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 given function shows imply that the graph g(x) is shifted two units right and three units up.
Option B is correct.
<h3>What is the transformation of a function?</h3>
The transformation of a function occurs in a fancy way such that a function maps itself. f: x → x.
From the given information:
Let's take a look at the function f(x) that goes through 0 just when x = 0. Now we want to move it to the right by 2. It implies that it has to go through 0 when x = +2.
Now, we have to add 2 to x, then the function becomes f'(x) = f(x-2) will be shifted by 2 units to the right.
Similarly, the same scenario occurs when shifting up. Again imagine your function passes 0 when x = 0. We have to add 3. Now, the function f’’(x) = f(x) + 3 will be shifted by 3 units up.
Combining the two transformations, we have:
Therefore, we can conclude that the function implies that the graph g(x) is shifted two units right and three units up.
Learn more about the transformation of functions here:
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Answer: 5 years
14,800 students enrolled
Step-by-step explanation:
Let x represent the number of years and
Let y represent the number of students enrolled
College A: y = 12,300 + 500x
College B: y = 18,550 - 750x
Use substitution Method to solve:
12,300 + 500x = 18,550 - 750x
+750x +750x
12,300 + 1250x = 18,550
-12,300 -12,300
1250x = 6250
x = 5
Input x = 5 into one of the equations to solve for y.
y = 12,300 + 500x
= 12,300 + 500(5)
= 12,300 + 2500
= 14,800
Read more on Brainly.com - brainly.com/question/12387804#readmore
Answer:
Step-by-step explanation:
The formula for determining the distance between two points on a straight line is expressed as
Distance = √(x2 - x1)² + (y2 - y1)²
Where
x2 represents final value of x on the horizontal axis
x1 represents initial value of x on the horizontal axis.
y2 represents final value of y on the vertical axis.
y1 represents initial value of y on the vertical axis.
From the points given,
x2 = 0
x1 = 9
y2 = - 33
y1 = 7
Therefore,
Distance = √(0 - 9)² + (- 33 - 7)²
Distance = √(- 9² + (- 40)² = √(81 + 1600) = √1681
Distance = 41
The formula determining the midpoint of a line is expressed as
[(x1 + x2)/2 , (y1 + y2)/2]
[(9 + 0) , (7 - 33)]
= (9, - 26]
