Question Number 216058 by mokys last updated on 26/Jan/25 Commented by mokys last updated on 26/Jan/25 $${graph}\:{the}\:{function} \\ $$ Commented by mokys last updated on…
Question Number 216055 by efronzo1 last updated on 26/Jan/25 $$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:^{\mathrm{2}} \mathrm{2x}}{\:\sqrt[{\mathrm{3}}]{\mathrm{cos}\:\mathrm{x}}−\sqrt[{\mathrm{4}}]{\mathrm{cos}\:\mathrm{x}}}\:=? \\ $$ Answered by golsendro last updated on 27/Jan/25 $$\:\:=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{4cos}\:^{\mathrm{2}} \mathrm{x}\left(\mathrm{1}−\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}\right)}{\:\sqrt[{\mathrm{3}}]{\mathrm{cos}\:\mathrm{x}}−\sqrt[{\mathrm{4}}]{\mathrm{cos}\:\mathrm{x}}}…
Question Number 216050 by hardmath last updated on 26/Jan/25 $$\mathrm{x},\mathrm{y},\mathrm{z}\:\in\:\mathbb{N} \\ $$$$\mathrm{lcd}\left(\mathrm{x};\mathrm{y}\right)=\mathrm{72} \\ $$$$\mathrm{lcd}\left(\mathrm{x};\mathrm{z}\right)=\mathrm{600} \\ $$$$\mathrm{lcd}\left(\mathrm{y};\mathrm{z}\right)=\mathrm{900} \\ $$$$\mathrm{Find}:\:\:\:\mathrm{1}.\left(\mathrm{x};\mathrm{y};\mathrm{z}\right)=? \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{2}.\left(\mathrm{x};\mathrm{y};\mathrm{z}\right)=? \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{3}.\left(\mathrm{x};\mathrm{y};\mathrm{z}\right)=? \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:… \\…
Question Number 216046 by MATHEMATICSAM last updated on 26/Jan/25 $${x}\:=\:{bz}\:+\:{cy},\:{y}\:=\:{cx}\:+\:{az}\:\mathrm{and}\:{z}\:=\:{bx}\:+\:{ay} \\ $$$$\mathrm{then}\:\mathrm{prove}\:\mathrm{that}\:{a}^{\mathrm{2}} \:+\:{b}^{\mathrm{2}} \:+\:{c}^{\mathrm{2}} \:+\:\mathrm{2}{abc}\:=\:\mathrm{1}. \\ $$ Answered by A5T last updated on 26/Jan/25 $$\mathrm{x}=\mathrm{bz}+\mathrm{cy}…\left(\mathrm{i}\right);\:\mathrm{y}=\mathrm{cx}+\mathrm{az}…\left(\mathrm{ii}\right);\:\mathrm{z}=\mathrm{bx}+\mathrm{ay}…\left(\mathrm{iii}\right)…
Question Number 216042 by ajfour last updated on 26/Jan/25 $$\left({i}\right)\:\:\:\int\mathrm{sec}\:^{\mathrm{5}} \theta{d}\theta \\ $$$$\left({ii}\right)\:\:\int\:\frac{\sqrt{\mathrm{tan}\:\theta}\:{d}\theta}{\mathrm{cos}\:\theta} \\ $$ Commented by ajfour last updated on 26/Jan/25 https://youtu.be/VqEdd_VGxGI?si=VnVRn7bW5wENyi9Y Find radius of circle inscribed in half ellipse. Commented by…
Question Number 216032 by efronzo1 last updated on 26/Jan/25 $$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\mathrm{cos}\:\mathrm{x}\:\sqrt{\mathrm{cos}\:\mathrm{2x}}}{\mathrm{x}^{\mathrm{2}} }\:=? \\ $$ Answered by mr W last updated on 26/Jan/25 $$\mathrm{cos}\:{x}\sim\mathrm{1}−\frac{{x}^{\mathrm{2}} }{\mathrm{2}} \\…
Question Number 216033 by efronzo1 last updated on 26/Jan/25 Answered by mr W last updated on 26/Jan/25 Commented by mr W last updated on 26/Jan/25…
Question Number 216014 by mathlove last updated on 25/Jan/25 $$\underset{\Delta{x}\rightarrow{cos}\frac{\pi}{\mathrm{2}}} {\mathrm{lim}}\:\frac{\mathrm{sin}^{\mathrm{3}} \left(\Delta{x}+{x}\right)−{sin}^{\mathrm{3}} {x}}{\mathrm{2}^{−\mathrm{1}} \centerdot\Delta{x}}=? \\ $$ Answered by MrGaster last updated on 26/Jan/25 $$=\mathrm{2}\centerdot\underset{\Delta{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{sin}^{\mathrm{3}}…
if-the-fraction-m-2-25m-m-1-is-reductible-how-many-values-does-m-take-if-is-a-2-digit-number-thanks-
Question Number 215999 by lmcp1203 last updated on 25/Jan/25 $${if}\:{the}\:{fraction}\:\frac{{m}^{\mathrm{2}} +\mathrm{25}{m}}{{m}+\mathrm{1}}\:\:{is}\:{reductible}.\:{how}\:{many}\:{values}\:{does}\:{m}\:\:{take}\:{if}\:{is}\:{a}\:\mathrm{2}\:{digit}\:\:{number}?\:{thanks} \\ $$ Answered by Rasheed.Sindhi last updated on 25/Jan/25 $$\frac{{m}^{\mathrm{2}} +\mathrm{25}{m}}{{m}+\mathrm{1}}={m}\left(\frac{{m}+\mathrm{25}}{{m}+\mathrm{1}}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:={m}\left(\frac{{m}+\mathrm{1}+\mathrm{24}}{{m}+\mathrm{1}}\right)={m}\left(\mathrm{1}+\frac{\mathrm{24}}{{m}+\mathrm{1}}\right) \\…
Question Number 216010 by MATHEMATICSAM last updated on 25/Jan/25 $$\mathrm{Solve}\:\mathrm{for}\:{x}\:\mathrm{and}\:{y} \\ $$$${ax}^{\mathrm{2}} \:+\:{bxy}\:+\:{cy}^{\mathrm{2}} \:=\:{bx}^{\mathrm{2}} \:+\:{cxy}\:+\:{ay}^{\mathrm{2}} \:=\:{d}. \\ $$ Answered by mr W last updated on…