1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
gogolik [260]
3 years ago
11

The function h(t) = -16t^2 + 16t represents the height (in feet) of a horse (t) seconds after it jumps during a steeplechase.

Mathematics
1 answer:
Vladimir79 [104]3 years ago
7 0
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.
You might be interested in
Please help! Will mark brainliest!
Anestetic [448]

Each spinner has 5 numbers, the total combinations would be 5 x 5 = 25 combinations,

The answer is 25

6 0
3 years ago
Find all real values of $v$ that satisfy the equation $(v+6)^2 = 324$. If you find more than one, then list your values in incre
Karolina [17]
We have that

(v+6)^2 = 324-----> I raise to 1/2 both members----> [(v+6)^2]^(1/2)=(324)^(1/2)[(v+6)]=(324)^(1/2)-------------> v+6=√324
v=√324-6---------> 18-6=12
v=12

the answer is v=12
8 0
3 years ago
Read 2 more answers
How many square feet of carpet will we need for this hole??
vaieri [72.5K]
Bottom = 2x5 = 10ft
Middle = 2x6 ( 4+2) = 12
Top 4x2= 8
10ft+12ft+8ft= 30ft squared
6 0
4 years ago
Determine whether the relation is a function. -8, 0 -1, 5 4,10,11
11111nata11111 [884]
Vas happenin!


It’s a function because the Xs don’t repeat

Hope this helps

-Zayn Malik
6 0
3 years ago
Does the point (2, 6) lie on the line that connects (1, 4) and (0, 3)? Explain.
Mkey [24]

Answer:

The point does not lie on the line

Step-by-step explanation:

Find the slope of the equation with rise/run

This gets you -1/-1 = 1

The equation will be y = x + 3, given the y intercept at (0, 3)

Plug in the point (2, 6) to see if it works in the equation

6 = 2 +3

6 \neq 5

The point does not lie on the line

8 0
3 years ago
Other questions:
  • The perimeter of a geometric figure is the sum of the lengths of its sides. If the perimeter of the pentagon to the right (five-
    14·1 answer
  • 5. Order these from least to greatest.<br> 1/2,4/9, 2/3,5/6
    11·1 answer
  • Write 145,567 in expanded notation​
    11·1 answer
  • Helppppppppppppppppp
    10·2 answers
  • 10<br> 8<br> - 10<br> 10<br> - 10<br> 2 - 2 = 64
    7·1 answer
  • A self-serve frozen yogurt shop has 8 candy toppings and 4 fruit toppings to choose from. How many ways are there to top a froze
    9·1 answer
  • There are 15 students in the class and 8 are boys. What is the ratio of girls to students in the room?
    5·1 answer
  • Which exponential function matches the table?
    9·1 answer
  • View the lane below and calculate the slope<br> by using the slope formula
    9·2 answers
  • A ______ is a deduction from the original price of an item.
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!