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
If on a scale 75 feet is represented by 1 inch, then a scale of 1/5 inch represents how many feet?
lara [203]

Answer:

15 feet

Step-by-step explanation:

if 1 inch represents 75 and it 1/5 then you do 75 divided by 5 and it gives you 15 so it represents 15 feet

8 0
3 years ago
Tony was Challenged to a half-court shooting competition. For every half-court shot that he makes, he will earn 20 points. For e
Mkey [24]

Answer:

Tony make 4 half-court shots and misses 16 half-court shots.

Step-by-step explanation:

Given:

Points earned for every successful, half-court shots = 20

Points deducted for missing the shots = 5 or -5

Total number of shots in the game = 20

Final points earned by Tony = 0

According to the question:

Let the number of successful half-court shot be x

And the number of shots missed be 20-x

So,

In terms of points we can re-write it as:

⇒ 20(x)-5(20-x) =0

⇒ 20x-100+5x=0

⇒ 25x-100=0

⇒ 25x-100+100=100

⇒ 25x=100

⇒ \frac{25x}{25} =\frac{100}{25}

⇒ x=\frac{100}{25}

⇒ x=4

Tony make 'x' shots that is 4 and the number of shot he missed is (20-x) =(20-4)=16

6 0
3 years ago
Evaluate the following 1340five minus 242five​
vampirchik [111]

Answer:

10980 is the correct answer

4 0
2 years ago
What is the domain of f
frez [133]

Answer:

[ - 6 , 6 ]

Step-by-step explanation:

This is because the value of f(t) for x values only ranges from -6 to 6.

Please mark for Brainliest!! :D Thanks!!

For more questions or more information, please comment below!

8 0
3 years ago
WHOEVER GIVES THE BEST ANSWER WILL BE MARKED AS BRAILIEST!!!!!!!!!!
mojhsa [17]

Answer:

Step-by-step explanation:

8 0
3 years ago
Other questions:
  • In a bag of 100 ballons, 12 are red and 13 are green. What fraction of the balloons in the bag are not red or green?
    6·1 answer
  • Number of boys : number of girls = 11 : 9
    8·1 answer
  • Consider the function f(x) = x2 + 12x + 11. x-intercepts?
    10·2 answers
  • Solve the following exponential equations. Round your answers to 3 decimal place.
    13·2 answers
  • Ryan buys a new pair of headphones for $32. He has to pay 7.25% tax. What is his total bill
    10·2 answers
  • If x can be any number, how many solutions are there for the equation?
    12·2 answers
  • One manufacturer boxes screws so that each box weighs the same no matter what size the screws are. The graph shows the amount of
    6·1 answer
  • The line plot shows the favorite color of the students in class. How many students liked yellow and orange combined?
    11·1 answer
  • Answer all these questions correctly to get a brainlist
    7·1 answer
  • What is the scale factor from AABC to AUVW?
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!