1. Awesome Assorted Applications!!! (2.1c alliteration!!!)
Homework: p odd, 55, 57, 61

2. Dimensions: 11 ft by 14 ft x x + 3
The “Do Now”: A large painting in the style of Rubens is 3 ft
longer than it is wide. If the wooden frame is 12 in. wide, the
area of the picture and frame is 208 sq ft, find the dimensions of
the painting.
Total Area: 1 1 x 1
x + 3 1
Dimensions: 11 ft by 14 ft

3.  The ideal price should be $2.40 per box, which
Remember this model?:
Cereal boxes sold
Price per cereal box
Use this equation to develop a model for the total weekly revenue
on sales of a specific cereal.
Revenue equals the price per box (x) multiplied by the number
of boxes sold (y):
Graph and calculate the maximum!!!
 The ideal price should be $2.40 per box, which
would yield a maximum revenue of about $88,227.

4. Vertical Free-Fall Motion
What about models for FREE FALL?!?!
Vertical Free-Fall Motion
The height s and vertical velocity v of an object in free fall are
given by
and
is time (in seconds)
is the acceleration due to
gravity
is the initial vertical velocity of the object
is the initial height of the object

5. Free-Fall Motion Example: As a promotion for a new ballpark, a
competition is held to see who can throw a baseball the highest
from the front row of the upper deck of seats, 83 ft above field
level. The winner throws the ball with an initial vertical velocity
of 92 ft/sec and it lands on the infield grass.
1. Write the models for height and velocity in this situation.

6. The maximum height of the baseball is 215.25 feet above field level.
Free-Fall Motion Example: As a promotion for a new ballpark, a
competition is held to see who can throw a baseball the highest
from the front row of the upper deck of seats, 83 ft above field
level. The winner throws the ball with an initial vertical velocity
of 92 ft/sec and it lands on the infield grass.
2. Find the maximum height of the baseball.
Coordinates of the vertex:
The maximum height
of the baseball is
feet
above field level.

7. The baseball is in the air for approximately 6.543 seconds
Free-Fall Motion Example: As a promotion for a new ballpark, a
competition is held to see who can throw a baseball the highest
from the front row of the upper deck of seats, 83 ft above field
level. The winner throws the ball with an initial vertical velocity
of 92 ft/sec and it lands on the infield grass.
3. Find the amount of time the baseball is in the air.
Graph the height function, and calculate the positive-valued
zero of this function… window: [0, 7] by [–50, 250]
…because this is when it hits the ground!!!
The baseball is in the air for
approximately seconds

8. The baseball’s downward rate is 117.371 ft/sec when it hits the ground
Free-Fall Motion Example: As a promotion for a new ballpark, a
competition is held to see who can throw a baseball the highest
from the front row of the upper deck of seats, 83 ft above field
level. The winner throws the ball with an initial vertical velocity
of 92 ft/sec and it lands on the infield grass.
4. Find the vertical velocity of the baseball when
it hits the ground.
Use our answer for the previous question, plug into the
equation for vertical velocity!!!
The baseball’s downward rate is
ft/sec when it hits the ground

9. The following data were gathered by measuring the distance from
the ground to a rubber ball after it was thrown upward:
Time (sec) Height (m)
Use these data to write models for
the height and vertical velocity of
the ball.
First, create a scatter plot  what
type of regression should we use?
How well does this model fit the data?
How do we use this model to develop
an equation for vertical velocity?

10. The ball reaches a maximum height of
The following data were gathered by measuring the distance from
the ground to a rubber ball after it was thrown upward:
Time (sec) Height (m)
Use these models to predict the
maximum height of the ball and its
vertical velocity when it hits the
ground.
The ball reaches a maximum height of
approx m, and has a downward rate of
approx m/sec when it hits the ground.