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.
N + 1 = 4(n – 8)
Use distributive property for this part: 4(n – 8) ----> 4n - 32
n + 1 = 4n - 32
Get the variable on one side:
n + 1 = 4n - 32
-n -n
1= 3n - 32
Get the variable on its own:
1= 3n - 32
+32 +32
33 = 3n
Divide by 3 on both sides:
33/3 = 3n/3
n = 11
Answer:
4000
Step-by-step explanation:
Since there are 3 sides and each of those 3 sides are 9 cm, you would multiply 9*3 and your answer would be 27 cm.
The length of the fencing corresponds to the length of the perimeter of the garden:
We also know that the perimeter of a circle is given by:
where r is the radius of the circle.
Putting together the two equations, we have
from which we can find r, the radius of the garden:
