Answer: the average distance between the parabola is 2000
Step-by-step explanation:
Given that;
y = 30x(20 - x) and the x-axis on the interval [0, 20]
f(x) = y = 30x(20 - x); [0, 20] and a=0, b=20
the average distance between the parabola will be
Average value = 1/20-0 ²⁰∫₀ 30x(20-x) dx
= 1/20 ²⁰∫₀ (600x-30x²) dx
= 1/20 [(600x)/2 - (30x³)/3]₀²⁰
= 1/20 [300x - 10x³]₀²⁰
inputting the limits, we get
= 1/20 [(300 × 20 × 20 - 10 × 20 × 20 × 20) - 0 - 0]
= 1/20 ( 120000 - 80000)
= 0.05 × 40000
<h2>= 2000</h2>
Therefore the average distance between the parabola is 2000
<h3 />
The answer to this question is
B.The new volume will be 8 times the original volume.
The general formula for the lateral surface area of a regular pyramid is:

Where:
p=perimeter of a base
l=slant height
a.
a=3ft
l=4ft
p=5*a=5*3=15ft

b.
a=2.5ft
l=4ft
p=6*a=6*2.5=15ft

c.
a=1.9ft
l=4ft
p=8*a=8*1.9=15.2ft

d.
Based on a lateral surface area the blue umbrella is best choice. But, the best umbrella overall is the one with the greatest base area. General formula for regular polygon is:

For pentagon:
A=15.48ft^2
For hexagon:
A=16.24ft^2
For octagon:
A=17.43ft^2
Blue umbrella is still best choice.