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Category: Algebra

What-is-the-meaning-of-this-symbol-in-limit-please-or-as-used-in-convergent-divergent-series-

Question Number 92390 by I want to learn more last updated on 06/May/20 $$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{meaning}\:\mathrm{of}\:\mathrm{this}\:\mathrm{symbol}\:\:\left(\varepsilon\right)\:\mathrm{in}\:\mathrm{limit}\:\mathrm{please}. \\ $$$$\mathrm{or}\:\mathrm{as}\:\mathrm{used}\:\mathrm{in}\:\mathrm{convergent}/\mathrm{divergent}\:\mathrm{series} \\ $$ Commented by Joel578 last updated on 06/May/20…

5-2-5-4-5-6-5-2x-0-04-28-find-x-

Question Number 157913 by HongKing last updated on 29/Oct/21 $$\mathrm{5}^{\mathrm{2}} \:\centerdot\:\mathrm{5}^{\mathrm{4}} \:\centerdot\:\mathrm{5}^{\mathrm{6}} \:\centerdot\:…\:\centerdot\:\mathrm{5}^{\mathrm{2}\boldsymbol{\mathrm{x}}} \:=\:\mathrm{0},\mathrm{04}^{-\mathrm{28}} \\ $$$$\mathrm{find}\:\:\boldsymbol{\mathrm{x}}=? \\ $$ Answered by Rasheed.Sindhi last updated on 29/Oct/21…

a-n-in-numerical-series-7-9-11-13-2n-1-an-2-bn-c-find-a-b-c-

Question Number 157908 by HongKing last updated on 29/Oct/21 $$\left(\mathrm{a}_{\boldsymbol{\mathrm{n}}} \right)\:\mathrm{in}\:\mathrm{numerical}\:\mathrm{series} \\ $$$$\mathrm{7}+\mathrm{9}+\mathrm{11}+\mathrm{13}+…+\left(\mathrm{2n}+\mathrm{1}\right)=\mathrm{an}^{\mathrm{2}} +\mathrm{bn}+\mathrm{c} \\ $$$$\mathrm{find}\:\:\boldsymbol{\mathrm{a}}+\boldsymbol{\mathrm{b}}+\boldsymbol{\mathrm{c}}=? \\ $$ Answered by Rasheed.Sindhi last updated on 29/Oct/21…

f-x-px-1-2x-q-4-function-is-a-single-function-find-p-q-pq-

Question Number 157906 by HongKing last updated on 29/Oct/21 $$\mathrm{f}\left(\mathrm{x}\right)=\left(\mathrm{px}+\mathrm{1}\right)\left(\mathrm{2x}+\mathrm{q}+\mathrm{4}\right)\:\mathrm{function}\:\mathrm{is}\:\mathrm{a} \\ $$$$\mathrm{single}\:\mathrm{function},\:\mathrm{find}\:\boldsymbol{\mathrm{p}}+\boldsymbol{\mathrm{q}}+\boldsymbol{\mathrm{pq}}=? \\ $$$$ \\ $$ Commented by Rasheed.Sindhi last updated on 29/Oct/21 $${What}'{s}\:{meant}\:{by}\:'\mathrm{single}\:\mathrm{function}'? \\…

Solve-for-integers-x-x-4-5-3-y-1-

Question Number 157902 by HongKing last updated on 29/Oct/21 $$\mathrm{Solve}\:\mathrm{for}\:\mathrm{integers}: \\ $$$$\mathrm{x}\centerdot\left(\mathrm{x}\:+\:\mathrm{4}\right)\:=\:\mathrm{5}\centerdot\left(\mathrm{3}^{\boldsymbol{\mathrm{y}}} \:-\:\mathrm{1}\right) \\ $$$$ \\ $$ Commented by Rasheed.Sindhi last updated on 01/Nov/21 $$\mathrm{3}^{\mathrm{y}}…

1-sin-10-4-sin-70-

Question Number 157884 by HongKing last updated on 29/Oct/21 $$\frac{\mathrm{1}}{\mathrm{sin}\left(\mathrm{10}°\right)}\:-\:\mathrm{4}\:\mathrm{sin}\left(\mathrm{70}°\right)\:=\:? \\ $$ Answered by tounghoungko last updated on 29/Oct/21 $$\frac{\mathrm{1}}{\mathrm{sin}\:\mathrm{10}°}−\mathrm{4}\left(\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\:\mathrm{cos}\:\mathrm{10}°+\frac{\mathrm{1}}{\mathrm{2}}\mathrm{sin}\:\mathrm{10}°\right) \\ $$$$=\frac{\mathrm{1}}{\mathrm{sin}\:\mathrm{10}°}−\mathrm{2}\sqrt{\mathrm{3}}\:\mathrm{cos}\:\mathrm{10}°−\mathrm{2sin}\:\mathrm{10}° \\ $$$$=\frac{\mathrm{1}−\mathrm{2}\sqrt{\mathrm{3}}\:\mathrm{sin}\:\mathrm{10}°\:\mathrm{cos}\:\mathrm{10}°−\mathrm{2sin}\:^{\mathrm{2}} \mathrm{10}°}{\mathrm{sin}\:\mathrm{10}°}…

Question-157891

Question Number 157891 by HongKing last updated on 29/Oct/21 Answered by TheSupreme last updated on 29/Oct/21 $$\left(\frac{\mathrm{3}}{\mathrm{4}}+\frac{\mathrm{5}}{\mathrm{36}}+\frac{\mathrm{7}}{\mathrm{144}}+\frac{\mathrm{9}}{\mathrm{400}}+\frac{\mathrm{11}}{\mathrm{900}}\right){x}<\mathrm{70} \\ $$$$\left(\frac{\mathrm{2400}+\mathrm{500}+\mathrm{175}+\mathrm{81}+\mathrm{44}}{\mathrm{3600}}\right){x}<\mathrm{70} \\ $$$$\left(\frac{\mathrm{8}}{\mathrm{9}}\right){x}<\mathrm{70} \\ $$$${x}<\frac{\mathrm{630}}{\mathrm{8}}=\mathrm{78}.\mathrm{75} \\ $$$${largest}\:{x}\:=\:\mathrm{78}…