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
Nate's weekly pay increased from $710 to $770. Which of the following is closest to the
Lemur [1.5K]

Answer:

The answer is 8.5 hope this helped.

8 0
3 years ago
Let’s say a GWC coder is working on a project that includes 6 x (8 +7) lines of code. Rewrite this expression in words.
Sladkaya [172]
Six times (eight plus seven)
3 0
3 years ago
Find the circumference use 3.14 for the value of
Reil [10]

Answer:

the answer is 69.3

Step-by-step explanation:

5 0
3 years ago
4. (x+ 2)(2x2 + 9x+8)
vfiekz [6]

Answer:

2x3+9x2+8x+4x2+18x+16

2x3+13x2+26x+16

6 0
3 years ago
Simplify square root one minus cos squared theta, need explanation please​
Maurinko [17]
When you square root something’s it’s times by the same number
-1 squared =-1•-1
1•1=1
-•-=+
-1•-1=+1
=1
8 0
2 years ago
Other questions:
  • <img src="https://tex.z-dn.net/?f=y%20%7B%3F%7D%5E%7B2%7D%20%20-%2018y%20%2B%2081" id="TexFormula1" title="y {?}^{2} - 18y + 81
    12·1 answer
  • I need help ASAP!!!!!!!!!!!!!!!!!
    8·1 answer
  • Your company produces electrical components for a government project that are normally distributed with a mean frequency of 100
    8·1 answer
  • A certain clock is losing time. The clock loses 2/15 seconds every minute. How many seconds does the clock lose in one hour?
    7·2 answers
  • tia drinks 64 ounces of water each day, witch is equal to 8 cups . during school, she drinks 6 1/2 cups of water . tia wants to
    11·1 answer
  • What is x, the distance between points A and A'?
    7·2 answers
  • It took a plane 2 hours to go from Dallas to NY with the head wind and 1.5 hours to get back with the tail wind. If the speed of
    6·1 answer
  • I need help hurry please
    15·1 answer
  • En el mes de abril en la cancha Toto Hernández de Cucuta, habrán encuentros de
    5·1 answer
  • 2. Determine the cost to cover the top of the fire pit with a piece of sheet metal that costs $25 per square foot. (6 points)
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!