Question Number 19194 by mondodotto@gmail.com last updated on 06/Aug/17 Answered by allizzwell23 last updated on 06/Aug/17 $$\:\:\:\:\:\left(\frac{\mathrm{25}}{\mathrm{4}}\:\right)^{\mathrm{3}\left(\mathrm{x}−\mathrm{1}\right)} =\:\left(\frac{\mathrm{4}}{\mathrm{10}}\right)^{\mathrm{3}\left(\mathrm{5}−\mathrm{x}\right)} \\ $$$$\:\:\:\:\:\left(\frac{\mathrm{5}}{\mathrm{2}}\:\right)^{\mathrm{2}\left(\mathrm{x}−\mathrm{1}\right)} =\:\left(\frac{\mathrm{2}}{\mathrm{5}}\right)^{\left(\mathrm{5}−\mathrm{x}\right)} \\ $$$$\:\:\:\:\:\left(\frac{\mathrm{5}}{\mathrm{2}}\:\right)^{\mathrm{2}\left(\mathrm{x}−\mathrm{1}\right)} =\:\left(\frac{\mathrm{5}}{\mathrm{2}}\right)^{−\left(\mathrm{5}−\mathrm{x}\right)} \\…
Question Number 84728 by mr W last updated on 15/Mar/20 $${y}={x}\left[{x}\left[{x}\right]\right]\:{with}\:{x}\in{R}^{+} \\ $$$${find}\:{the}\:{range}\:{of}\:{function} \\ $$$${and}\:{solve}\:{x}\left[{x}\left[{x}\right]\right]=\mathrm{150}. \\ $$ Commented by MJS last updated on 16/Mar/20 Commented…
Question Number 19193 by Tinkutara last updated on 06/Aug/17 $$\mathrm{The}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{two}\:\mathrm{positive}\:\mathrm{integers}\:\mathrm{is}\:\mathrm{52} \\ $$$$\mathrm{and}\:\mathrm{their}\:\mathrm{LCM}\:\mathrm{is}\:\mathrm{168}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{numbers}. \\ $$ Answered by RasheedSindhi last updated on 06/Aug/17 $$\mathrm{Let}\:\mathrm{the}\:\mathrm{numbers}\:\mathrm{are}\:\mathrm{x}\:\mathrm{and}\:\mathrm{y} \\ $$$$\mathrm{and}\:\mathrm{their}\:\mathrm{HCF}\:\mathrm{is}\:\mathrm{h} \\…
Question Number 19192 by Tinkutara last updated on 06/Aug/17 $$\mathrm{Find}\:\mathrm{a}\:\mathrm{natural}\:\mathrm{number}\:'\mathrm{n}'\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{3}^{\mathrm{9}} \:+\:\mathrm{3}^{\mathrm{12}} \:+\:\mathrm{3}^{\mathrm{15}} \:+\:\mathrm{3}^{{n}} \:\mathrm{is}\:\mathrm{a}\:\mathrm{perfect}\:\mathrm{cube}\:\mathrm{of} \\ $$$$\mathrm{an}\:\mathrm{integer}. \\ $$ Commented by Tinkutara last updated…
Question Number 84726 by M±th+et£s last updated on 15/Mar/20 $${prove}\:{that} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \left({y}^{{y}} \right)^{\left({y}^{{y}} \right)^{\left({y}^{{y}} \right)^{.^{.^{.} } } } } {dy}=\frac{\pi^{\mathrm{2}} }{\mathrm{12}} \\ $$…
Question Number 150263 by dany last updated on 10/Aug/21 $$\underset{{k}=\mathrm{1}} {\overset{{n}} {\prod}}\left(\mathrm{1}+\frac{{k}^{\mathrm{2}} }{{n}^{\mathrm{2}} }\right)^{\frac{\mathrm{1}}{{n}}} \\ $$ Commented by puissant last updated on 10/Aug/21 $$\mathrm{limite}? \\…
Question Number 150259 by mathdanisur last updated on 10/Aug/21 $$\underset{\:\mathrm{0}} {\overset{\:\infty} {\int}}\:\frac{\mathrm{e}^{−\boldsymbol{\mathrm{st}}} \left(\mathrm{cosh}\left(\mathrm{2t}\right)−\mathrm{cosh}\left(\mathrm{5t}\right)\right)\mathrm{dt}}{\mathrm{t}}=? \\ $$ Answered by Ar Brandon last updated on 10/Aug/21 $${I}\left({s}\right)=\int_{\mathrm{0}} ^{\infty}…
Question Number 84718 by Power last updated on 15/Mar/20 Answered by mr W last updated on 15/Mar/20 $${AC}^{\mathrm{2}} ={PA}^{\mathrm{2}} +{PC}^{\mathrm{2}} −\mathrm{2}×{PA}×{PC}\:\mathrm{cos}\:\mathrm{120}° \\ $$$$\Rightarrow{AC}^{\mathrm{2}} ={PA}^{\mathrm{2}} +{PC}^{\mathrm{2}}…
Question Number 19182 by Tinkutara last updated on 06/Aug/17 $$\mathrm{Find}\:\mathrm{all}\:\mathrm{three}\:\mathrm{digit}\:\mathrm{numbers}\:{abc}\:\left(\mathrm{with}\right. \\ $$$$\left.\mathrm{a}\:\neq\:\mathrm{0}\right)\:\mathrm{such}\:\mathrm{that}\:\mathrm{a}^{\mathrm{2}} \:+\:\mathrm{b}^{\mathrm{2}} \:+\:\mathrm{c}^{\mathrm{2}} ,\:\mathrm{is}\:\mathrm{divisible} \\ $$$$\mathrm{by}\:\mathrm{26}. \\ $$ Answered by RasheedSindhi last updated on…
Question Number 84713 by john santu last updated on 15/Mar/20 $$\int\overset{\:\:\mathrm{1}} {\:}_{\mathrm{0}} \mathrm{cos}^{−\mathrm{1}} \left(\mathrm{x}^{\mathrm{2}} −\mathrm{x}+\mathrm{1}\right)\:\mathrm{dx}\:? \\ $$ Commented by TANMAY PANACEA last updated on 15/Mar/20…