<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.
</span>
A = (45/360)×16^2×pi
A = 32pi
Essentially, we must take 5% of $1250. When we drop the percent sign, we move the decimal 2 places to the left, giving .05. Then "of" means multiply. We take $1250 and multiply times .05, giving
<span>$62..50 </span>
<span>Another way to do it is to take 10%, or $125. </span>
<span>Then 5% is half of that. Half of $125 is $62.50 We can do that by dividing $125 by 2. I did it in my head. Others might do it on paper. Still others might have a calculator handy and say $125 divided by 2 on the calculator. We should all get the same answer unless one person spaces out or is tired. It happens!</span>
Answer:
The relation between inputs and outputs is given by an equation called the equation of function. Since the outputs are also real values, hence, reasoning by analogy, you may use the arithmetical operation between functions (addition, subtraction, multiplication, division) to produce new functions.
