120229 Polynomial application problems

Suppose you make the following measurements as a

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how far out on the board the person stands. Suppose you make the following measurements as a person moves out on the diving board: x = distance out on the board y = distance that the board bends 0 feet 0.0 inches 1 foot 0.1 inches 2 feet 0.5 inches 3 feet 1.0 inches 4 feet 2.0 inches a. It turns out that a cubic function is a good model for y as a function of x . Use your calculator to find the cubic function that best fits the given data. b. If the total length of the diving board is 6 feet, and a person stands at the end of the board, how much would the board bend? c. Suppose that a diving board is considered safe if it bends by 12 inches or less. What would be the maximum acceptable length for the diving board? 6. Let S ( n ) stand for the sum of the cubes of the first n positive integers. For example, S (4) = 1 3 + 2 3 + 3 3 + 4 3 . a. Make a table of values for S ( n ), for n = 1, 2, 3, …, 8. b. S ( n ) can be modeled using a quartic (degree 4) polynomial. Use regression on your calculator to find this quartic polynomial? c. Does the quartic polynomial appear to fit S ( n ) exactly, or only approximately? Explain.
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