Answer:
A(w) = w(1 + 3w) + pi(w/2)^2/2
Explanation:
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lambobacon3244
07/24/2018
Mathematics
High School
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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
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