Answer [(a.) t = 300 hours] 1. In differential equation determine the following: (A.) the time when the tank overflows. In a 1500-gallon tank initially contains 600 gallons of water with 5 pounds of salt dissolved in it. Water enters the tank at a rate of nine gal/hr and the water entering the tank has a salt concentration of (1/5)(1 + cos t) lb/gal. If a well-mixed solution leaves the tank at a rate of 6 gph.(B.) Find the amount of salt as a function of t, and;(C.) the amount of salt in the tank when it overflows. Answer [b) Q = (9/5)(40,000t +1,200t^2 + (t^3/3) + (39,998 + 400t + t^2)(sin t) + (400 +2t)(cos t) + 996,400/9)/(200 + t)2 ] Answer [c) Q = 280.04lb.]
Answer [(a.) t = 300 hours] 1. In differential equation determine the following: (A.) the time when the tank overflows. In a 1500-gallon tank initially contains 600 gallons of water with 5 pounds of salt dissolved in it. Water enters the tank at a rate of nine gal/hr and the water entering the tank has a salt concentration of (1/5)(1 + cos t) lb/gal. If a well-mixed solution leaves the tank at a rate of 6 gph.(B.) Find the amount of salt as a function of t, and;(C.) the amount of salt in the tank when it overflows. Answer [b) Q = (9/5)(40,000t +1,200t^2 + (t^3/3) + (39,998 + 400t + t^2)(sin t) + (400 +2t)(cos t) + 996,400/9)/(200 + t)2 ] Answer [c) Q = 280.04lb.]
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Answer [(a.) t = 300 hours] 1. In differential equation determine the following: (A.) the time when the tank overflows. In a 1500-gallon tank initially contains 600 gallons of water with 5 pounds of salt dissolved in it. Water enters the tank at a rate of nine gal/hr and the water entering the tank has a salt concentration of (1/5)(1 + cos t) lb/gal. If a well-mixed solution leaves the tank at a rate of 6 gph.(B.) Find the amount of salt as a function of t, and;(C.) the amount of salt in the tank when it overflows.
Answer [b) Q = (9/5)(40,000t +1,200t^2 + (t^3/3) + (39,998 + 400t + t^2)(sin t) + (400 +2t)(cos t) + 996,400/9)/(200 + t)2 ]
Answer [c) Q = 280.04lb.]
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