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Simon has a certain length of fencing to enclose a rectangular area. The function A models the rectangle's area (in square meters) as a function of its width (in meters).

2 Answers

2 votes

Answer:

When there is no width the area is 0m^2

Explanation:

I took the quiz.

User Mayya
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Answer:

The maximum area is 1,600 square meters

Explanation:

The complete question is

What is the maximum area possible?

The given function area is modeled by A(w)=-w(w-80)

we know that

The given function is a vertical parabola open downward

The vertex is a maximum

The x-coordinate of the vertex represent the width for the maximum area

The y-coordinate of the vertex represent the maximum area

Convert the quadratic function in vertex form


A(w)=-w(w-80)\\\\A(w)=-w^(2)+80w

Factor -1


A(w)=-(w^(2)-80w)

Complete the square


A(w)=-(w^(2)-80w+1,600)+1,600

Rewrite as perfect squares


A(w)=-(w-40)^(2)+1,600 ----> function in vertex form

The vertex is the point (40,1,600)

therefore

The maximum area is 1,600 square meters

User Jgosmann
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