The-two-side-of-rectangle-are-2x-and-5-2x-units-respectively-For-what-value-of-x-the-area-of-rectangle-will-be-maximum-

Question Number 134874 by bemath last updated on 08/Mar/21

$$\mathrm{The}\:\mathrm{two}\:\mathrm{side}\:\mathrm{of}\:\mathrm{rectangle}\:\mathrm{are} \\ $$$$\mathrm{2}{x}\:\mathrm{and}\:\left(!\mathrm{5}−\mathrm{2}{x}\right)\:\mathrm{units}\:\mathrm{respectively} \\ $$$$\mathrm{For}\:\mathrm{what}\:\mathrm{value}\:\mathrm{of}\:{x}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of} \\ $$$$\mathrm{rectangle}\:\mathrm{will}\:\mathrm{be}\:\mathrm{maximum}? \\ $$

Commented by Ñï= last updated on 08/Mar/21

!5=5!(1−1!+(1/(2!))−(1/(3!))+(1/(4!))−(1/(5!)))=44 I got it.

$$!\mathrm{5}=\mathrm{5}!\left(\mathrm{1}−\mathrm{1}!+\frac{\mathrm{1}}{\mathrm{2}!}−\frac{\mathrm{1}}{\mathrm{3}!}+\frac{\mathrm{1}}{\mathrm{4}!}−\frac{\mathrm{1}}{\mathrm{5}!}\right)=\mathrm{44} \\ $$$${I}\:{got}\:{it}. \\ $$

Answered by mr W last updated on 08/Mar/21

A=(2x)×(5−2x)≤((2x+(5−2x))/2)=(5/2) max.=(5/2) when 2x=5−2x, i.e x=(5/4)

$${A}=\left(\mathrm{2}{x}\right)×\left(\mathrm{5}−\mathrm{2}{x}\right)\leqslant\frac{\mathrm{2}{x}+\left(\mathrm{5}−\mathrm{2}{x}\right)}{\mathrm{2}}=\frac{\mathrm{5}}{\mathrm{2}} \\ $$$${max}.=\frac{\mathrm{5}}{\mathrm{2}}\:{when}\:\mathrm{2}{x}=\mathrm{5}−\mathrm{2}{x},\:{i}.{e}\:{x}=\frac{\mathrm{5}}{\mathrm{4}} \\ $$

Commented by bemath last updated on 08/Mar/21

$$\mathrm{this}\:\left(!\mathrm{5}−\mathrm{2x}\right)\:\mathrm{sir}\:? \\ $$

Commented by mr W last updated on 08/Mar/21

what do you want to say with !5? if you mean !5=44, you can replace 5 with 44.

$${what}\:{do}\:{you}\:{want}\:{to}\:{say}\:{with}\:!\mathrm{5}?\:{if} \\ $$$${you}\:{mean}\:!\mathrm{5}=\mathrm{44},\:{you}\:{can}\:{replace}\:\mathrm{5} \\ $$$${with}\:\mathrm{44}. \\ $$

Commented by bemath last updated on 08/Mar/21