Question Number 157098 by mathocean1 last updated on 19/Oct/21 $${n}\:\in\:\mathbb{N}^{\ast} \:;\:{n}\:{is}\:{not}\:{a}\:{square}\:{of}\:{any} \\ $$$${integer}.\:{Show}\:{that}\:\sqrt{{n}}\:\notin\:{Q}\:. \\ $$ Answered by mindispower last updated on 19/Oct/21 $$\sqrt{{n}}=\frac{{p}}{{q}},\:{p} {q}=\mathrm{1}\Rightarrow \\…
Question Number 157087 by henderson last updated on 19/Oct/21
Question Number 157061 by mathocean1 last updated on 19/Oct/21 $$ \\ $$$${Show}\:{that}\:\forall\:{n}\:\in\:\mathbb{N},\: \\ $$$$\lfloor\left(\sqrt{{n}}+\sqrt{{n}+\mathrm{1}}\right)^{\mathrm{2}} \rfloor=\mathrm{4}{n}+\mathrm{1} \\ $$ Answered by apriadodir last updated on 19/Oct/21 $$\mathrm{answer}:…
Question Number 91509 by kikomssn@gmail.com last updated on 01/May/20 $${does}\:{anyone}\:{know}\:{Glauss}'\:{law}\:{for}\:{magnetism}?\:{tanks} \\ $$ Commented by jagoll last updated on 01/May/20 $${Gauss}\:{or}\:{Glauss}\:? \\ $$ Commented by Tony…
Question Number 25972 by mondodotto@gmail.com last updated on 17/Dec/17 Answered by rita1608 last updated on 17/Dec/17 $${differentiating}\:{on}\:{both}\:{sides}\: \\ $$$${we}\:{get}\:\frac{{d}}{{dx}}\left({logx}^{\mathrm{2}} \right)=\frac{\mathrm{1}}{\mathrm{25}} \\ $$$$\:\:\:\:\:\:\:\:\frac{\mathrm{1}}{{x}^{\mathrm{2}} }×\mathrm{2}{x}=\frac{\mathrm{1}}{\mathrm{25}} \\ $$$$\:\:\:\:\:\:\:\:\frac{\mathrm{2}}{{x}}=\frac{\mathrm{1}}{\mathrm{25}}…
Question Number 91500 by kikomssn@gmail.com last updated on 01/May/20 $${v}=\pi\int_{\mathrm{1}} ^{\mathrm{4}} \left[\left(\frac{\mathrm{1}}{\mathrm{4}}.{x}^{\mathrm{2}} \right)^{\mathrm{2}} {dx}\right. \\ $$ Commented by john santu last updated on 01/May/20 $$=\:\frac{\pi}{\mathrm{16}}×\frac{\mathrm{1}}{\mathrm{5}}×\left(\mathrm{4}^{\mathrm{5}}…
Question Number 91497 by kikomssn@gmail.com last updated on 01/May/20 $${v}=\pi\int_{\mathrm{0}} ^{\mathrm{2}} {x}^{\mathrm{2}} {dx} \\ $$ Commented by jagoll last updated on 01/May/20 $$\left.=\:\frac{\pi{x}^{\mathrm{3}} }{\mathrm{3}}\:\right]_{\mathrm{0}} ^{\mathrm{2}}…
Question Number 157031 by PRITHWISH SEN 2 last updated on 18/Oct/21 $$\mathrm{If}\:\:\mathrm{xcos}\:\theta+\mathrm{ycos}\:\emptyset+\mathrm{zcos}\:\psi=\mathrm{0}, \\ $$$$\:\:\:\:\:\:\mathrm{xsin}\:\theta+\mathrm{ysin}\:\emptyset+\mathrm{zsin}\:\psi=\mathrm{0} \\ $$$$\mathrm{and}\:\mathrm{xsec}\:\theta+\mathrm{ysec}\:\emptyset+\mathrm{zsec}\:\psi=\mathrm{0} \\ $$$$\mathrm{then}\:\mathrm{prove}\:\mathrm{that} \\ $$$$\:\:\:\:\:\:\:\:\:\:\left(\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} −\mathrm{z}^{\mathrm{2}} \right)^{\mathrm{2}} =\:\mathrm{4x}^{\mathrm{2}} \mathrm{y}^{\mathrm{2}}…
Question Number 157010 by aliyn last updated on 18/Oct/21 Commented by aliyn last updated on 18/Oct/21 $${prove}\:\left({x}−{h}\right)^{\mathrm{2}} =\mathrm{4}{p}\:\left({y}−{k}\right) \\ $$ Commented by aliyn last updated…
Question Number 157007 by Armindo last updated on 18/Oct/21 Commented by Armindo last updated on 18/Oct/21 I need help, for to solve This exercice. Answered by TheHoneyCat last updated on 21/Oct/21 $$\frac{\mathrm{1}}{\:^{\mathrm{4}}…