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.

### Answer & Explanation

estenutC

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

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