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
TiliK225 [7]
3 years ago
12

A ball is thrown into the air from a height of 4 feet at time t = 0. The function that models this situation is h(t) = -16t2 + 6

3t + 4, where t is measured in seconds and h is the height in feet.
a) What is the height of the ball after 3 seconds?
b) What is the maximum height of the ball? Round to the nearest foot.
c) When will the ball hit the ground?
d) What domain makes sense for the function?

please show ur work !!!

Mathematics
1 answer:
katrin2010 [14]3 years ago
6 0

Answer:

Part a) The height of the ball after 3 seconds is 49\ ft

Part b) The maximum height is 66 ft

Part c) The ball hit the ground for t=4 sec

Part d) The domain of the function that makes sense is the interval

[0,4]

Step-by-step explanation:

we have

h(t)=-16t^{2} +63t+4

Part a) What is the height of the ball after 3 seconds?

For t=3 sec

Substitute in the function and solve for h

h(3)=-16(3)^{2} +63(3)+4=49\ ft

Part b) What is the maximum height of the ball? Round to the nearest foot.

we know that

The maximum height of the ball is the vertex of the quadratic equation

so

Convert the function into a vertex form

h(t)=-16t^{2} +63t+4

Group terms that contain the same variable, and move the constant to the opposite side of the equation

h(t)-4=-16t^{2} +63t

Factor the leading coefficient

h(t)-4=-16(t^{2} -(63/16)t)

Complete the square. Remember to balance the equation by adding the same constants to each side

h(t)-4-16(63/32)^{2}=-16(t^{2} -(63/16)t+(63/32)^{2})

h(t)-(67,600/1,024)=-16(t^{2} -(63/16)t+(63/32)^{2})

Rewrite as perfect squares

h(t)-(67,600/1,024)=-16(t-(63/32))^{2}

h(t)=-16(t-(63/32))^{2}+(67,600/1,024)

the vertex is the point (1.97,66.02)

therefore

The maximum height is 66 ft

Part c) When will the ball hit the ground?

we know that

The ball hit the ground when h(t)=0 (the x-intercepts of the function)

so

h(t)=-16t^{2} +63t+4

For h(t)=0

0=-16t^{2} +63t+4

using a graphing tool

The solution is t=4 sec

see the attached figure

Part d) What domain makes sense for the function?

The domain of the function that makes sense is the interval

[0,4]

All real numbers greater than or equal to 0 seconds and less than or equal to 4 seconds

Remember that the time can not be a negative number

You might be interested in
You need to buy some chicken for dinner tonight. You found an ad showing that the store across town has it on sale for $2.89 a p
ASHA 777 [7]

Answer:

   1. Going to the close store is cheaper.

Step-by-step explanation:

The difference in the prices of chicken is 3.19 -2.89 = 0.30 per pound, so for 5 pounds of chicken, the far store offers a price that totals 5×$0.30 = $1.50 less.

The difference in travel distances is 8.4 -2.4 = 6 miles, so the total round-trip distance difference is 12 miles. The cost of gas is ...

  ($3.81 /gal)/(23 mi/gal) = $0.1656 /mi

so the cost of gas for the 12-mile longer trip would be

  12×$0.1656 ≈ $1.99

Traveling to the far store, you would spend $1.99 more on gas to save $1.50 on the price of chicken. Going to the close store is cheaper.

3 0
3 years ago
Which situation can be modeled by the equation y=3x+25
Gnesinka [82]

For this case we have the following situation:

The monthly cost of a gym in the city is $ 3. The initial registration is $ 25. Write a mathematical expression that models the problem.

So we have to define variables:

x: number of months

y: total cost

The mathematical expression that models the problem is:

y = 3x + 25

7 0
3 years ago
Find the Perimeter and area
Maslowich
Perimeter is 36. This is because the radius and side lengths are the same in a regular hexagon. 

Are is roughly 93.53. 
6 0
3 years ago
The table below represents the equation: y = 1.5x – 2 If you completed this table, would each input have exactly one output? yes
stealth61 [152]

Answer:

Step-by-step explanation: y=1.5(3)-2

y=2.5

7 0
3 years ago
Read 2 more answers
How many modes does the following data set have?<br> 5, 5, 6, 7, 8, 12, 12, 12, 150, 150, 150
Feliz [49]

Answer:

2

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Other questions:
  • What is the multiplicative inverse of n/3
    10·1 answer
  • I don't understand how can I find the answer?
    9·1 answer
  • What is the probability of not drawing a red marble?<br><br><br> 5/5 <br> 3/5<br> 50%<br> 30%
    6·2 answers
  • In Illinois, 10 % of all drivers arrested for DUI (Driving Under the Influence) are repeat offenders; that is, they have been ar
    11·1 answer
  • Plsssss help due todayy!!
    13·1 answer
  • What is an interim math checkpoint?
    15·1 answer
  • Arrange The Steps Below To Solve For X.
    11·2 answers
  • Use the Distributive Property to write 2(−5 + 3) as an equivalent expression. What is the value of the expression?
    7·2 answers
  • -5 = 1/3(-1-w)<br><br> pls help! i will give brainly
    14·2 answers
  • 5. Name the side included by <br><br> AB<br> AC<br> BC<br> none of these.
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!