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Author: Tinku Tara

Question-208384

Question Number 208384 by efronzo1 last updated on 14/Jun/24 $$\:\:\:\:\downharpoonleft\underline{\:} \\ $$ Answered by A5T last updated on 14/Jun/24 $${log}_{{abc}} \left({a}\right)+{log}_{{abc}} \left({b}\right)=\mathrm{2}+\mathrm{3}=\mathrm{5}\Rightarrow{log}_{{abc}} \left({ab}\right)=\mathrm{5} \\ $$$${log}_{{abc}}…

if-fof-x-f-x-x-and-f-1-1-find-fofofofofofofofofof-1-

Question Number 208370 by lmcp1203 last updated on 14/Jun/24 $${if}\:\:\:\left({fof}\right)\left({x}\right)={f}\left({x}\right)+{x}\:\:{and}\:{f}\left(\mathrm{1}\right)=\mathrm{1}\:\:\: \\ $$$${find}\:\:{fofofofofofofofofof}\left(\mathrm{1}\right) \\ $$ Commented by A5T last updated on 14/Jun/24 $${f}\left({f}\left({x}\right)\right)={f}\left({x}\right)+{x}\Rightarrow\:{f}\left({f}\left(\mathrm{1}\right)\right)={f}\left(\mathrm{1}\right)+\mathrm{1} \\ $$$$\Rightarrow{f}\left(\mathrm{1}\right)={f}\left(\mathrm{1}\right)+\mathrm{1}\Rightarrow\mathrm{1}\overset{?} {=}\mathrm{0}…

1-Find-the-length-of-each-of-the-following-a-x-3-lt-x-lt-7-b-x-2-x-6-3-x-1-c-x-2-x-lt-5-1-lt-x-7-2-Let-I-a-b-Prove-that-I-is-mea

Question Number 208367 by Mastermind last updated on 13/Jun/24 $$\mathrm{1}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{length}\:\mathrm{of}\:\mathrm{each}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following} \\ $$$$\:\:\:\:\:\left(\mathrm{a}\right)\:\left\{\mathrm{x}\::\:−\mathrm{3}\:<\:\mathrm{x}\:<\:\mathrm{7}\right\} \\ $$$$\:\:\:\:\:\left(\mathrm{b}\right)\:\left\{\mathrm{x}\::\:\mathrm{2}\:\leqslant\:\mathrm{x}\:\leqslant\:\mathrm{6}\right\}\:\cup\:\left\{−\mathrm{3}\:\leqslant\:\mathrm{x}\:\leqslant\:−\mathrm{1}\right\} \\ $$$$\:\:\:\:\:\left(\mathrm{c}\right)\:\left\{\mathrm{x}\::\:−\mathrm{2}\:\leqslant\:\mathrm{x}\:<\:\mathrm{5}\right\}\:\cup\:\left\{\mathrm{1}\:<\:\mathrm{x}\:\leqslant\:\mathrm{7}\right\} \\ $$$$ \\ $$$$\mathrm{2}.\:\mathrm{Let}\:\mathrm{I}=\left(\mathrm{a},\:\mathrm{b}\right).\:\mathrm{Prove}\:\mathrm{that}\:\mathrm{I}\:\mathrm{is}\:\mathrm{measurable} \\ $$$$\mathrm{and}\:\mathrm{m}\left(\mathrm{I}\right)\:=\:\mathrm{L}\left(\mathrm{I}\right). \\ $$ Terms…

P-x-is-polynomial-P-x-x-4-2ax-3-bx-5-x-1-2-Find-b-

Question Number 208362 by hardmath last updated on 13/Jun/24 $$\mathrm{P}\left(\mathrm{x}\right)\:\:\mathrm{is}\:\mathrm{polynomial} \\ $$$$\mathrm{P}\left(\mathrm{x}\right)\:=\:\frac{\mathrm{x}^{\mathrm{4}} \:+\:\mathrm{2ax}^{\mathrm{3}} \:−\:\mathrm{bx}\:−\:\mathrm{5}}{\left(\mathrm{x}\:+\:\mathrm{1}\right)^{\mathrm{2}} } \\ $$$$\mathrm{Find}:\:\:\:\boldsymbol{\mathrm{b}}\:=\:? \\ $$ Answered by mr W last updated…

a-b-c-N-x-4-2a-5-6-b-9-9-c-1-find-min-x-a-b-c-

Question Number 208342 by hardmath last updated on 13/Jun/24 $$\mathrm{a},\mathrm{b},\mathrm{c}\in\mathbb{N} \\ $$$$\mathrm{x}\:=\:\mathrm{4}\left(\mathrm{2a}+\mathrm{5}\right)\:=\:\mathrm{6}\left(\mathrm{b}+\mathrm{9}\right)\:=\:\mathrm{9}\left(\mathrm{c}−\mathrm{1}\right) \\ $$$$\mathrm{find}:\:\:\:\boldsymbol{\mathrm{min}}\left(\mathrm{x}+\mathrm{a}+\mathrm{b}+\mathrm{c}\right)\:=\:? \\ $$ Answered by A5T last updated on 13/Jun/24 $${c}=\frac{\mathrm{6}\left({b}+\mathrm{9}\right)}{\mathrm{9}}+\mathrm{1}=\frac{\mathrm{2}{b}}{\mathrm{3}}+\mathrm{7}\Rightarrow{b}=\mathrm{3}{k} \\…