Question

A rectangular window is topped with a semicircle the height of the rectangle part is 1 more than 3 times its width W meters which function represents the total area A of the window in terms of the width

Answer 1

Answer:

A(w) = w(1 + 3w) + pi(w/2)^2/2

Step-by-step explanation:

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lambobacon3244

07/24/2018

Mathematics

High School

+5 pts

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A rectangular window is topped with a semicircle on top. the height of the rectangular part is 1 more than 3 times its width , w meters which function represents the total area?

A.) A(w) = w(1 + 3w) + pi(w/2)^2

B.) A(w) = w(1 + 3w) + pi(w/2)^2/2

C.) A(w) = w(1 + 3w) + pi(w)^2/2

D.) A(w) = w(1 + 3w) + pi(w)^2

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DeanR

DeanRGenius

In general for a rectangle of dimensions w by h and a semicircle of diameter w we get an area:

A = wh + \frac 1 2 \pi (\frac w 2)^2

The halfs are because a semicircle is half a circle and a radius is half a diameter.

We're told

h = 1+ 3w

Substituting,

A(w) = w(1+3w) + \frac 1 2 \pi (\frac w 2)^2

tats

Answer 2

Answer:

A = 3W² + W + 1/8πW²

Step-by-step explanation:

rectangular window is L x W

semicircle is 1/2 πr²

r = 1/2 W

L = 3W + 1

A = W(3W + 1) + 1/2 π(1/2W)²

A = 3W² + W + 1/8πW²