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Category: Algebra

Prove-that-5-divide-n-4n-2-1-6n-2-1-for-any-natural-number-n-

Question Number 158240 by HongKing last updated on 01/Nov/21 $$\mathrm{Prove}\:\mathrm{that}\:\mathrm{5}\:\mathrm{divide} \\ $$$$\mathrm{n}\left(\mathrm{4n}^{\mathrm{2}} \:+\:\mathrm{1}\right)\left(\mathrm{6n}^{\mathrm{2}} \:+\:\mathrm{1}\right) \\ $$$$\mathrm{for}\:\mathrm{any}\:\mathrm{natural}\:\mathrm{number}\:\boldsymbol{\mathrm{n}} \\ $$ Answered by Rasheed.Sindhi last updated on 01/Nov/21…

Solve-for-real-numbers-x-y-5-3-x-3-1-5-y-5-6-1-5-1-

Question Number 158187 by HongKing last updated on 31/Oct/21 $$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\begin{cases}{\sqrt{\mathrm{x}}\:-\:\mathrm{y}^{\mathrm{5}} \:=\:\mathrm{3}}\\{\sqrt[{\mathrm{5}}]{\sqrt{\mathrm{x}}\:-\:\mathrm{3}}\:-\:\sqrt[{\mathrm{5}}]{\mathrm{y}^{\mathrm{5}} \:+\:\mathrm{6}}\:=\:-\:\mathrm{1}}\end{cases}\: \\ $$$$ \\ $$ Answered by MJS_new last updated on 31/Oct/21…

the-intrest-on-a-certain-sum-of-money-at-the-end-of-6-25-year-was-5-16-of-the-sum-itself-what-is-the-rate-percent-

Question Number 27103 by ktomboy1992 last updated on 02/Jan/18 $$\mathrm{the}\:\mathrm{intrest}\:\mathrm{on}\:\mathrm{a}\:\mathrm{certain}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{money}\:\mathrm{at}\:\mathrm{the} \\ $$$$\mathrm{end}\:\mathrm{of}\:\mathrm{6}.\mathrm{25}\:\mathrm{year}\:\mathrm{was}\:\frac{\mathrm{5}}{\mathrm{16}}\:\mathrm{of}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{itself}.\mathrm{what} \\ $$$$\mathrm{is}\:\mathrm{the}\:\mathrm{rate}\:\mathrm{percent}? \\ $$ Commented by mrW1 last updated on 02/Jan/18 $$\Rightarrow\:{Q}\mathrm{27016} \\…

if-1-x-x-2-0-find-the-value-of-A-x-1-x-6-x-2-1-x-2-6-x-100-1-x-100-6-

Question Number 27094 by abdo imad last updated on 02/Jan/18 $${if}\:\mathrm{1}+{x}+{x}^{\mathrm{2}} =\mathrm{0}\:{find}\:{the}\:{value}\:{of}\: \\ $$$${A}=\:\left({x}+\frac{\mathrm{1}}{{x}}\right)^{\mathrm{6}} \:+\left(\:{x}^{\mathrm{2}} +\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right)^{\mathrm{6}} \:\:+…\:\left(\:\:{x}^{\mathrm{100}} +\frac{\mathrm{1}}{{x}^{\mathrm{100}} }\right)^{\mathrm{6}} \:. \\ $$ Commented by…

Question-92608

Question Number 92608 by jagoll last updated on 08/May/20 Commented by john santu last updated on 08/May/20 $$\mathrm{g}\left(\mathrm{t}\right)\:=\:\begin{cases}{−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{t}\:,−\mathrm{4}\leqslant\mathrm{t}\leqslant\mathrm{0}}\\{−\sqrt{\mathrm{9}−\left(\mathrm{t}−\mathrm{3}\right)^{\mathrm{2}} },\:\mathrm{0}\leqslant\mathrm{t}\leqslant\mathrm{6}}\\{\mathrm{3}\:,\:\mathrm{6}<\mathrm{t}\leqslant\mathrm{8}}\end{cases} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{3x}+\underset{\mathrm{0}} {\overset{\mathrm{x}} {\int}}\:\mathrm{g}\left(\mathrm{t}\right)\:\mathrm{dt}\: \\ $$$$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{3x}+\begin{cases}{−\frac{\mathrm{1}}{\mathrm{4}}\mathrm{x}^{\mathrm{2}}…