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Category: Algebra

x-y-xyz-1-4-y-z-xyz-1-24-x-z-xyz-1-24-

Question Number 160677 by tounghoungko last updated on 04/Dec/21 $$\:\:\:\begin{cases}{\frac{\mathrm{x}+\mathrm{y}}{\mathrm{xyz}}\:=\:−\frac{\mathrm{1}}{\mathrm{4}}}\\{\frac{\mathrm{y}+\mathrm{z}}{\mathrm{xyz}}\:=\:−\frac{\mathrm{1}}{\mathrm{24}}}\\{\frac{\mathrm{x}+\mathrm{z}}{\mathrm{xyz}}\:=\:\frac{\mathrm{1}}{\mathrm{24}}}\end{cases}\: \\ $$$$\:\: \\ $$ Commented by bobhans last updated on 04/Dec/21 $$\Leftrightarrow\:\frac{\mathrm{1}}{\mathrm{xyz}}\left(\mathrm{x}+\mathrm{y}+\mathrm{2z}\right)=\mathrm{0}\:\Rightarrow\mathrm{x}+\mathrm{y}=−\mathrm{2z} \\ $$$$\Leftrightarrow\:\frac{−\mathrm{2z}}{\mathrm{xyz}}\:=\:−\frac{\mathrm{1}}{\mathrm{4}}\:;\:\mathrm{xy}=\mathrm{8} \\…

Question-95127

Question Number 95127 by unknown last updated on 23/May/20 Commented by unknown last updated on 23/May/20 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{solution}\:\left({n},{k}\right).\:\mathrm{If}\:\left({n},{k}\right)\:\mathrm{is}\:\mathrm{natural}\:\mathrm{number}. \\ $$ Terms of Service Privacy Policy Contact:…

Find-lim-x-0-4x-1-4x-

Question Number 160658 by HongKing last updated on 04/Dec/21 $$\boldsymbol{\mathrm{Find}}:\:\:\:\underset{\boldsymbol{\mathrm{x}}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\mathrm{4}\boldsymbol{\mathrm{x}}\:\left[\:\frac{\mathrm{1}}{\mathrm{4}\boldsymbol{\mathrm{x}}}\:\right]\:=\:? \\ $$$$ \\ $$ Commented by mr W last updated on 04/Dec/21 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}4}{x}\left[\frac{\mathrm{1}}{\mathrm{4}{x}}\right]…

King-s-inequality-if-a-b-n-m-then-a-n-b-m-2-1-b-2-m-n-a-b-2-n-

Question Number 160644 by HongKing last updated on 03/Dec/21 $$\mathrm{King}'\mathrm{s}\:\mathrm{inequality} \\ $$$$\mathrm{if}\:\:\:\mathrm{a}\leqslant\mathrm{b}\:\:\:;\:\:\:\mathrm{n}\leqslant\mathrm{m}\:\:\:\mathrm{then}: \\ $$$$\frac{\mathrm{a}^{\boldsymbol{\mathrm{n}}} \:+\:\mathrm{b}^{\boldsymbol{\mathrm{m}}} }{\mathrm{2}}\:\geqslant\:\left(\frac{\mathrm{1}\:+\:\mathrm{b}}{\mathrm{2}}\right)^{\boldsymbol{\mathrm{m}}-\boldsymbol{\mathrm{n}}} \:\centerdot\:\left(\frac{\mathrm{a}\:+\:\mathrm{b}}{\mathrm{2}}\right)^{\boldsymbol{\mathrm{n}}} \\ $$ Terms of Service Privacy Policy Contact:…

Solve-x-2-y-2-13-i-2x-2-3y-2xy-2-ii-

Question Number 95093 by I want to learn more last updated on 22/May/20 $$\mathrm{Solve}: \\ $$$$\:\:\:\:\:\:\:\:\mathrm{x}^{\mathrm{2}} \:\:+\:\:\mathrm{y}^{\mathrm{2}} \:\:=\:\:\mathrm{13}\:\:\:\:\:\:\:\:\:\:…….\:\left(\mathrm{i}\right) \\ $$$$\:\:\:\:\:\:\mathrm{2x}^{\mathrm{2}} \:\:+\:\:\mathrm{3y}\:\:=\:\:\mathrm{2xy}^{\mathrm{2}} \:\:\:\:\:\:\:\:\:\:…….\:\left(\mathrm{ii}\right) \\ $$ Answered…

to-make-an-open-fish-tank-a-glass-sheet-of-2mm-gauge-is-used-the-outer-length-breadth-and-height-are-60-4-40-4-40-2-respectively-how-much-maximum-volume-of-water-will-be-contained-in-it-

Question Number 29520 by bbbbbb last updated on 09/Feb/18 $$\mathrm{to}\:\mathrm{make}\:\mathrm{an}\:\mathrm{open}\:\mathrm{fish}\:\mathrm{tank}\:\mathrm{a}\:\mathrm{glass}\:\mathrm{sheet}\:\mathrm{of}\: \\ $$$$\mathrm{2mm}\:\mathrm{gauge}\:\mathrm{is}\:\mathrm{used}\:.\mathrm{the}\:\mathrm{outer}\:\mathrm{length} \\ $$$$,\mathrm{breadth}\:\mathrm{and}\:\mathrm{height}\:\mathrm{are}\:\mathrm{60}.\mathrm{4}\:,\:\mathrm{40}.\mathrm{4},\: \\ $$$$\mathrm{40}.\mathrm{2}\:\mathrm{respectively}\:.\mathrm{how}\:\mathrm{much}\:\mathrm{maximum} \\ $$$$\mathrm{volume}\:\mathrm{of}\:\mathrm{water}\:\mathrm{will}\:\mathrm{be}\:\mathrm{contained}\:\mathrm{in}\:\mathrm{it}\:? \\ $$$$ \\ $$ Answered by Rasheed.Sindhi…