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
To solve the equation below by completing the square, what is your first step?<br> 3x^2+18x=21
Margarita [4]

Answer:

Multiply both sides of the equation by 1/3

Step-by-step explanation:

3x^2+18x=21

The first step is to get the x term with a coefficient of 1, so divide by 3 on both sides of the equation

This is the same as multiplying by 1/3

1/3 * (3x^2+18x)=21*1/3

x^2 +6x = 7

6 0
3 years ago
If x=9 and y=−2, evaluate the following expression : 6x−8y
Mazyrski [523]

6(9)-8(-2)

6*9=54

8*(-2)=-16

54-16=38

38<-----

4 0
3 years ago
Read 2 more answers
Find the value of y.<br> 18
Advocard [28]

Answer:30

Step-by-step explanation:

Since it is a right angled triangle we can apply Pythagoras principle to get y

Adjacent=a=18

Opposite=k=24

Hypotenuse =y

y=√(k^2+a^2)

y=√(24^2+18^2)

y=√(24x24+18x18)

y=√(576+342)

y=√(900)

y=30

8 0
3 years ago
HELP!!!!!! An Instagram photo is measured ″ 4″ by ″ 4″. A poster enlargement is being printed with a scale factor of 8.5. What i
Anika [276]

The given measurement of the Instagram photo is "4" by "4". And a poster enlargement is being printed with a scale factor of 8.5 .

So on using the scale factor of 8.5 , lengths of new sides are "8.5 *4" by "8.5 *4"

= " 34" by "34" .

So the new lengths of the enlarged pictures are of dimension "34" by "34" .

7 0
3 years ago
Read 2 more answers
Solve for w, simplify your answer as much as possible
Akimi4 [234]

Answer:

W=3

Step-by-step explanation:

(6w + 4w)/48=5/8(taking lcm)

6w+4w=5/8*48

10w=30

W=3

Thanks for putting qsn, makes me remember this againa

6 0
3 years ago
Other questions:
  • identify the following probability as theoretical or empirical. After tossing the same coin 10 times, you are surprised to find
    10·2 answers
  • What does figure 50 look like
    14·1 answer
  • What is the measure of ∠A, to the nearest degree?<br> 17°<br> 33°<br> 57°<br> 73°
    7·2 answers
  • Snow is 0.02 m deep after 1 hour and 0.06 m deep after 3 hours. State the independent variable and the dependent variable. Then
    11·1 answer
  • What is d in this problem 2/5d-1=3/5d-3
    12·1 answer
  • Solve the inequality: x + 9 &lt; -8
    9·2 answers
  • Find the volume of a cylinder with radius 3cm and height 7cm​
    12·1 answer
  • What is 10% of 100,000
    6·2 answers
  • You are going to make cookies for a party. The recipe requires 3 cups of flour, 2 cups of chocolate chips and other ingredients.
    9·1 answer
  • You will be marked brainlest
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!