In these problems you are asked to find a function that models a real-life situa

tricotasu

tricotasu

Answered question

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

estenutC

Skilled2021-09-13Added 81 answers

The model we want is a function that gives the radius of the circle.
For the circle,
Area=π(radius)2
Ler R and A be the radius and area of the circle respectively. Then, we have
A=πR2
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=πR2
Divide by π,
Aπ=R2
Taking the square root on both sides,
Aπ=R2
=R
Thus, R=Aπ
Therefore, the model is the function R that gives the radius of the circle in terms of area A is given by,
R(A)=Aπ,A>0
Thus, the radius of the circle modeled by the function R(A)=Aπ,A>0.
FInal statement:
The radius of the circle modeled by the function R(A)=Aπ,A>0.

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