A.) To find the maximum height, we can take the derivative of h(t). This will give us the rate at which the horse jumps (velocity) at time t.
h'(t) = -32t + 16
When the horse reaches its maximum height, its position on h(t) will be at the top of the parabola. The slope at this point will be zero because the line tangent to the peak of a parabola is a horizontal line. By setting h'(t) equal to 0, we can find the critical numbers which will be the maximum and minimum t values.
-32t + 16 = 0
-32t = -16
t = 0.5 seconds
b.) To find out if the horse can clear a fence that is 3.5 feet tall, we can plug 0.5 in for t in h(t) and solve for the maximum height.
h(0.5) = -16(0.5)^2 + 16(-0.5) = 4 feet
If 4 is the maximum height the horse can jump, then yes, it can clear a 3.5 foot tall fence.
c.) We know that the horse is in the air whenever h(t) is greater than 0.
-16t^2 + 16t = 0
-16t(t-1)=0
t = 0 and 1
So if the horse is on the ground at t = 0 and t = 1, then we know it was in the air for 1 second.
From the table we can see:
Number of songs: Cost:
0 $ 0
1 $1.25
2 $2.50
3 $3.75
4 $5.00
Therefore the rate of change is: (2.50 - 1.25) / ( 2 - 1 ) = $1.25
Answer:
It means that : C. The cost increases $1.25 for each additional song that is downloaded.
3,000 feet i think since the formula is width *height *length so it should be correct.
Answer:
a) By graphing just one interval of length 
. b) Infinite number of angles, c) Infinite times.
Step-by-step explanation:
Any function is periodical when:
, 
Where is the period of the function. The periodicity of the function allows us to limit the graphing of the function to just an interval of one period and according to the definition, you can expect same output with n different angles (infinite number of angles and same output infinite times).
Answer: 
, or 
<em>Hope this helps and have a great day!!!</em>
