Category: Algebra

Question Number 207127 by hardmath last updated on 07/May/24 $$\mathrm{If}\:\:\:\:\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\mathrm{sin}^{\mathrm{4}} \:\mathrm{2x} \\ $$$$\mathrm{Find}\:\:\:\:\:\mathrm{f}\:^{'} \:\left(\frac{\pi}{\mathrm{12}}\right)\:=\:? \\ $$ Answered by Skabetix last updated on 07/May/24 $$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{sin}^{\mathrm{4}} \left(\mathrm{2x}\right)…

Question Number 207092 by hardmath last updated on 06/May/24 $$\begin{cases}{\mathrm{x}^{\mathrm{2}} \:=\:\mathrm{x}\:−\:\mathrm{6y}}\\{\mathrm{y}^{\mathrm{2}} \:=\:\mathrm{y}\:−\:\mathrm{6x}}\end{cases}\:\:\:\:\:\Rightarrow\:\:\:\:\mathrm{x}\:+\:\mathrm{y}\:=\:? \\ $$ Answered by A5T last updated on 06/May/24 $${x}^{\mathrm{2}} −{y}^{\mathrm{2}} ={x}−{y}−\mathrm{6}{y}+\mathrm{6}{x}=\mathrm{7}{x}−\mathrm{7}{y} \\…

Question Number 207043 by necx122 last updated on 04/May/24 $${Solve}\:{for}\:{the}\:{domain}\:{and}\:{range}\:{of}\:{f}\left({x}\right)\:{if} \\ $$$${f}\left({x}\right)\:=\:\sqrt{\frac{\mathrm{3}{x}−\mathrm{5}}{{x}+\mathrm{3}}} \\ $$ Answered by Frix last updated on 04/May/24 $$\mathrm{1}.\:{x}+\mathrm{3}\neq\mathrm{0} \\ $$$${x}\neq−\mathrm{3} \\…

Question Number 206987 by hardmath last updated on 02/May/24 $$\frac{\mathrm{120}}{\mid\mathrm{x}−\mathrm{1}\mid\:+\:\mid\mathrm{x}−\mathrm{3}\mid\:+\:\mid\mathrm{x}−\mathrm{5}\mid}\:\:\:\Rightarrow\:\:\:\mathrm{max}\:=\:? \\ $$ Answered by Frix last updated on 02/May/24 $$\frac{\mathrm{120}}{{f}\left({x}\right)}\:\mathrm{is}\:\mathrm{max}\:\Rightarrow\:{f}\left({x}\right)\:\mathrm{is}\:\mathrm{min} \\ $$$$\mathrm{4}\leqslant\mid{x}−\mathrm{1}\mid+\mid{x}−\mathrm{3}\mid+\mid{x}−\mathrm{5}\mid \\ $$$$\Rightarrow\:\mathrm{Answer}\:\mathrm{is}\:\frac{\mathrm{120}}{\mathrm{4}}=\mathrm{30} \\…

Question Number 206939 by Tawa11 last updated on 01/May/24 In how many ways can the word KINECTIC be arranged so that no vowels can be…