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Note: Figure not drawn to scale
If a = 33 in and b = 44 in, which of the following is closest to the area of the window?
A.
2,307.3 in2
B.
2,904 in 2
C. 1,452 in2
D.
1,879.65 in?

Work Shown:

The rectangle has area 33*44 = 1452 square inches. This is just part of the answer. The semicircle up top must be accounted for as well.

This semicircle has a radius of r = a/2 = 33/2 = 16.5 inches

The area of the semicircle is (1/2)*pi*r^2 = (1/2)*3.14*(16.5)^2 = 427.4325

This adds to the area of the rectangle to get 427.4325+1452 = 1,879.4325

This is fairly close to choice D, though we're a bit off.

The reason for the error is because of how pi = 3.14 is an approximation. A more accurate version is pi = 3.1415926535898

Therefore, the area of the semicircle is closer to

(1/2)*pi*r^2 = (1/2)*3.1415926535898*(16.5)^2 = 427.649299969911

then we add on the rectangle area:

427.649299969911+1452 = 1,879.64929996991

that rounds to 1,879.65

the solution is x=1

step-by-step explanation:

we are given our   equation as

let's assume

left side function is

right side function is

now, we can draw graph

and then we can get intersection point

the intersection point will be solution

so, the solution is

x=1