Awesome Assorted Applications!!! (2.1c alliteration!!!)

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Awesome Assorted Applications!!! (2.1c alliteration!!!)

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Awesome Assorted Applications!!! (2.1c alliteration!!!)

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AwesomeAssortedApplications!!!(2.1c alliteration!!!)

Homework: p. 177-180 45-49 odd, 55, 57, 61

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

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.

What about models for FREE FALL?!?!

Vertical Free-Fall Motion

The heights and vertical velocityv 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

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.

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

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.

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 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.

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

117.371 ft/sec when it hits the ground

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)

0.00001.03754

0.10801.40205

0.21501.63806

0.32251.77412

0.43001.80392

0.53751.71522

0.64501.50942

0.75251.21410

0.86000.83173

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?

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)

0.00001.03754

0.10801.40205

0.21501.63806

0.32251.77412

0.43001.80392

0.53751.71522

0.64501.50942

0.75251.21410

0.86000.83173

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. 1.800 m, and has a downward rate of

approx. 5.800 m/sec when it hits the ground.