What is the average distance between the parabola y=30x(20-x) and the x-axis on the interval [0, 20]?

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

Therefore the average distance between the parabola is 2000

b. the decimal could be two-tenths.

step-by-step explanation:

answer: evaluate the objective function at each vertex to determine which - and -values, if any, maximize or minimize the function. example: find the minimum value and maximum value of the objective function f ( x , y ) = 4 x + 5 y , subject to the following constraints