Suppose an object is launched from ground level directly upward at 57.4 f/s Write a function to represent the object’s height over time.

Answer: p(t) = (-16 ft/s^2)*t^2 + (57.4 ft/s)*t

Step-by-step explanation:

We can suppose that the only force acting on the object is the gravitational force, then the acceleration of the object will be equal to the gravitational acceleration.

Then we can write:

a(t) = -32 ft/s^2

Where the negative sign is because this acceleration is downwards.

Now, to get the vertical velocity of the object, we need to integrate over time to get:

v(t) = (-32 ft/s^2)*t + v0

where t represents time in seconds and v0 is the constant of integration, and in this case, is the initial vertical velocity.

In this case, the initial velocity is 57.4 ft/s upwards, then the velocity equation is:

v(t) = (-32 ft/s^2)*t + 57.4 ft/s

To get the position equation we need to integrate over time again, to get:

p(t) = (1/2)*(-32 ft/s^2)*t^2 + (57.4 ft/s)*t + p0

Where p0 is the initial height of the object, as it was launched from the ground, then the initial position is p0 = 0ft.

then the position equation (that is the function that represents the height of the object as a function over time) is:

p(t) = (1/2)*(-32 ft/s^2)*t^2 + (57.4 ft/s)*t

p(t) = (-16 ft/s^2)*t^2 + (57.4 ft/s)*t

Ming and Daniel are selling cheese cakes for a school fundraiser. Customers can buy French silk cheesecakes and apple cheesecakes. Ming sold 6 French silk cheesecakes and 3 apple cheesecakes for a total of $114. Daniel sold 4 French silk cheesecakes and 5 apple cheesecakes for a total of $124. Find the cost of each of one French silk cheesecakes and one apple cheesecake.

Rewrite in simplest terms: 8(-10r - 9) + 9r

yoo someone help asaapp!​

Have to find x,y and z.

Brianliest for correct answer

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please answer the questions.​

What are the values of x and y?
A.
x equals 136 over 15 and y equals 17 over 15
B.
x equals 64 over 15 and y equals 17 over 15
C.
x equals 8 over 15 and y equals 136 over 15
D.
x equals 64 over 15 and y equals 136 over 15

PLS HELP
PLSSSSSSSSSSS

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A.They vibrate in place
B.They slide past each other.
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D.They cause the solid to have definite volume and shape.

8t=−32

Help a sister out

In the function y= 1/3x^2,
what effect does the number 1/3 have on the graph,
as compared to the graph of the function y= x^2

A. It stretches the graph horizontally by a factor of 3.
B. It shrinks the graph horizontally to 1/3 its original width.
C. It shrinks the graph vertically to 1/3 its original height.
D. It stretches the graph vertically by a factor of 3.

s=ut+ 1/2 at²
u=10 a= -2 t= 1/2
work out the value of s

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A
12
30°
B
60°
14

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The junior class sold 120 turkey dinner plates and 200 chicken dinner plates for a total of $2,150. The senior class sold 100 turkey plates and 300 chicken plates, raising $2,625. What was the cost of each turkey dinner plate? What is the cost of each chicken plate?

Graph the line with the equation y = 22 - 2.
y
10
9
8
7
6
5
4
3
2
-10 -9
-8
-7 -6
-5
-4
-3
-2
-
1
2
3
4
5 6
7
8
9 10
-1

Try the following puzzle:

A bat and ball cost $1.10.

The bat costs one dollar more than the ball.

How much does the ball cost?

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Which of the following relative frequencies match the expected probability?

Please help clarify answer and step by step explanation

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yes
no

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A. 13y
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On Friday, a local restaurant served 150 customers. Of these, 114

people ordered soup. What percent of the customers ordered soup?


A: 13%

B: 66%

C: 34%

D: 76%