Mathematics: Find the smallest perimeter and the dimensions for a rectangle with an area of 36 in squared. The smallest perimeter for a rectangle with an area of 36 in squared is nothing in. (Simplify your answer.) The dimensions of this rectangle are nothing in. (Simplify your answers. Use a comma to separate answers.)

Find the smallest perimeter and the dimensions for

lillybritn

24.01.2022

The dimensions of the rectangle are: $6\sqrt{2},3\sqrt{2}$

The smallest perimeter therefore will be: $18\sqrt{2}$

Step-by-step explanation:

Let the dimension of the rectangle be x and y

Area of the Rectangle = xy

Area=36 Inch Squared

Therefore: xy=36

$x=\frac{36}{y}$

Perimeter of the Rectangle, P(x,y)=2(x+y)

Substituting $x=\frac{36}{y}$ into P(x,y)

$P(y)=2(\frac{36}{y}+y)=\frac{72+y^2}{y}$

The minimum value of the perimeter occurs at the point where the derivative =0.

$P'(y)=\frac{y^2-72}{y^2}$

$Setting\:P'(y)=0\\\frac{y^2-72}{y^2}=0\\y^2-72=0\\y^2=72\\y=\sqrt{72}=6 \sqrt{2}$

Recall:

$x=\frac{36}{y}\\=\frac{36}{6\sqrt{2} }\\x=3\sqrt{2}$

The dimensions of the rectangle are: $6\sqrt{2},3\sqrt{2}$

The smallest perimeter therefore will be:

$=2(6\sqrt{2}+3\sqrt{2}) \\=2(9\sqrt{2})\\=18\sqrt{2}$

0,0(0 оценок)

sindy35111

08.11.2021

The answer would be: A. 31,275

to solve this you would take the population (18,922) and multiply it as shown below:

18,922(1+0.03)^17

This would equal 31,275 which would be your answer.

Hope this helps! :3

0,0(0 оценок)