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A tank holds 3,000 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. 10 15 20 25 30 t (min) 5 V (gal) 2,064 1,329 765 339 87 0 (a) If Pis the point (15, 765) 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 (5, 2,064) (10, 1,329) (20, 339) (25, 87) (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.)

A tank holds 3,000 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. 10 15 20 25 30 t (min) 5 V (gal) 2,064 1,329 765 339 87 0 (a) If Pis the point (15, 765) 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 (5, 2,064) (10, 1,329) (20, 339) (25, 87) (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.)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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A tank holds 3,000 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. 20 25 30 t (min) 10 15 V (gal) 2,064| 1,329 87 0 765 339 (a) If Pis the point (15, 765) 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 (5, 2,064) (10, 1,329) (20, 339) (25, 87) (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.)
Transcribed Image Text:A tank holds 3,000 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. 20 25 30 t (min) 10 15 V (gal) 2,064| 1,329 87 0 765 339 (a) If Pis the point (15, 765) 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 (5, 2,064) (10, 1,329) (20, 339) (25, 87) (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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