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Category: Algebra

let-x-and-y-be-positive-reals-such-that-x-3-y-3-x-y-3-30xy-2000-show-that-x-y-10-

Question Number 169445 by infinityaction last updated on 30/Apr/22 $$ \\ $$$$\:\:\:\mathrm{let}\:\mathrm{x}\:\mathrm{and}\:\mathrm{y}\:\mathrm{be}\:\mathrm{positive}\:\mathrm{reals}\:\mathrm{such}\:\mathrm{that} \\ $$$$\:\:\:\:\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{y}^{\mathrm{3}} \:+\:\left(\mathrm{x}+\mathrm{y}\right)^{\mathrm{3}} \:+\mathrm{30xy}\:=\:\mathrm{2000} \\ $$$$\:\:\:\:\mathrm{show}\:\mathrm{that}\:\mathrm{x}+\mathrm{y}\:=\:\mathrm{10} \\ $$ Commented by mr W…

find-all-such-numbers-if-we-make-its-last-digit-say-k-as-its-first-digit-the-number-becomes-k-times-large-as-before-k-k-k-k-

Question Number 103888 by mr W last updated on 18/Jul/20 $${find}\:{all}\:{such}\:{numbers}: \\ $$$${if}\:{we}\:{make}\:{its}\:{last}\:{digit},\:{say}\:{k},\:{as}\:{its} \\ $$$${first}\:{digit},\:{the}\:{number}\:{becomes}\:{k} \\ $$$${times}\:{large}\:{as}\:{before}. \\ $$$$\left(\Box\Box…\Box{k}\right)\rightarrow\left({k}\Box\Box…\Box\right)={k}×\left(\Box\Box…\Box{k}\right) \\ $$ Answered by MAB last…

Question-169407

Question Number 169407 by Shrinava last updated on 29/Apr/22 Answered by Rasheed.Sindhi last updated on 01/May/22 $$\mathrm{If}\:\mathbb{N}=\left\{\mathrm{0},\mathrm{1},\mathrm{2},…\right\} \\ $$$$\mathrm{M}=\left\{\left(\mathrm{0},\mathrm{0},\mathrm{0},\mathrm{0}\right)\right\} \\ $$$$\Omega=\mathrm{0} \\ $$$$\mathrm{16}^{{x}} +\mathrm{16}^{\frac{\mathrm{1}}{{x}}} =\mathrm{8}\:{has}\:{no}\:{solution}.…

1-2-y-dx-dy-2-x-2-y-2-dx-2xydy-3-xdx-1-y-dy-0-4-dy-3x-2-dx-5-2y-2-dx-x-1-y-2-dy-0-6-4x-3-dx-dy-0-

Question Number 169389 by Shrinava last updated on 29/Apr/22 $$\mathrm{1}.\:\mathrm{2}\sqrt{\mathrm{y}}\:\mathrm{dx}\:=\:\mathrm{dy} \\ $$$$\mathrm{2}.\:\left(\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2}} \right)\mathrm{dx}\:=\:\mathrm{2xydy} \\ $$$$\mathrm{3}.\:\mathrm{xdx}\:+\:\frac{\mathrm{1}}{\mathrm{y}}\:\mathrm{dy}\:=\:\mathrm{0} \\ $$$$\mathrm{4}.\:\mathrm{dy}\:=\:\mathrm{3x}^{\mathrm{2}} \:\mathrm{dx} \\ $$$$\mathrm{5}.\:\mathrm{2y}^{\mathrm{2}} \mathrm{dx}\:+\:\mathrm{x}\left(\mathrm{1}\:+\:\mathrm{y}^{\mathrm{2}} \right)\:\mathrm{dy}\:=\:\mathrm{0} \\ $$$$\mathrm{6}.\:\mathrm{4x}^{\mathrm{3}}…

find-the-value-of-v-if-v-denotes-maximum-value-of-x-2-y-2-where-x-5-2-y-12-2-14-hint-repersent-greatest-integer-function-of-

Question Number 169382 by infinityaction last updated on 29/Apr/22 $$\:\:\:\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{value}}\:\boldsymbol{\mathrm{of}}\:\:\left[\boldsymbol{\mathrm{v}}\right]\:\boldsymbol{\mathrm{if}}\:\boldsymbol{\mathrm{v}}\:\boldsymbol{\mathrm{den}{o}\mathrm{tes}}\:\boldsymbol{\mathrm{maximum}}\:\: \\ $$$$\:\:\:\boldsymbol{\mathrm{value}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{x}}^{\mathrm{2}} \:+\:\boldsymbol{\mathrm{y}}^{\mathrm{2}} \:,\:\boldsymbol{\mathrm{where}}\:\left(\boldsymbol{\mathrm{x}}+\mathrm{5}\right)^{\mathrm{2}} \:+\:\left(\boldsymbol{\mathrm{y}}−\mathrm{12}\right)^{\mathrm{2}} \:=\:\mathrm{14} \\ $$$$\:\:\:\:\left(\boldsymbol{\mathrm{hint}}\:\left[\bullet\right]\:\boldsymbol{\mathrm{repersent}}\:\boldsymbol{\mathrm{greatest}}\:\boldsymbol{\mathrm{integer}}\:\boldsymbol{\mathrm{function}}\:\boldsymbol{\mathrm{of}}\:“\:\bullet''\right) \\ $$$$ \\ $$$$\: \\ $$ Commented…

1-y-arcsin-sinx-y-2-y-sin-x-1-y-3-y-ln-5-sinx-y-4-y-cos-2x-3-y-

Question Number 169356 by Shrinava last updated on 29/Apr/22 $$\mathrm{1}.\:\mathrm{y}\:=\:\mathrm{arcsin}\left(\mathrm{sinx}\right)\:\Rightarrow\:\mathrm{y}^{'} =? \\ $$$$\mathrm{2}.\:\mathrm{y}\:=\:\mathrm{sin}\:\sqrt{\mathrm{x}\:+\:\mathrm{1}}\:\Rightarrow\:\mathrm{y}^{'} =? \\ $$$$\mathrm{3}.\:\mathrm{y}\:=\:\mathrm{ln}^{\mathrm{5}} \:\mathrm{sinx}\:\Rightarrow\:\mathrm{y}^{'} =? \\ $$$$\mathrm{4}.\:\mathrm{y}\:=\:\mathrm{cos}\left(\mathrm{2x}\:+\:\mathrm{3}\right)\:\Rightarrow\:\mathrm{y}^{'} =? \\ $$ Answered by…