Category: Arithmetic

Question Number 213522 by efronzo1 last updated on 07/Nov/24 $$\mathrm{The}\mathrm{two}\mathrm{corner}\mathrm{points}\mathrm{of}\mathrm{a}\mathrm{square}$$$$\mathrm{lie}\mathrm{on}\mathrm{curve}\mathrm{f}\left(\mathrm{x}\right)={\mathrm{x}}^2-2\mathrm{x}-3\mathrm{and}$$$$\mathrm{the}\mathrm{other}\mathrm{two}\mathrm{corner}\mathrm{points}\mathrm{lie}\mathrm{on}$$$$\mathrm{curve}\mathrm{g}\left(\mathrm{x}\right)=-{\mathrm{x}}^2+2\mathrm{x}+3.\mathrm{It}\mathrm{is}\mathrm{known}$$$$\mathrm{that}\mathrm{the}\mathrm{area}\mathrm{of}\mathrm{a}\mathrm{square}\mathrm{can}\mathrm{be}$$$$\mathrm{expressed}\mathrm{by}\mathrm{p}+\mathrm{q}\sqrt{\mathrm{r}},\mathrm{for}\mathrm{a}\mathrm{natural}$$$$\:\mathrm{number}\:\mathrm{p},\mathrm{q}\:,\mathrm{r}\:\mathrm{where}\:\mathrm{r}\:\mathrm{is}\:\mathrm{not}\:\mathrm{divisible}\: \…

Question Number 213100 by MathematicalUser2357 last updated on 30/Oct/24 $$\mathrm{Find}\mathrm{this}\mathrm{numeric}\mathrm{expression}\mathrm{using}:$$$$\mathrm{The}\mathrm{arithmetic}\mathrm{division}\mathrm{rule}a\mathbf{÷}b\left(c\right)=a\mathbf{÷}b\times c,$$$$\mathrm{The}\mathrm{solvable}\mathrm{incorrect}\mathrm{syntax}\mathrm{rule}\left(a\right)b=a\times b,\mathrm{where}b\mathrm{is}\mathrm{a}\mathrm{number}:$$$$12\mathbf{÷}4(10-8+1)2\mathbf{÷}6\times 2=?$$ Commented by A5T last updated on 30/Oct/24…

Question Number 212496 by efronzo1 last updated on 15/Oct/24 $$\mathrm{If}1.1!+3.2!+\dots +(2\mathrm{n}-1).\mathrm{n}!$$$$=\mathrm{a}.(\mathrm{n}+1)!+\mathrm{b}(1!+2!+\dots +(\mathrm{n}+1)!)+\mathrm{c}$$$$\mathrm{for}\mathrm{a},\mathrm{b},\mathrm{c}\mathrm{integers}\mathrm{number}$$$$\mathrm{find}2\mathrm{a}-\mathrm{b}+3\mathrm{c}$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 211979 by Spillover last updated on 25/Sep/24 Answered by BHOOPENDRA last updated on 25/Sep/24 $$\int \frac{dx}{(x^2{\tan }^{-1}x+{\tan }^{-1}x+x^2\pi +\pi )}$$$$\int\frac{{dx}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)\left(\mathrm{tan}^{−\mathrm{1}} {x}+\pi\right)}…

Question Number 211895 by Spillover last updated on 23/Sep/24 Answered by mehdee7396 last updated on 23/Sep/24 $${lim}_{x\to \mathrm{\infty }}(1+\frac{a}{x}-\frac{4}{x^2}-1)2x$$$$={lim}_{x\to \mathrm{\infty }}\left(\frac{ax-4}{x^2}\right)2x=2a$$$$\Rightarrow{lim}_{{x}\rightarrow\infty}…