Answered

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Determine a function a(w) that models the area of the top surface of the swimming pool in terms of the width , w

Sagot :

MrRoyal

Answer:

[tex]A(w) = (40 - w) * w[/tex]

Step-by-step explanation:

Given

[tex]P = 80[/tex] ---- perimeter

Required

Write the area as a function of width

The perimeter of a rectangle is:

[tex]P =2(l + w)[/tex]

Where

[tex]l \to length\\ w \to width[/tex]

So, we have:

[tex]80 = 2*(l+w)[/tex]

Divide by 2

[tex]40 = l + w[/tex]

Make l the subject

[tex]l =40 - w[/tex]

The area of a rectangle is:

[tex]A = l * w[/tex]

Substitute: [tex]l =40 - w[/tex]

[tex]A = (40 - w) * w[/tex]

Hence, the function is:

[tex]A(w) = (40 - w) * w[/tex]

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