A tank holds 5000 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) 15 20 25 30 5 10 3440 2190 1300 510 135 0 V (gal) (a) If P is the point (15, 1300) on the graph of V, find the slopes of the secant lines PQ when Q is the point on the graph with the following values. (Round your answers to one decimal place.) Q (5, 3440) (10, 2190) (20, 510) (25, 135) (30, 0) slope (b) Estimate the slope of the tangent line at P by averaging the slopes of two adjacent secant lines. (Round your answer to one decimal place.)
A tank holds 5000 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) 15 20 25 30 5 10 3440 2190 1300 510 135 0 V (gal) (a) If P is the point (15, 1300) on the graph of V, find the slopes of the secant lines PQ when Q is the point on the graph with the following values. (Round your answers to one decimal place.) Q (5, 3440) (10, 2190) (20, 510) (25, 135) (30, 0) slope (b) Estimate the slope of the tangent line at P by averaging the slopes of two adjacent secant lines. (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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Question 1
Transcribed Image Text:A tank holds 5000 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)
15 20 25 30
5 10
3440 2190 1300 | 510 135 0
V (gal)
(a) If P is the point (15, 1300) on the graph of V, find the slopes of the secant lines PQ when Q is the point on the graph with the following values. (Round your answers to one decimal
place.)
Q
(5, 3440)
(10, 2190)
(20, 510)
(25, 135)
(30, 0)
slope
(b) Estimate the slope of the tangent line at P by averaging the slopes of two adjacent secant lines. (Round your answer to one decimal place.)
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