<span>Part
A:
a) What do the x-intercepts and maximum value of the graph represent?
The x-intercepts are the distances at which the ball is on the ground.
First, at x = 0, that is when the ball is kicked; second, at x = 30, when the ball falls (return) to the ground.
b) What are the intervals where the function is increasing and decreasing,
and what do they represent about the distance and height? (6 points)
The function is increasing in the interval (0, 15) and is decreasing in the interval (15,30)
The increasing interval (0,15) is the horizontal distance from the point the the ball was kicked until it reached its highest altitude, this is where the ball was going upward.
The decreasing interval (15,30) is the horizontal distance from the point where the ball reached its highest altitude until it landed on the ground, this is where the ball was falling down.
Part B: What is an approximate average rate of change of the graph from x
= 22 to x = 26, and what does this rate represent
On the graph you can read that at x = 22, f(x) ≈ 12, and at x = 26 f(x) ≈ 7.
So, an approximate rate of change from x = 22 to x = 26 is given by the equation below:
change on f(x) 7 - 12
average rate of change = --------------------- = ----------- = -5/4
change of x 26 - 22
That rate represents that the ball fell about 5 ft per 4 ft in that interval.
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The smallest value it could be is 4 and the largest value it could be is 10.
The triangle inequality theorem states that any two sides of a triangle must have a sum greater than the third side. Given the two sides we have, 7 and 4, the sum would be 11; this would mean that the missing side could be no more than 10.
If we take the unknown side and the smallest one we're given, we would have the inequality
n+4>7
Subtracting 4 from both sides we would have n>3. That means it would have to be the next integer up, which would be 4.
Answer:
if im not mistaken.. i would say its -3.5 or -7/2
Step-by-step explanation:
