A tank holds 1,000 gallons of water, which drains from the bottom of the tank in half an hour. The values in the table show the volume V of water remaining in the tank (in gallons) after t minutes. A tank holds 1,000 gallons of water, which drains from the bottom of the tank in half an hour. The values in the table show the volume V of water remaining in the tank (in gallons) after t minutes.t (min) 5 10 15 20 25 30V (gal)690 442 255 116 27 0(a) If P is the point (15, 255) on the graph of V, find the slopes of the secant lines PQ when Q is the point on the graph with t = 5, 10, 20, 25, and 30. (Round your answers to one decimal place.)SlopeQ(5, 690)(10, 442)(20, 116)(25, 27)(30, 0)(b) Estimate the slope of the tangent line at P by averaging the slopes of the two adjacent secant lines corresponding to the two points closest to P. (Round your answer to one decimal place.)

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A tank holds 1,000 gallons of water, which drains from the bottom of the tank in half an hour. The values in the table show the volume V of water remaining in the tank (in gallons) after t minutes. t (min) 5 10 15 20 25 30 V (gal) (a) If P is the point (15, 255) on the graph of V, find the slopes of the secant lines PQ when Q is the point on the graph with t = 5, 10, 20, 25, and 30. (Round your answers to one decimal place.) Slope Q (5, 690) (10, 442) (20, 116) (25, 27) (30, 0) 690 442 255 116 27 0 (b) Estimate the slope of the tangent line at P by averaging the slopes of the two adjacent secant lines corresponding to the two points closest to P. (Round your answer to one decimal place.)

A tank holds 1,000 gallons of water, which drains from the bottom of the tank in half an hour. The values in the table show the volume V of water remaining in the tank (in gallons) after t minutes. t (min) 5 10 15 20 25 30 V (gal) (a) If P is the point (15, 255) on the graph of V, find the slopes of the secant lines PQ when Q is the point on the graph with t = 5, 10, 20, 25, and 30. (Round your answers to one decimal place.) Slope Q (5, 690) (10, 442) (20, 116) (25, 27) (30, 0) 690 442 255 116 27 0 (b) Estimate the slope of the tangent line at P by averaging the slopes of the two adjacent secant lines corresponding to the two points closest to P. (Round your answer to one decimal place.)

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A tank holds 1,000 gallons of water, which drains from the bottom of the tank in half an hour. The values in the table show the volume V of water remaining in the tank (in gallons) after t minutes.

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