Find the rate of change for this linear function Y equals MX plus be

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

katrin2010 [14]

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

6 0

3 years ago

Tell me the answer!!

algol [13]

Answer:

I think answer number 1 and number 4

Step-by-step explanation:

to find the perimeter you add all the sides together, there are 4 sides in the square so it will be 2+2+2+2 which will give you 8 and you can also multiply 2 by the 4 sides which will also give you 8

6 0

3 years ago

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Which point plotted below has coordinates (4, -2)?

Lady bird [3.3K]

Point d that is option d

7 0

3 years ago

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Solve the following Linear equation 15 POINTS

GenaCL600 [577]

Answer:

24 - 6 = 2(12 - 3)

24 - 6 = 24 - 6

Subtract 24 from both sides of the equation

24 - 24 - 6 = 24 - 6 - 24

-6 = -6

Add 6 to both sides of the equation

6 - 6 = -6 + 6

0 = 0

The input is an identity: it is true for all values

-TheUnknownScientist

7 0

3 years ago

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A.35 B.25 C.50 D.The distance cannot be determined

solniwko [45]

Answer:

A. 25

Step-by-step explanation:

1- See the length of XA

2- Divide length by 2

3- 50 divided by 2 equals 25

7 0

3 years ago

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