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1. A poster is 17 inches longer than it is wide. Find a function that models its area \( A \) in terms of its width \( w \).

\[ A(w) = w(w + 17) \]

2. Find a function that models the radius \( r \) of a circle in terms of its area \( A \).

\[ f(A) = \sqrt{\frac{A}{\pi}} \]

3. An isosceles triangle has a perimeter of 18 cm. Find a function that models its area \( A \) in terms of the length of its base \( b \).

\[ A(b) = \frac{1}{4}b\sqrt{4(18-b)^2-b^2} \]

Answer :

1. The function that models the area of the poster in terms of its width is A(w) = w(w + 17).

2. The function that models the radius of a circle in terms of its area is r = √(A/π).

3. The function that models the area of an isosceles triangle in terms of the length of its base is A(b) = (b/4) * √(16b² - b⁴).

1. For the poster's area A in terms of its width w, the function is:

A(w) = w(w + 17)

To find the area of the poster, we need to multiply its length and width. Given that the poster is 17 inches longer than it is wide, we can express the width as w and the length as (w + 17). Therefore, the area of the poster can be represented by the function A(w) = w(w + 17).

2. For the radius r of a circle in terms of its area A, the function is:

r = √(A/π)

The formula to calculate the area of a circle is A = πr², where A represents the area and r represents the radius. By rearranging the formula, we can solve for the radius:

r = √(A/π)

This equation gives us the function to find the radius of a circle based on its area.

3. For the area A of an isosceles triangle in terms of the length of its base b, the function is:

A(b) = (b/4) * √(16b² - b⁴)

In an isosceles triangle, two sides have the same length, and the remaining side is the base. The formula to calculate the area of an isosceles triangle is A = (b/4) * √(4a² - b²), where A represents the area and b represents the base. Since the perimeter is given as 18 cm, each of the equal sides will have a length of (18 - b)/2. Substituting this value into the area formula, we obtain the function A(b) = (b/4) * √(16b² - b⁴) for the area of an isosceles triangle in terms of the base length.

To know more about finding the function for each scenario, refer here:

https://brainly.com/question/28135558#

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