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.
Answer:
A composite number has more than two factors. In this case, the number 13233345364715 has more than two factors, so it is composite.
Step-by-step explanation:
Numbers can be classified as prime or composite. Prime numbers have only two factors, 1 and the number itself. For example, 13 is a prime number because only 1 and 13 can be multiplied together to get 13. However, a composite number has more than two factors. In the case of the numer 13233345364715, I know that there are more than two factors because the number ends in 5, which means it has a factor of 5. To confirm, divide 13233345364715/5 = 2646669072943. This large of a number may also have other factors, however, since you now know it has at least four factors, it is composite.
It is 14% as you add up all of the numbers and divide 10 by that number and finally multiply by 100 for a percent
