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Category: Algebra

Solve-the-system-following-of-equations-x-y-z-2-2x-3y-z-1-x-2-y-2-2-z-1-2-9-

Question Number 110087 by 1549442205PVT last updated on 27/Aug/20 $$\mathrm{Solve}\:\mathrm{the}\:\mathrm{system}\:\mathrm{following}\:\mathrm{of}\:\mathrm{equations} \\ $$$$\begin{cases}{\mathrm{x}+\mathrm{y}+\mathrm{z}=\mathrm{2}}\\{\mathrm{2x}+\mathrm{3y}+\mathrm{z}=\mathrm{1}}\\{\mathrm{x}^{\mathrm{2}} +\left(\mathrm{y}+\mathrm{2}\right)^{\mathrm{2}} +\left(\mathrm{z}−\mathrm{1}\right)^{\mathrm{2}} =\mathrm{9}}\end{cases} \\ $$ Commented by bemath last updated on 27/Aug/20 $$\:\:\:\left[\bigtriangleup\frac{{be}}{{math}}\bigtriangledown\right]…

the-domain-of-f-x-log-x-x-denote-the-fractional-part-is-

Question Number 175620 by infinityaction last updated on 04/Sep/22 $${the}\:{domain}\:{of}\:\:{f}\left({x}\right)\:\:=\:\:\sqrt{\mathrm{log}_{{x}} \left\{{x}\right\}}\:\:; \\ $$$$\left\{.\right\}\:{denote}\:{the}\:{fractional}\:{part}\:{is} \\ $$ Commented by mahdipoor last updated on 04/Sep/22 $$\left(\mathrm{0},+\infty\right)−\mathrm{N}= \\ $$$$\left(\mathrm{0},\mathrm{1}\right)\cup\left(\mathrm{1},\mathrm{2}\right)\cup\left(\mathrm{2},\mathrm{3}\right)\cup\left(\mathrm{3},\mathrm{4}\right)\cup……

If-y-f-x-ax-2-bx-c-and-at-some-x-say-x-p-0-p-ydx-y-p-y-p-y-p-p-then-find-p-

Question Number 44543 by ajfour last updated on 01/Oct/18 $${If}\:\:{y}\:={f}\left({x}\right)\:=\:{ax}^{\mathrm{2}} +{bx}+{c} \\ $$$${and}\:\:{at}\:{some}\:{x},\:{say}\:\:{x}=\:{p} \\ $$$$\int_{\mathrm{0}} ^{\:\:{p}} {ydx}\:=\:{y}\left({p}\right)=\:{y}\:'\left({p}\right)\:=\:{y}\:''\left({p}\right)=\:{p}\:, \\ $$$${then}\:{find}\:\boldsymbol{{p}}\:. \\ $$ Commented by MrW3 last…

If-0-lt-a-b-then-prove-that-determinant-1-a-log-a-a-1-a-2-b-2-2-a-2-b-2-8-log-a-2-b-2-2-1-b-log-b-b-0-

Question Number 175593 by Shrinava last updated on 03/Sep/22 $$\mathrm{If}\:\:\:\mathrm{0}<\mathrm{a}\leqslant\mathrm{b}\:\:\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that}: \\ $$$$\begin{vmatrix}{\mathrm{1}}&{\mathrm{a}}&{\mathrm{log}\left(\mathrm{a}^{\boldsymbol{\mathrm{a}}} \right)}\\{\mathrm{1}}&{\sqrt{\frac{\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} }{\mathrm{2}}}\:\sqrt{\frac{\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} }{\mathrm{8}}}\:\centerdot\:\mathrm{log}\left(\frac{\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} }{\mathrm{2}}\right)}&{}\\{\mathrm{1}}&{\mathrm{b}}&{\mathrm{log}\left(\mathrm{b}^{\boldsymbol{\mathrm{b}}} \right)}\end{vmatrix}\geqslant\:\mathrm{0} \\ $$ Commented by Rasheed.Sindhi…

If-a-gt-b-and-c-gt-d-prove-that-a-c-may-be-greater-than-equal-to-or-less-than-b-d-

Question Number 44502 by Tip Top last updated on 30/Sep/18 $$\mathrm{If}\:\mathrm{a}>\mathrm{b},\mathrm{and}\:\mathrm{c}>\mathrm{d},\mathrm{prove}\:\mathrm{that}\:\mathrm{a}−\mathrm{c}\:\mathrm{may}\:\mathrm{be}\:\mathrm{greater}\:\mathrm{than}, \\ $$$$\mathrm{equal}\:\mathrm{to}\:\mathrm{or}\:\mathrm{less}\:\mathrm{than}\:\mathrm{b}−\mathrm{d}. \\ $$$$ \\ $$ Answered by MrW3 last updated on 30/Sep/18 $${a}={b}+\delta,\:\delta>\mathrm{0}…