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No calculator is allowed for the following problem. Water is pumped into a tank at a rate of R(t) = 8√2t gallons per minute over the interval 0 st≤ 8. Water leaks out of the tank at a constant rate of 2 gallons per minute. The tank originally contains 10 gallons of water and can hold 200 gallons. a) How many gallons of water are pumped into the tank during the entire 8-minute interval? b) Is the amount of water in the tank increasing or decreasing at time t = 2? Justify your answer.

No calculator is allowed for the following problem. Water is pumped into a tank at a rate of R(t) = 8√2t gallons per minute over the interval 0 st≤ 8. Water leaks out of the tank at a constant rate of 2 gallons per minute. The tank originally contains 10 gallons of water and can hold 200 gallons. a) How many gallons of water are pumped into the tank during the entire 8-minute interval? b) Is the amount of water in the tank increasing or decreasing at time t = 2? Justify your answer.

Advanced Engineering Mathematics
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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Student Guide (continued) FRQ 2 No calculator is allowed for the following problem. Water is pumped into a tank at a rate of R(t) = 8V2i gallons per minute over the interval 0 sts 8. Water leaks out of the tank at a constant rate of 2 gallons per minute. The tank originally contains 10 gallons of water and can hold 200 gallons. a) How many gallons of water are pumped into the tank during the entire 8-minute interval? b) Is the amount of water in the tank increasing or decreasing at time t = 2? Justify your answer. c) What is the minimum amount of water in the tank over the interval 0sts 8? Justify your answer. d) Assume water continues to be pumped into the tank and leaks from the tank at the given rates after t = 8 minutes. Write, but do not solve, an equation that gives the time k at which the tank reaches its capacity.
Transcribed Image Text:Student Guide (continued) FRQ 2 No calculator is allowed for the following problem. Water is pumped into a tank at a rate of R(t) = 8V2i gallons per minute over the interval 0 sts 8. Water leaks out of the tank at a constant rate of 2 gallons per minute. The tank originally contains 10 gallons of water and can hold 200 gallons. a) How many gallons of water are pumped into the tank during the entire 8-minute interval? b) Is the amount of water in the tank increasing or decreasing at time t = 2? Justify your answer. c) What is the minimum amount of water in the tank over the interval 0sts 8? Justify your answer. d) Assume water continues to be pumped into the tank and leaks from the tank at the given rates after t = 8 minutes. Write, but do not solve, an equation that gives the time k at which the tank reaches its capacity.
FRQ 1 No calculator is allowed for the following problem. Consider the differential equation -xy?. a) On the axes provided, sketch a slope field for the given differential equation at the 15 points indicated. 2 1 b) Let y = fx) be the particular solution to the differential equation with the initial condition fl-1) =1. Write an equation for the line tangent to the graph of y = f(x) at x = -1. Use your equation to approximate fl-0.9). c) Find the particular solution y = f(x) to the given differential equation with the initial condition A-1) = 1.
Transcribed Image Text:FRQ 1 No calculator is allowed for the following problem. Consider the differential equation -xy?. a) On the axes provided, sketch a slope field for the given differential equation at the 15 points indicated. 2 1 b) Let y = fx) be the particular solution to the differential equation with the initial condition fl-1) =1. Write an equation for the line tangent to the graph of y = f(x) at x = -1. Use your equation to approximate fl-0.9). c) Find the particular solution y = f(x) to the given differential equation with the initial condition A-1) = 1.
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