1. A tank contains 50 gallons of a solution composed of 90% water and 10% alcohol.A second solution containing half water and half alcohol is added to the tank ata rate of 5 gallons per minute. At the same time, the tank is being drained at therate of 5 gallons per minute. Assuming that the solution is stirred constantly,how much alcohol will be in the tank after 10 minutes? 1. A thermometer reading 18 °F is brought into a room where the temperature is 70°F; 1 minute later the thermometer reading is 31 °F. Determine the temperaturereading as a function of time and, in particular, find the temperature reading 5minutes after the thermometer is first brought into the room.

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Answered: 1. A tank contains 50 gallons of a…

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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Consider a large vat containing sugar water that is to be made into soft drinks (see figure below). A B Suppose: The vat contains 230 gallons of liquid, which never changes. Sugar water with a concentration of 7 tablespoons/gallon flows through pipe A into the vat at the rate of 5 gallons/minute. • Sugar water with a concentration of 3 tablespoons/gallon flows through pipe B into the vat at the rate of 25 gallons/minute. The liquid in the vat is kept well-mixed. • Sugar water leaves the vat through pipe C at the rate of 30 gallons/minute. Let S(t) represent the number of tablespoons of sugar in the vat at time t, where t is given in minutes. (A) Write the DE model for the time rate of change of sugar in the vat: dS dt (B) Solve the differential equation to find the amount of sugar in the vat as a function of time. Your function will have an arbitrary constant K in it. Assume that K > 0. S(t) = (C) Suppose that there are 22 tablespoons of sugar in the vat at t = 0. How many tablespoons…
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Two chemicals A and B are combined to form a chemical C. The rate, or velocity, of the reaction is proportional to the product of the instantaneous amounts of A and B not converted to chemical C. Initially, there are 40 grams of A and 50 grams of B, and for each gram of B, 2 grams of A is used. It is observed that 20 grams of C is formed in 6 minutes. How much (in grams) is formed in 12 minutes? (Round your answer to one decimal place.) grams What is the limiting amount (in grams) of C after a long time? grams How much (in grams) of chemicals A and B remains after a long time? A B Need Help? grams grams Read It Watch It Master
"MixtureA tank contains 100 gallons of a solution composed of 70% water and 30% alcohol. A second solution containing 75% alcohol and 25% water is added to the tank at a rate of 12 gallons per minute. As the second solution is being added, the tank is being drained at a rate of 15 gallons per minute. The solution in the tank is stirred constantly. How much alcohol is in the tank after 15 minutes"

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