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Category: Algebra

Question-209633

Question Number 209633 by Abdullahrussell last updated on 17/Jul/24 Answered by som(math1967) last updated on 17/Jul/24 $$\left({x}+\mathrm{1}\right)\left(\mathrm{3}{x}+\mathrm{2}\right)\left(\mathrm{6}{x}+\mathrm{5}\right)^{\mathrm{2}} =\mathrm{6} \\ $$$$\Rightarrow\left(\mathrm{3}{x}^{\mathrm{2}} +\mathrm{5}{x}+\mathrm{2}\right)\left(\mathrm{36}{x}^{\mathrm{2}} +\mathrm{60}{x}+\mathrm{25}\right)=\mathrm{6} \\ $$$$\Rightarrow\left({a}+\mathrm{2}\right)\left(\mathrm{12}{a}+\mathrm{25}\right)=\mathrm{6} \\…

If-a-n-gt-0-and-lim-n-a-n-0-Find-lim-n-1-n-k-1-n-ln-k-n-a-n-

Question Number 209580 by hardmath last updated on 15/Jul/24 $$\mathrm{If}\:\:\:\mathrm{a}_{\boldsymbol{\mathrm{n}}} >\mathrm{0}\:\:\:\mathrm{and}\:\:\:\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{a}_{\boldsymbol{\mathrm{n}}} \:=\:\mathrm{0} \\ $$$$\mathrm{Find}:\:\:\:\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{1}}{\mathrm{n}}\:\underset{\boldsymbol{\mathrm{k}}=\mathrm{1}} {\overset{\boldsymbol{\mathrm{n}}} {\sum}}\:\mathrm{ln}\:\left(\frac{\mathrm{k}}{\mathrm{n}}\:+\:\mathrm{a}_{\boldsymbol{\mathrm{n}}} \right)\:=\:? \\ $$ Answered by mr W…

If-a-n-is-absolutely-convergent-prove-that-a-n-n-is-also-absolutely-convergent-

Question Number 209514 by depressiveshrek last updated on 12/Jul/24 $$\mathrm{If}\:\Sigma\:{a}_{{n}} \:\mathrm{is}\:\mathrm{absolutely}\:\mathrm{convergent},\:\mathrm{prove}\:\mathrm{that} \\ $$$$\Sigma\:\frac{{a}_{{n}} }{{n}}\:\mathrm{is}\:\mathrm{also}\:\mathrm{absolutely}\:\mathrm{convergent}. \\ $$ Answered by MM42 last updated on 13/Jul/24 $$\frac{\mid{a}_{{n}} \mid}{{n}}\:<\mid{a}_{{n}}…

x-y-z-1-42x-44y-30z-42-x-y-z-1-0-0-yes-but-solution-

Question Number 209436 by hardmath last updated on 10/Jul/24 $$\begin{cases}{\mathrm{x}\:+\:\mathrm{y}\:+\:\mathrm{z}\:=\:\mathrm{1}}\\{\mathrm{42x}\:+\:\mathrm{44y}\:+\:\mathrm{30z}\:=\:\mathrm{42}}\end{cases} \\ $$$$\left(\mathrm{x},\mathrm{y},\mathrm{z}\right)=\left(\mathrm{1},\mathrm{0},\mathrm{0}\right)\:\mathrm{yes},\:\mathrm{but}\:\mathrm{solution}… \\ $$ Commented by mr W last updated on 10/Jul/24 $${you}\:{mean}\:{integer}\:{solutions}. \\ $$…

Question-209456

Question Number 209456 by peter frank last updated on 10/Jul/24 Answered by Ghisom last updated on 10/Jul/24 $${c}=\mathrm{cos}\:\alpha\:\:\:\:\:{s}=\mathrm{sin}\:\alpha\:\:\:\:\:{t}=\mathrm{tan}\:\alpha\:=\frac{{s}}{{c}} \\ $$$${c}=\sqrt{\mathrm{1}−{s}^{\mathrm{2}} }=\frac{\mathrm{1}}{\:\sqrt{{t}^{\mathrm{2}} +\mathrm{1}}} \\ $$$${s}=\sqrt{\mathrm{1}−{c}^{\mathrm{2}} }=\frac{{t}}{\:\sqrt{{t}^{\mathrm{2}}…

Question-209404

Question Number 209404 by Tawa11 last updated on 09/Jul/24 Answered by mr W last updated on 09/Jul/24 $${s}=\mathrm{4}{t}+{at}^{\mathrm{2}} +{bt}^{\mathrm{3}} \\ $$$${v}=\frac{{ds}}{{dt}}=\mathrm{4}+\mathrm{2}{at}+\mathrm{3}{bt}^{\mathrm{2}} \\ $$$${a}=\frac{{dv}}{{dt}}=\mathrm{2}{a}+\mathrm{6}{bt} \\ $$$${at}\:{v}_{{max}}…