I don’t really understand can someone help

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

y varies directly as x, y=14 when x=18. Determine x when y=31. Estimate your answer to two places after the decimal, if necessar

laiz [17]

Y : x
14 : 18
31 : x
18*31/14=x
39.85714286

ANSWER
x=39.86

8 0

3 years ago

Solve the system of linear equations by elimination.<br><br> −x+3y=0<br><br> x+3y=12

Natali5045456 [20]

Answer:

(6,2)

Step by Step explanation:

1- Add the two equations so the Xs cancel out

2- find y by dividing 6 from both sides

3- plug in the y value in the place of the y in one of the equations

4- solve the equation to find X

5 - put answer in correct format (x,y)

5 0

3 years ago

Is y=3/4x a direct variation? if so, find the constant of variation

xxMikexx [17]

Yes because without a y-intercept it goes through 0. and can you explain the next part?

8 0

3 years ago

70 years later from 1590

Snowcat [4.5K]

Answer: 1660

Step-by-step explanation: 70 + 1590 = QUICK MATHS

6 0

3 years ago

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