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A pond is approximately circular, with a diameter of 400 feet. Starting at the center, the depth of the water is measured every 25 feet and recorded in the table (see figure). 25 so 75 100 12s 150 175 200 Depth 20 1 19 17 15

A pond is approximately circular, with a diameter of 400 feet. Starting at the center, the depth of the water is measured every 25 feet and recorded in the table (see figure). 25 so 75 100 12s 150 175 200 Depth 20 1 19 17 15

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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A pond is approximately circular, with a diameter of 400 feet. Starting at the center, the depth of the water is measured every 25 feet and recorded in the table (see figure). 025 so 75 100 125 150 175s 200 Desth 20 19 19 12 15 14 10 (a) Use the regression capabilities of a graphing utility to find a quadratic model for the depths recorded in the table. (Round your coefficients to six decimal places.) d = -0.0005a" + 0.018874x + 19.393939 Use the graphing utility to plot the depths and graph the model. (b) Use the integration capabilities of a graphing utility and the model in part (a) to approximate the volume (in ft³) of water in the pond. (Round your answer to the nearest whole number.) ft3 (c) Use the result of part (b) to approximate the number of gallons of water in the pond. (Hint: 1 cubic foot of water is approximately 7.48 gallons. Round your answer to the nearest whole number.) gal
Transcribed Image Text:A pond is approximately circular, with a diameter of 400 feet. Starting at the center, the depth of the water is measured every 25 feet and recorded in the table (see figure). 025 so 75 100 125 150 175s 200 Desth 20 19 19 12 15 14 10 (a) Use the regression capabilities of a graphing utility to find a quadratic model for the depths recorded in the table. (Round your coefficients to six decimal places.) d = -0.0005a" + 0.018874x + 19.393939 Use the graphing utility to plot the depths and graph the model. (b) Use the integration capabilities of a graphing utility and the model in part (a) to approximate the volume (in ft³) of water in the pond. (Round your answer to the nearest whole number.) ft3 (c) Use the result of part (b) to approximate the number of gallons of water in the pond. (Hint: 1 cubic foot of water is approximately 7.48 gallons. Round your answer to the nearest whole number.) gal
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