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Awesome Assorted Applications!!! (alliteration!!!) Sec. 2.1c, you are too cool…

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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: Dimensions: 11 ft by 14 ft x x + 3 11 1 1

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Remember this model?: Price per cereal box Cereal boxes sold 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.

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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

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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.

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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.

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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] The baseball is in the air for approximately 6.543 seconds …because this is when it hits the ground!!!

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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. The baseball’s downward rate is 117.371 ft/sec when it hits the ground Use our answer for the previous question, plug into the equation for vertical velocity!!!

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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?

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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.

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