Answer:
The correct option is;
21 ft
Step-by-step explanation:
The equation of the parabolic arc is as follows;
y = a(x - h)² + k
Where the height is 25 ft and the span is 40 ft, the coordinates of the vertex (h, k) is then (20, 25)
We therefore have;
y = a(x - 20)² + 25
Whereby the parabola starts from the origin (0, 0), we have;
0 = a(0 - 20)² + 25
0 = 20²a + 25 → 0 = 400·a + 25
∴a = -25/400 = -1/16
The equation of the parabola is therefore;

To find the height 8 ft from the center, where the center is at x = 20 we have 8 ft from center = x = 20 - 8 = 12 or x = 20 + 8 = 28
Therefore, plugging the value of x = 12 or 28 in the equation for the parabola gives;
.
1. 56 : 35 = 1.6
2. 1.6* 100 = 160
3. The answer is 160
The large van has 23 seats and the small van has 17 seats
Set the to equal:
x^2 - 4x+4 = 2x-4
solve for X
subtract 2x from each side:
x^2 -6x + 4 = -4
subtract 4 from each side:
x^2 -6x = -8
add 8 to both sides:
x^2 -6x +8 = 0
factor the polynomial:
x = 4 and x = 2
using the line equation replace x with 2 and 4 and solve for y
y = 2(2) - 4 = 0
y = 2(4)-4 = 4
so the 2 points the line crosses the curve is (2,0) and (4,4)
using those 2 points you can calculate the length:
distance = sqrt((x2-x1)^2 +(y2-y1)^2
distance = sqrt( (4-2)^2 + (4-0)^2)
distance = sqrt (2^2 + 4^2)
distance = sqrt (4+16)
= sqrt 20
= 2 sqrt(5) EXACT LENGTH