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Author: Tinku Tara

Find-all-x-R-that-satisfy-the-following-inequalities-a-4x-3-11-b-x-2-gt-x-1-c-x-x-2-2-x-8-

Question Number 193079 by Mastermind last updated on 03/Jun/23 $$\mathrm{Find}\:\mathrm{all}\:\mathrm{x}\in\mathbb{R}\:\mathrm{that}\:\mathrm{satisfy}\:\mathrm{the}\:\mathrm{following} \\ $$$$\mathrm{inequalities}: \\ $$$$\left.\mathrm{a}\right)\:\mid\mathrm{4x}−\mathrm{3}\mid\leqslant\mathrm{11} \\ $$$$\left.\mathrm{b}\right)\:\mid\mathrm{x}−\mathrm{2}\mid>\mid\mathrm{x}+\mathrm{1}\mid \\ $$$$\left.\mathrm{c}\right)\:\mid\mathrm{x}\mid\:+\:\mid\mathrm{x}+\mathrm{2}\mid\:+\:\mid\mathrm{2}−\mathrm{x}\mid\leqslant\mathrm{8} \\ $$ Commented by MM42 last updated…

m-n-N-d-is-the-greatest-common-divisor-of-m-and-n-we-suppose-m-dm-and-n-dn-with-m-and-n-N-show-that-u-v-Z-such-that-mu-nv-d-

Question Number 127540 by mathocean1 last updated on 30/Dec/20 $${m},\:{n},\:\in\:\mathbb{N}\:;\:{d}\:{is}\:{the}\:{greatest} \\ $$$${common}\:{divisor}\:{of}\:{m}\:{and}\:{n}.\: \\ $$$${we}\:{suppose}\:{m}={dm}'\:{and}\:{n}={dn}'\: \\ $$$${with}\:{m}'\:{and}\:{n}'\:\in\:\mathbb{N}. \\ $$$${show}\:{that}\:\exists\:{u},{v}\:\in\:\mathbb{Z}\:{such}\: \\ $$$${that}\:{mu}−{nv}={d} \\ $$ Terms of Service…

1-Prove-that-if-gt-0-and-a-x-R-then-a-x-lt-iff-x-lt-a-lt-x-help-

Question Number 193078 by Mastermind last updated on 03/Jun/23 $$\left.\mathrm{1}\right)\:\mathrm{Prove}\:\mathrm{that}\:\mathrm{if}\:\varepsilon>\mathrm{0}\:\mathrm{and}\:\mathrm{a},\mathrm{x}\in\mathbb{R},\:\mathrm{then} \\ $$$$\mid\mathrm{a}−\mathrm{x}\mid<\varepsilon\:\mathrm{iff}\:\mathrm{x}−\varepsilon<\mathrm{a}<\mathrm{x}+\varepsilon \\ $$$$ \\ $$$$\mathrm{help} \\ $$ Answered by Subhi last updated on 03/Jun/23…

Question-193073

Question Number 193073 by Tawa11 last updated on 03/Jun/23 Answered by Subhi last updated on 03/Jun/23 $$ \\ $$$${the}\:{system}\:{is}\:{in}\:{equalibrium} \\ $$$$\Sigma{f}\:=\:\mathrm{0}\:{at}\:{x},{y}\:{axis} \\ $$$${p}.{cos}\left(\mathrm{30}\right)+\mathrm{2}.{sin}\left(\mathrm{45}\right)−{Q}.{sin}\left(\mathrm{60}\right)=\mathrm{0} \\ $$$$\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}.{p}−\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}{Q}\:=\:−\sqrt{\mathrm{2}}…