Menu Close

Category: Algebra

Question-203206

Question Number 203206 by hardmath last updated on 12/Jan/24 Answered by mr W last updated on 12/Jan/24 $$\underset{{k}=\mathrm{1}} {\overset{\mathrm{100}} {\sum}}\mid{i}−{k}\mid \\ $$$$=\underset{{k}=\mathrm{1}} {\overset{{i}} {\sum}}\mid{i}−{k}\mid+\underset{{k}={i}+\mathrm{1}} {\overset{\mathrm{100}}…

Question-203157

Question Number 203157 by navin12345 last updated on 11/Jan/24 Answered by witcher3 last updated on 11/Jan/24 $$\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{z}^{\mathrm{2}} −\mathrm{2x}−\mathrm{2z}+\mathrm{2}=\mathrm{0} \\ $$$$\left(\mathrm{x}−\mathrm{1}\right)^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\left(\mathrm{z}−\mathrm{1}\right)^{\mathrm{2}} =\mathrm{0}…

1-y-tg-2-x-y-2-lim-x-0-ln-1-2x-sin-2x-

Question Number 203158 by hardmath last updated on 11/Jan/24 $$\mathrm{1}.\:\mathrm{y}\:=\:\mathrm{tg}^{\mathrm{2}} \:\mathrm{x}\:\:\:\Rightarrow\:\:\:\mathrm{y}^{'} \:=\:? \\ $$$$\mathrm{2}.\:\:\underset{\boldsymbol{\mathrm{x}}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{ln}\:\left(\mathrm{1}\:+\:\mathrm{2x}\right)}{\mathrm{sin}\:\mathrm{2x}}\:=\:? \\ $$ Answered by shunmisaki007 last updated on 11/Jan/24 $$\mathrm{1}.\:\mathrm{Are}\:{t},\:{g},\:\mathrm{and}\:{x}\:\mathrm{all}\:\mathrm{variable}\:\mathrm{or}\:\mathrm{one}\:\mathrm{or}\:\mathrm{two}\:\mathrm{of}\:\mathrm{them}\:\mathrm{constant}?…

If-a-2-b-2-2-Then-2a-7-2b-7-6-

Question Number 203149 by hardmath last updated on 11/Jan/24 $$\mathrm{If}\:\:\:\mathrm{a}^{\mathrm{2}} \:+\:\mathrm{b}^{\mathrm{2}} \:=\:\mathrm{2} \\ $$$$\mathrm{Then}\:\:\:\sqrt{\mathrm{2a}\:+\:\mathrm{7}}\:+\:\sqrt{\mathrm{2b}\:+\:\mathrm{7}}\:\leqslant\:\mathrm{6} \\ $$ Commented by mr W last updated on 12/Jan/24 $$\underset{{a}={b}=−\mathrm{1}}…

when-f-x-sinx-pi-lt-x-2pi-cosx-pi-2-x-pi-find-f-2pi-

Question Number 203144 by mustafazaheen last updated on 11/Jan/24 $$\mathrm{when}\:\:\:\:\mathrm{f}\left(\mathrm{x}\right)=\begin{cases}{\mathrm{sinx}\:\:\:\:\:\pi<\mathrm{x}\leqslant\mathrm{2}\pi}\\{\mathrm{cosx}\:\:\:\:\:\frac{\pi}{\mathrm{2}}\leqslant\mathrm{x}\leqslant\pi}\end{cases}\:\:\:\:\:\:\:\:\mathrm{find}\:\:{f}'\left(\mathrm{2}\pi\right)=? \\ $$ Commented by mr W last updated on 13/Jan/24 $$\mathrm{f}'\left(\mathrm{2}\pi\right)\:{doesn}'{t}\:{exist},\:{since}\:{f}\left({x}\right)\:{is}\:{not} \\ $$$${defined}\:{for}\:{x}>\mathrm{2}\pi. \\ $$…

If-y-tan-Find-y-

Question Number 203169 by hardmath last updated on 11/Jan/24 $$\mathrm{If}\:\:\:\mathrm{y}\:=\:\mathrm{tan} \\ $$$$\mathrm{Find}\:\:\:\mathrm{y}^{'} \:=\:? \\ $$ Answered by a.lgnaoui last updated on 11/Jan/24 $$\mathrm{y}'=\frac{\mathrm{cos}^{\mathrm{2}} +\mathrm{sin}\:^{\mathrm{2}} }{\mathrm{cos}\:^{\mathrm{2}}…

if-p-x-2-x-2-x-1-2-x-4-1-4-x-2-and-x-4-x-2-then-show-that-32-p-2-80-

Question Number 203066 by mathlove last updated on 09/Jan/24 $${if}\:{p}=\frac{{x}^{\mathrm{2}} }{{x}−\mathrm{2}}−\frac{{x}}{\mathrm{1}+\frac{\mathrm{2}}{{x}}}−\frac{\mathrm{4}}{\mathrm{1}+\frac{\mathrm{4}}{{x}^{\mathrm{2}} }}\:\:\:{and}\:{x}−\frac{\mathrm{4}}{{x}}=\mathrm{2} \\ $$$${then}\:{show}\:{that}\:\:\left(\frac{\mathrm{32}}{{p}}\right)^{\mathrm{2}} =\mathrm{80} \\ $$ Answered by Rasheed.Sindhi last updated on 09/Jan/24 $${if}\:{p}=\frac{{x}^{\mathrm{2}}…