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.
28, by the way you could’ve just used a calculator
Answer:
Given:
cherry tree seedlings : 64
peach tree seedlings : 96
64/96 : Simplify this fraction
64 / 8 = 8 / 4 = 2
96 / 8 = 12 / 4 = 3
2 and 3 number of seedlings per row
64 / 2 = 32
96 / 3 = 32
number of rows
The maximum number of rows that the owner can plant is 32 rows with 2 cherry tree seedlings and 3 peach tree seedlings.
Answer: x = -2
Step-by-step explanation: vertical lines are the x axis
1/4/3 = 1/12
hope you understand
