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Category: Algebra

If-2A-3B-4C-find-the-value-of-A-B-C-

Question Number 25053 by Sattwik Chakraborty last updated on 02/Dec/17 $${If}\:\mathrm{2}{A}=\mathrm{3}{B}=\mathrm{4}{C}\:{find}\:{the}\:{value}\:{of}\:{A}:{B}:{C} \\ $$ Answered by $@ty@m last updated on 02/Dec/17 $$\mathrm{2}{A}=\mathrm{3}{B} \\ $$$$\Rightarrow{A}:{B}=\mathrm{3}:\mathrm{2}\:\:{or}\:{A}:{B}=\mathrm{6}:\mathrm{4} \\ $$$$\:\:{Similarly}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{B}:{C}=\mathrm{4}:\mathrm{3}…

Show-that-a-N-10-143-1-9-is-composite-and-b-N-has-two-factors-each-of-which-is-a-series-of-a-G-P-

Question Number 25046 by Tinkutara last updated on 02/Dec/17 $${Show}\:{that} \\ $$$$\left({a}\right)\:{N}=\frac{\mathrm{10}^{\mathrm{143}} −\mathrm{1}}{\mathrm{9}}\:{is}\:{composite},\:{and} \\ $$$$\left({b}\right)\:{N}\:{has}\:{two}\:{factors}\:{each}\:{of}\:{which}\:{is} \\ $$$${a}\:{series}\:{of}\:{a}\:{G}.{P}. \\ $$ Answered by Rasheed.Sindhi last updated on…

If-I-k-1-98-k-k-1-k-1-x-x-1-dx-then-1-I-gt-49-50-2-I-lt-49-50-3-I-lt-log-e-99-4-I-gt-log-e-99-

Question Number 25049 by Tinkutara last updated on 02/Dec/17 $$\mathrm{If}\:{I}\:=\:\underset{{k}=\mathrm{1}} {\overset{\mathrm{98}} {\sum}}\underset{{k}} {\overset{{k}+\mathrm{1}} {\int}}\frac{{k}\:+\:\mathrm{1}}{{x}\left({x}\:+\:\mathrm{1}\right)}{dx},\:\mathrm{then} \\ $$$$\left(\mathrm{1}\right)\:{I}\:>\:\frac{\mathrm{49}}{\mathrm{50}} \\ $$$$\left(\mathrm{2}\right)\:{I}\:<\:\frac{\mathrm{49}}{\mathrm{50}} \\ $$$$\left(\mathrm{3}\right)\:{I}\:<\:\mathrm{log}_{{e}} \mathrm{99} \\ $$$$\left(\mathrm{4}\right)\:{I}\:>\:\mathrm{log}_{{e}} \mathrm{99} \\…

1-1-x-x-1-1-1-2019-2019-

Question Number 156107 by cortano last updated on 08/Oct/21 $$\:\:\:\:\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{x}}\right)^{\mathrm{x}+\mathrm{1}} =\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2019}}\right)^{\mathrm{2019}} \\ $$ Commented by mr W last updated on 08/Oct/21 $$\left(\mathrm{1}+\frac{\mathrm{1}}{{x}}\right)^{{x}+\mathrm{1}} \\ $$$$=\left(\frac{{x}+\mathrm{1}}{{x}}\right)^{{x}+\mathrm{1}} \\…

If-a-4-b-4-c-4-d-4-16-prove-that-a-5-b-5-c-5-d-5-32-for-a-b-c-d-R-

Question Number 25025 by tawa tawa last updated on 01/Dec/17 $$\mathrm{If}\:\:\:\:\mathrm{a}^{\mathrm{4}} \:+\:\mathrm{b}^{\mathrm{4}} \:+\:\mathrm{c}^{\mathrm{4}} \:+\:\mathrm{d}^{\mathrm{4}} \:=\:\mathrm{16},\:\:\mathrm{prove}\:\mathrm{that}:\:\:\mathrm{a}^{\mathrm{5}} \:+\:\mathrm{b}^{\mathrm{5}} \:+\:\mathrm{c}^{\mathrm{5}} \:+\:\mathrm{d}^{\mathrm{5}} \:\leqslant\:\mathrm{32} \\ $$$$\mathrm{for}\:\:\mathrm{a},\:\mathrm{b},\:\mathrm{c},\:\mathrm{d}\:\in\:\mathbb{R} \\ $$ Answered by…

Find-the-area-enclose-by-the-line-y-x-1-and-the-parabola-y-2-2x-6-

Question Number 90557 by I want to learn more last updated on 24/Apr/20 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{enclose}\:\mathrm{by}\:\mathrm{the}\:\mathrm{line}\:\:\:\mathrm{y}\:\:=\:\:\mathrm{x}\:\:−\:\:\mathrm{1}\:\:\mathrm{and} \\ $$$$\mathrm{the}\:\mathrm{parabola}\:\:\:\mathrm{y}^{\mathrm{2}} \:\:=\:\:\mathrm{2x}\:\:+\:\:\mathrm{6} \\ $$ Commented by I want to learn…

Consider-the-function-f-x-which-satisfying-the-functional-equation-2f-x-f-1-x-x-2-1-x-R-and-g-x-3f-x-1-The-range-of-x-g-x-1-g-x-1-is-

Question Number 25023 by Tinkutara last updated on 01/Dec/17 $$\mathrm{Consider}\:\mathrm{the}\:\mathrm{function}\:{f}\left({x}\right)\:\mathrm{which} \\ $$$$\mathrm{satisfying}\:\mathrm{the}\:\mathrm{functional}\:\mathrm{equation} \\ $$$$\mathrm{2}{f}\left({x}\right)\:+\:{f}\left(\mathrm{1}\:−\:{x}\right)\:=\:{x}^{\mathrm{2}} \:+\:\mathrm{1},\:\forall\:{x}\:\in\:{R} \\ $$$$\mathrm{and}\:{g}\left({x}\right)\:=\:\mathrm{3}{f}\left({x}\right)\:+\:\mathrm{1}.\:\mathrm{The}\:\mathrm{range}\:\mathrm{of} \\ $$$$\phi\left({x}\right)\:=\:{g}\left({x}\right)\:+\:\frac{\mathrm{1}}{{g}\left({x}\right)\:+\:\mathrm{1}}\:\mathrm{is} \\ $$ Answered by prakash jain…