tricotasu

2021-09-12

In these problems you are asked to find a function that models a real-life situations. Use the principle of modeling described in this Focus to help you.

Radius Find a function that models the radius r of a circle in terms of its area V.

Radius Find a function that models the radius r of a circle in terms of its area V.

estenutC

Skilled2021-09-13Added 81 answers

The model we want is a function that gives the radius of the circle.

For the circle,

$Area=\pi {\left(radius\right)}^{2}$

Ler R and A be the radius and area of the circle respectively. Then, we have

$A=\pi {R}^{2}$

There is one varying quantity, which is the area A of the circle.

Because the function we want depends on its area A. then, we must express the radius R in terms of its area A.

Consider,$A=\pi {R}^{2}$

Divide by$\pi$ ,

$\frac{A}{\pi}={R}^{2}$

Taking the square root on both sides,

$\sqrt{\frac{A}{\pi}}=\sqrt{{R}^{2}}$

$=R$

Thus,$R=\sqrt{\frac{A}{\pi}}$

Therefore, the model is the function R that gives the radius of the circle in terms of area A is given by,

$R\left(A\right)=\sqrt{\frac{A}{\pi}},A>0$

Thus, the radius of the circle modeled by the function$R\left(A\right)=\sqrt{\frac{A}{\pi}},A>0$ .

FInal statement:

The radius of the circle modeled by the function$R\left(A\right)=\sqrt{\frac{A}{\pi}},A>0$ .

For the circle,

Ler R and A be the radius and area of the circle respectively. Then, we have

There is one varying quantity, which is the area A of the circle.

Because the function we want depends on its area A. then, we must express the radius R in terms of its area A.

Consider,

Divide by

Taking the square root on both sides,

Thus,

Therefore, the model is the function R that gives the radius of the circle in terms of area A is given by,

Thus, the radius of the circle modeled by the function

FInal statement:

The radius of the circle modeled by the function