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Category: Algebra

Question-209972

Question Number 209972 by Abdullahrussell last updated on 27/Jul/24 Answered by efronzo1 last updated on 27/Jul/24 $$\:\:\mathrm{x}^{\mathrm{2}} \:+\frac{\mathrm{9x}^{\mathrm{2}} }{\left(\mathrm{x}−\mathrm{3}\right)^{\mathrm{2}} }\:=\:\mathrm{16}\: \\ $$$$\:\:\mathrm{x}^{\mathrm{2}} \left(\left(\mathrm{x}−\mathrm{3}\right)^{\mathrm{2}} +\mathrm{9}\right)=\:\mathrm{16}\left(\mathrm{x}−\mathrm{3}\right)^{\mathrm{2}} \\…

Find-0-x-x-x-1-dx-x-fractional-part-x-full-part-

Question Number 209918 by hardmath last updated on 25/Jul/24 $$\mathrm{Find}:\:\:\:\int_{\mathrm{0}} ^{\:\infty} \:\frac{\left\{\mathrm{x}\right\}^{\left[\boldsymbol{\mathrm{x}}\right]} }{\left[\mathrm{x}\right]\:+\:\mathrm{1}}\:\mathrm{dx}\:=\:? \\ $$$$\left\{\mathrm{x}\right\}\:\rightarrow\:\mathrm{fractional}\:\mathrm{part} \\ $$$$\left[\mathrm{x}\right]\:\:\:\rightarrow\:\mathrm{full}\:\mathrm{part} \\ $$ Answered by MM42 last updated on…

1-6-2x-2-3-2x-2-2-x-find-x-

Question Number 209876 by hardmath last updated on 24/Jul/24 $$\mathrm{1},\mathrm{6}\:\:=\:\:\frac{\left(\mathrm{2x}\right)^{\mathrm{2}} }{\left(\mathrm{3}−\mathrm{2x}\right)^{\mathrm{2}} \:\centerdot\:\left(\mathrm{2}−\mathrm{x}\right)}\:\:\:\mathrm{find}:\:\:\boldsymbol{\mathrm{x}}\:=\:? \\ $$ Answered by Frix last updated on 24/Jul/24 $$\mathrm{Transform} \\ $$$${x}^{\mathrm{3}} −\mathrm{4}.\mathrm{375}{x}^{\mathrm{2}}…

Find-n-1-arctan-2-n-2-

Question Number 209852 by hardmath last updated on 23/Jul/24 $$\mathrm{Find}:\:\:\:\underset{\boldsymbol{\mathrm{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\:\mathrm{arctan}\:\left(\frac{\mathrm{2}}{\mathrm{n}^{\mathrm{2}} }\right)\:=\:? \\ $$ Answered by mr W last updated on 24/Jul/24 $$\frac{\mathrm{2}}{{n}^{\mathrm{2}} }=\frac{\left({n}+\mathrm{1}\right)−\left({n}−\mathrm{1}\right)}{\mathrm{1}+\left({n}+\mathrm{1}\right)\left({n}−\mathrm{1}\right)}…

if-the-series-n-1-1-n-2-converges-to-k-find-the-convergence-value-of-n-1-1-2n-1-2-

Question Number 209837 by lmcp1203 last updated on 23/Jul/24 $$ \\ $$$${if}\:{the}\:{series}\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\:{converges}\:{to}\:{k}\:.\:\:{find}\:\:{the}\:{convergence}\:{value}\:{of}\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\left(\mathrm{2}{n}+\mathrm{1}\right)^{\mathrm{2}} } \\ $$ Answered by mr W last…