log}_{\mathrm{2}} \mathrm{20}}+\frac{\mathrm{3}}{{log}_{\mathrm{5}} \mathrm{20}}= \\ $$$$\frac{\mathrm{1}}{\mathrm{2}+{log}_{\mathrm{2}}…