Question Number 162429 by Ari last updated on 29/Dec/21 $${put}\:{the}\:{digits}\:\mathrm{0},\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{5},\mathrm{6},\mathrm{7},\mathrm{8},\mathrm{9},{in}\:{place}\:{of}\:{the}\:{letters}\:{in}\:{order}\:{to}\:{perform}\:{the}\:{edditon} \\ $$ Commented by Ari last updated on 29/Dec/21 Terms of Service Privacy Policy Contact:…
Question Number 162416 by HongKing last updated on 29/Dec/21 $$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\underset{\:\mathrm{0}} {\overset{\:\frac{\boldsymbol{\pi}}{\mathrm{4}}} {\int}}\:\frac{\mathrm{4}\:\mathrm{ln}\:\left(\mathrm{cot}\boldsymbol{\mathrm{x}}\right)}{\mathrm{cos}\left(\mathrm{2x}\:+\:\mathrm{2022}\boldsymbol{\pi}\right)}\:\mathrm{dx}\:=\:\mathrm{3}\boldsymbol{\zeta}\left(\mathrm{2}\right) \\ $$ Commented by smallEinstein last updated on 29/Dec/21 Answered by…
Question Number 162417 by HongKing last updated on 29/Dec/21 $$\mathrm{Prove} \\ $$$$\underset{\:\mathrm{0}} {\overset{\:\frac{\boldsymbol{\pi}}{\mathrm{2}}} {\int}}\:\mathrm{sin}^{\mathrm{8}} \left(\mathrm{x}\right)\:+\:\underset{\:\mathrm{0}} {\overset{\:\mathrm{1}} {\int}}\:\mathrm{sin}^{-\mathrm{1}} \:\left(\sqrt[{\mathrm{8}}]{\mathrm{x}}\right)\:\geqslant\:\frac{\pi}{\mathrm{2}} \\ $$ Commented by mr W last…
Prove-the-Identity-for-any-a-n-in-Real-Number-1-a-a-n-a-a-2-n-2-a-2-n-1-2-Greatest-Integer-Function-
Question Number 162414 by HongKing last updated on 29/Dec/21 $$\mathrm{Prove}\:\mathrm{the}\:\mathrm{Identity}\:\mathrm{for}\:\mathrm{any}\:\left(\mathrm{a},\mathrm{n}\right)\:\mathrm{in}\:\mathrm{Real}\:\mathrm{Number} \\ $$$$\left(\mathrm{1}\:+\:\mathrm{a}\right)\centerdot\mathrm{a}^{\left[\boldsymbol{\mathrm{n}}\right]} \:=\:\mathrm{a}\:\centerdot\:\mathrm{a}^{\mathrm{2}\left[\frac{\boldsymbol{\mathrm{n}}}{\mathrm{2}}\right]} \:+\:\mathrm{a}^{\mathrm{2}\left[\frac{\boldsymbol{\mathrm{n}}+\mathrm{1}}{\mathrm{2}}\right]} \\ $$$$\left[\ast\right]\:\mathrm{Greatest}\:\mathrm{Integer}\:\mathrm{Function} \\ $$ Answered by mindispower last updated on 31/Dec/21…
Question Number 162411 by HongKing last updated on 29/Dec/21 $$\mathrm{Prove}\:\mathrm{the}\:\mathrm{identity}\:\mathrm{for}\:\mathrm{any}\:'\boldsymbol{\mathrm{n}}'\:\mathrm{in}\:\mathrm{Real}\:\mathrm{number} \\ $$$$\left[\frac{\mathrm{n}}{\mathrm{2}}\right]\:\centerdot\:\left[\frac{\mathrm{n}\:+\:\mathrm{1}}{\mathrm{2}}\right]\:=\:\frac{\mathrm{1}}{\mathrm{4}}\left(\left[\mathrm{n}\right]^{\mathrm{2}} \:+\:\mathrm{2}\left[\frac{\mathrm{n}}{\mathrm{2}}\right]\:-\:\left[\mathrm{n}\right]\right) \\ $$$$\left[\ast\right]\:\mathrm{Greatest}\:\mathrm{Integer}\:\mathrm{Function} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 31336 by NECx last updated on 06/Mar/18 $${Find}\:{the}\:{principal}\:{value}\:{of} \\ $$$${z}=\left(\mathrm{1}−{i}\right)^{\mathrm{1}+{i}} .{Hence}\:{find}\:{the} \\ $$$${modulus}\:{of}\:{the}\:{result}. \\ $$ Commented by abdo imad last updated on 06/Mar/18…
Question Number 96868 by me2love2math last updated on 05/Jun/20 Commented by prakash jain last updated on 05/Jun/20 $$\mathrm{2}^{\mathrm{5}{x}+\mathrm{1}} +\mathrm{5}^{\mathrm{2}{x}+\mathrm{2}} =\mathrm{1250}? \\ $$ Terms of Service…
Question Number 31335 by NECx last updated on 06/Mar/18 $${Find}\:{the}\:{pricipal}\:{value}\:{of}\: \\ $$$${z}=\left(\mathrm{1}−{i}\right)^{{i}} \\ $$ Commented by abdo imad last updated on 06/Mar/18 $${we}\:{have}\:{z}={e}^{{iln}\left(\mathrm{1}−{i}\right)} \:\:{and}\:{ln}\:{here}\:{mesnd}\:{the}\:{complexe}\:{log} \\…
Question Number 31323 by jasno91 last updated on 06/Mar/18 Answered by Joel578 last updated on 06/Mar/18 $$\mathrm{3}\frac{\mathrm{2}}{\mathrm{3}}\:−\:\mathrm{1}\frac{\mathrm{1}}{\mathrm{2}}\:=\:\frac{\mathrm{11}}{\mathrm{3}}\:−\:\frac{\mathrm{3}}{\mathrm{2}}\:=\:\frac{\mathrm{22}}{\mathrm{6}}\:−\:\frac{\mathrm{9}}{\mathrm{6}}\:=\:\frac{\mathrm{13}}{\mathrm{6}}\:=\:\mathrm{2}\frac{\mathrm{1}}{\mathrm{6}} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 31324 by jasno91 last updated on 06/Mar/18 Answered by Joel578 last updated on 06/Mar/18 $$\left(\mathrm{15}\right) \\ $$$$\frac{\mathrm{2}}{\mathrm{3}}\:=\:\frac{\mathrm{6}}{\mathrm{9}} \\ $$$$\mathrm{So}\:\frac{\mathrm{6}}{\mathrm{9}}\:>\:\frac{\mathrm{5}}{\mathrm{9}}\:\:\:\left(\frac{\mathrm{6}}{\mathrm{9}}\:\mathrm{is}\:\frac{\mathrm{1}}{\mathrm{9}}\:\mathrm{greater}\:\mathrm{than}\:\frac{\mathrm{5}}{\mathrm{9}}\right) \\ $$$$ \\ $$$$\left(\mathrm{16}\right)…