Answer:
Step-by-step explanation:
Refer to the attached digram.
The track's perimeter consists of the rectangle's perimeter plus the perimeters of the two semicircles.
The perimeter of a rectangle can be expressed as 2(x+r) where:
x is the length
2r represents the rectangle's width, equivalent to the semicircle's diameter.
The perimeter of one semicircle is calculated as 2πr/2, simplifying to πr.
Thus, the total perimeter contributed by the two semicircles is 2πr.
Therefore, the full track perimeter is expressed as 2(x+2r) + 2πr
where r indicates the semicircle's radius.
Expanding this gives us
Perimeter of the track = 2x + 4r + 2πr
which can also be represented as Perimeter of the track = 2(x + 2r + πr)
b) Given P = 2(x + 2r + πr), we need to rearrange the equation to isolate x.
P = 2x + 4r + 2πr
By subtracting 4r and 2πr from both sides, we get P - 4r - 2πr = 2x
Next, we divide each side by 2.
(P - 4r - 2πr) / 2 = 2x
Thus, x = (P - 4r - 2πr) / 2
c) Given
P = 600ft
r = 50ft
x = (600 - 4(50) - 2π(50)) / 2
x = (600 - 200 - 100(3.14)) / 2
x = 400 - 314 / 2
x = 86 / 2
x = 43ft
Therefore, rounding to the nearest foot, the value of x is 43ft
