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Category: Algebra

there-are-25-persons-in-a-conical-tent-every-person-needs-an-area-of-4-sq-m-on-the-ground-under-the-tent-if-height-if-the-tent-is-18m-find-the-volume-of-the-tent-

Question Number 29264 by bbbbbb last updated on 06/Feb/18 $$\mathrm{there}\:\mathrm{are}\:\mathrm{25}\:\mathrm{persons}\:\mathrm{in}\:\mathrm{a}\:\mathrm{conical}\:\mathrm{tent} \\ $$$$\mathrm{every}\:\mathrm{person}\:\mathrm{needs}\:\mathrm{an}\:\mathrm{area}\:\mathrm{of}\:\mathrm{4}\:\mathrm{sq}\:\mathrm{m}\: \\ $$$$\mathrm{on}\:\mathrm{the}\:\mathrm{ground}\:\mathrm{under}\:\mathrm{the}\:\mathrm{tent}.\:\mathrm{if} \\ $$$$\mathrm{height}\:\mathrm{if}\:\mathrm{the}\:\mathrm{tent}\:\mathrm{is}\:\mathrm{18m}.\mathrm{find}\:\mathrm{the}\:\mathrm{volume} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{tent}. \\ $$ Answered by Rasheed.Sindhi last updated…

x-y-N-0-1-x-y-find-z-N-with-z-x-y-

Question Number 94786 by MJS last updated on 21/May/20 $${x},\:{y}\:\in\mathbb{N}\backslash\left\{\mathrm{0},\:\mathrm{1}\right\}\:\wedge\:{x}\leqslant{y} \\ $$$$\mathrm{find}\:{z}\in\mathbb{N}\:\mathrm{with}\:{z}!={x}!{y}! \\ $$ Commented by hknkrc46 last updated on 21/May/20 $$\left(\mathrm{a}\right)\:\mathrm{x}!=\mathrm{y}+\mathrm{1}\:\Rightarrow\:\mathrm{z}!=\left(\mathrm{y}+\mathrm{1}\right)!\:\Rightarrow\:\mathrm{z}=\mathrm{y}+\mathrm{1}\: \\ $$$$\left(\mathrm{a}.\mathrm{1}\right)\:\mathrm{x}=\mathrm{3}\Rightarrow\mathrm{y}=\mathrm{5}\Rightarrow\mathrm{z}=\mathrm{6} \\…

x-x-4-12-2x-7-x-

Question Number 94780 by Abdulrahman last updated on 20/May/20 $$\mathrm{x}!\left(\mathrm{x}−\mathrm{4}\right)!=\mathrm{12}\left(\mathrm{2x}−\mathrm{7}\right)! \\ $$$$\mathrm{x}=? \\ $$ Commented by MJS last updated on 21/May/20 $${x}\geqslant\mathrm{4} \\ $$$$\mathrm{trying} \\…

find-the-period-of-the-function-y-tan-pix-k-cos-2pix-k-5-

Question Number 160310 by HongKing last updated on 27/Nov/21 $$\mathrm{find}\:\mathrm{the}\:\mathrm{period}\:\mathrm{of}\:\mathrm{the}\:\mathrm{function}: \\ $$$$\mathrm{y}\:=\:\mathrm{tan}\:\frac{\pi\mathrm{x}}{\mathrm{k}}\:+\:\mathrm{cos}\:\frac{\mathrm{2}\pi\mathrm{x}}{\mathrm{k}\:+\:\mathrm{5}} \\ $$ Commented by mr W last updated on 27/Nov/21 $${period}={lcm}\left({k},\:{k}+\mathrm{5}\right) \\ $$…

Question-160296

Question Number 160296 by mathlove last updated on 27/Nov/21 Commented by bobhans last updated on 27/Nov/21 $$\:\:\:\:\:\:\:\:\:\:\left(\mathrm{3}\right)^{\frac{\mathrm{3}}{\mathrm{x}+\mathrm{1}}} \:=\:\left(\mathrm{3}\right)^{\frac{\mathrm{2}}{\mathrm{x}}} \:\Leftrightarrow\:\mathrm{3x}=\mathrm{2x}+\mathrm{2}\:;\:\mathrm{x}=\mathrm{2} \\ $$ Answered by Rasheed.Sindhi last…

Question-160302

Question Number 160302 by cortano last updated on 27/Nov/21 Answered by Rasheed.Sindhi last updated on 27/Nov/21 $$\begin{cases}{\mathrm{8}{x}^{\mathrm{2}} −\mathrm{8}{y}^{\mathrm{2}} =\mathrm{24}}\\{\mathrm{3}{x}^{\mathrm{2}} +\mathrm{3}{xy}+\mathrm{6}{y}^{\mathrm{2}} =\mathrm{24}}\end{cases}\Rightarrow\mathrm{5}{x}^{\mathrm{2}} −\mathrm{3}{xy}−\mathrm{14}{y}^{\mathrm{2}} =\mathrm{0} \\ $$$$\Rightarrow\mathrm{5}{x}^{\mathrm{2}}…

n-1-1-n-2n-1-2-

Question Number 160289 by amin96 last updated on 27/Nov/21 $$\underset{{n}\geqslant\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{n}\left(\mathrm{2}{n}+\mathrm{1}\right)^{\mathrm{2}} }=? \\ $$ Answered by qaz last updated on 27/Nov/21 $$\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\mathrm{n}\left(\mathrm{2n}+\mathrm{1}\right)^{\mathrm{2}}…