Question Number 226006 by Linton last updated on 18/Nov/25 $$\left(\mathrm{3}/\mathrm{7}\right)^{\mathrm{0}} \:\:\:{prove}\:{and}\:{evalute}\:{show}\:{all} \\ $$$${working} \\ $$ Commented by mr W last updated on 18/Nov/25 $${for}\:{any}\:{a}\neq\mathrm{0}\:{we}\:{have} \\…
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Question Number 226097 by Jubr last updated on 18/Nov/25 I have multiple rectangular boxes whose sides are x and y. I need to fit n…
Question Number 226053 by Linton last updated on 18/Nov/25 $${The}\:{coefficient}\:{of}\:{x}^{\mathrm{2}} \:{in}\:{the}\:{expansion} \\ $$$${of}\:\left(\mathrm{1}+\:\left(\mathrm{2}/{p}\right){x}\right)^{\mathrm{5}} \:+\:\left(\mathrm{1}+{px}\right)^{\mathrm{6}} \:{is}\:\mathrm{70}. \\ $$$${Find}\:{the}\:{possible}\:{values}\:{of}\:{the} \\ $$$${constant}\:{p}. \\ $$ Answered by mr W…
Question Number 226022 by fantastic2 last updated on 18/Nov/25 $$\int_{\mathrm{0}} ^{\mathrm{1}} \left({x}^{{x}} \right)^{\left({x}^{{x}} \right)^{\left({x}^{{x}} \right)^{…} } } {dx}=? \\ $$ Commented by fantastic2 last updated…
Question Number 226049 by ajfour last updated on 18/Nov/25 Commented by ajfour last updated on 18/Nov/25 Commented by ajfour last updated on 18/Nov/25 $$\left(\frac{\mathrm{2}{a}}{\:\sqrt{\mathrm{3}}}\right)^{\mathrm{2}} +\left\{\sqrt{\left({a}+{b}\right)^{\mathrm{2}}…
Question Number 225980 by fantastic2 last updated on 17/Nov/25 Commented by mr W last updated on 18/Nov/25 $$\alpha_{{max}} =\mathrm{sin}^{−\mathrm{1}} \frac{{m}\mu}{\left({m}+{M}\right)\sqrt{\mathrm{1}+\mu^{\mathrm{2}} }} \\ $$ Commented by…
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Question Number 225994 by Spillover last updated on 17/Nov/25 Answered by Simurdiera last updated on 18/Nov/25 $${Soluci}\acute {{o}n} \\ $$$$\int_{\mathrm{1}/\mathrm{2}} ^{\:\mathrm{1}} \frac{\sqrt{\mathrm{1}\:−\:{x}^{\mathrm{2}} }}{{x}\centerdot\mathrm{sin}\left(\mathrm{arccos}\left({x}\right)\right)\:+\:\mathrm{arcsin}\left({x}\right)}\centerdot\frac{\sqrt{\mathrm{1}\:−\:{x}^{\mathrm{2}} }}{\:\sqrt{\mathrm{1}\:−\:{x}^{\mathrm{2}} }}\:{dx}…
Question Number 225970 by fantastic2 last updated on 17/Nov/25 $$\mathrm{2}^{\mathrm{100}!} \:?\:\mathrm{2}^{\mathrm{100}} !\left[=,<{or}\:>\right] \\ $$ Commented by Ghisom_ last updated on 18/Nov/25 $${b}^{{n}!} \:\mathrm{vs}.\:{b}^{{n}} !\:\:\mathrm{where}\:{b},\:{n}\:\in\mathbb{N}\wedge{b}\geqslant\mathrm{2} \\…