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:
b
Step-by-step explanation:
To be able to give the answer to this item, we are to represent first with any variables the amount he earns each weekend for mowing the same field. Also, we represent the number of weeks he had worked by the variable y. The total amount of money he will have after working for y weeks is,
T = xy
Since, we are not given with any other information of the other expenses that have to be paid then we can say that if T is already equal to the price of the new lawnmower then, Tom will be able to purchase it and begin his lawn mowing business in due time.
Its 2 because u see how many 4s go into 8
Step-by-step explanation:
There are four types of angles:
- Acute angles are angles that have a measurement less than 90°
- Right angles are angles that have a measurement of 90°
- Obtuse angles are angles that have a measurement from 90° to 180°
- Reflex angles are angles that have a measurement from 180° to 360°
Knowing this information, we can conclude that an angle of 200° is a <u>reflex</u> angle.
