Question Number 109082 by 1777 last updated on 21/Aug/20 $${prove}\:{that}\:: \\ $$$$\int_{−\frac{\pi}{\mathrm{2}}} ^{−\frac{\pi}{\mathrm{4}}} \mathrm{2}{cos}\left({x}\right)+{sin}\left({x}\right){dx}\leqslant\int_{−\frac{\pi}{\mathrm{2}}} ^{−\frac{\pi}{\mathrm{4}}} {cos}\left({x}\right)−{sin}\left({x}\right){dx} \\ $$ Answered by malwan last updated on 21/Aug/20…
Question Number 174619 by cortano1 last updated on 06/Aug/22 Answered by aleks041103 last updated on 06/Aug/22 $$\Rightarrow{z}=\left({ae}^{{i}\alpha} \right)^{{n}} ={a}^{{n}} {e}^{{in}\alpha} \\ $$$${re}\left({z}\right)=\mathrm{0}\Rightarrow{cos}\left({n}\alpha\right)=\mathrm{0} \\ $$$$\Rightarrow{n}\alpha=\left({k}+\frac{\mathrm{1}}{\mathrm{2}}\right)\pi,\:{k}\in\mathbb{Z} \\…
Question Number 174613 by Mastermind last updated on 05/Aug/22 $$\mathrm{In}\:\mathrm{a}\:\mathrm{mixture}\:\mathrm{of}\:\:\mathrm{Skettles}\:\mathrm{and}\:\mathrm{M\&M}'\mathrm{s}, \\ $$$$\mathrm{80\%}\:\mathrm{of}\:\mathrm{the}\:\mathrm{pieces}\:\mathrm{are}\:\mathrm{M\&M}'\mathrm{s}.\:\mathrm{A}\:\mathrm{fourth} \\ $$$$\mathrm{of}\:\mathrm{this}\:\mathrm{mixture}\:\mathrm{is}\:\mathrm{replaced}\:\mathrm{by}\:\mathrm{a}\:\mathrm{second} \\ $$$$\mathrm{mixture},\:\mathrm{resulting}\:\mathrm{in}\:\mathrm{combination} \\ $$$$\mathrm{which}\:\mathrm{contain}\:\mathrm{16\%}\:\mathrm{Skittles}\:\mathrm{in}\:\mathrm{total}. \\ $$$$\mathrm{What}\:\mathrm{was}\:\mathrm{the}\:\mathrm{percentage}\:\mathrm{of}\:\mathrm{Skittles} \\ $$$$\mathrm{in}\:\mathrm{the}\:\mathrm{second}\:\mathrm{mixture}? \\ $$ Answered…
Question Number 174612 by Mastermind last updated on 05/Aug/22 Commented by Mastermind last updated on 05/Aug/22 $$\mathrm{Floor},\:\mathrm{help}\:\mathrm{us}\:\mathrm{out} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 174591 by Mastermind last updated on 05/Aug/22 $$\mathrm{The}\:\mathrm{drawing}\:\mathrm{below}\:\mathrm{shows}\:\mathrm{two}\: \\ $$$$\mathrm{equilateral}\:\mathrm{triangles}\:\mathrm{with}\:\mathrm{side}\:\mathrm{length} \\ $$$$\boldsymbol{\mathrm{a}}.\:\mathrm{The}\:\mathrm{triangle}\:\mathrm{are}\:\mathrm{horizontally}\:\mathrm{shifted} \\ $$$$\mathrm{by}\:\frac{\mathrm{a}}{\mathrm{2}}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{intersection}\:\mathrm{area}\:\mathrm{A}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{two}\:\mathrm{triangles}\:\left(\mathrm{grey}\:\mathrm{area}\right). \\ $$$$ \\ $$$$ \\ $$$$ \\…
Question Number 174594 by Mastermind last updated on 05/Aug/22 $$\mathrm{Let}\:\sigma\left(\mathrm{n}\right)\:\mathrm{be}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{all}\:\mathrm{positive} \\ $$$$\mathrm{divisors}\:\mathrm{of}\:\mathrm{the}\:\mathrm{integer}\:\mathrm{n}\:\mathrm{and}\:\mathrm{let}\:\mathrm{p}\:\mathrm{be} \\ $$$$\mathrm{any}\:\mathrm{prime}\:\mathrm{number}.\:\mathrm{show}\:\mathrm{that}\: \\ $$$$\sigma\left(\mathrm{n}\right)<\mathrm{2n}\:\mathrm{holds}\:\mathrm{true}\:\mathrm{for}\:\mathrm{all}\:\mathrm{n}\:\mathrm{of}\:\mathrm{the}\: \\ $$$$\mathrm{form}\:\mathrm{n}=\mathrm{p}^{\mathrm{2}} . \\ $$$$ \\ $$$$\mathrm{Mastermind} \\ $$…
Question Number 43481 by kumar123 last updated on 11/Sep/18 $$\frac{\left(\mathrm{1}+\mathrm{2}{i}\right)^{\mathrm{3}} }{\left(\mathrm{3}+{i}\right)}= \\ $$ Answered by Joel578 last updated on 11/Sep/18 $$\frac{\mathrm{1}\:+\:\mathrm{6}{i}\:+\:\mathrm{12}{i}^{\mathrm{2}} \:+\:\mathrm{8}{i}^{\mathrm{3}} }{\mathrm{3}\:+\:{i}}\:.\:\left(\frac{\mathrm{3}\:−\:{i}}{\mathrm{3}\:−\:{i}}\right) \\ $$$$=\:\frac{\mathrm{3}\:+\:\mathrm{17}{i}\:+\:\mathrm{30}{i}^{\mathrm{2}}…
Question Number 43470 by Tawa1 last updated on 11/Sep/18 $$\mathrm{Please}\:\mathrm{what}\:\mathrm{topic}\:\mathrm{is}\:\mathrm{all}\:\mathrm{the}\:\mathrm{question}\:\mathrm{that}\:\mathrm{has}\:\mathrm{the}\:\mathrm{summation}\:\mathrm{sign}. \\ $$$$\Sigma.\:\:\:\:\mathrm{How}\:\mathrm{can}\:\mathrm{i}\:\mathrm{study}\:\mathrm{the}\:\mathrm{summation}\:\mathrm{by}\:\mathrm{using}\:\mathrm{it}\:\mathrm{to}\:\mathrm{solve}\:\mathrm{some}\:\mathrm{continuous} \\ $$$$\mathrm{equation}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 174528 by Mastermind last updated on 03/Aug/22 Answered by behi834171 last updated on 05/Aug/22 $$\mathrm{4}\boldsymbol{{A}}=\frac{\boldsymbol{{a}}^{\mathrm{2}} \sqrt{\mathrm{3}}}{\mathrm{4}}\Rightarrow\boldsymbol{{A}}=\frac{\boldsymbol{{a}}^{\mathrm{2}} \sqrt{\mathrm{3}}}{\mathrm{16}}\:\:\:\:.\blacksquare \\ $$ Terms of Service Privacy…
Question Number 174522 by Mastermind last updated on 03/Aug/22 $$\mathrm{Let}\:\sigma\left(\mathrm{n}\right)\:\mathrm{be}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{all}\:\mathrm{positive}\:\mathrm{divisors} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{integer}\:\mathrm{n}\:\mathrm{and}\:\mathrm{let}\:\mathrm{p}\:\mathrm{be}\:\mathrm{any}\:\mathrm{prime} \\ $$$$\mathrm{number}.\:\mathrm{Show}\:\mathrm{that}\:\sigma\left(\mathrm{n}\right)<\mathrm{2n}\:\mathrm{holds}\:\mathrm{true} \\ $$$$\mathrm{for}\:\mathrm{all}\:\mathrm{n}\:\mathrm{of}\:\mathrm{the}\:\mathrm{form}\:\mathrm{n}=\mathrm{p}^{\mathrm{2}} . \\ $$$$ \\ $$$$\mathrm{Mastermind} \\ $$ Terms of…