( pointIf a tank holds 6000 gallons of water, whichdrains from the bottom of the tank in 40minutes, then Torricelli's Law gives the volumeV of water remaining in the tank after t minutes2t6000(10

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Answered: If a tank holds 6000 gallons of water,…

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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A weather balloon that contains 540 m3 of helium springs a leak and empties in 60 seconds. Suppose that the volume of helium in the balloon as a function of time is given by V (t)= 540(1-t/60)^3. Find (a) the average rate of change of volume during the 60 seconds it takes to empty. b) the volume of the balloon after 40 seconds. c) the instantaneous rate of change of the volume at 40 seconds.
A brine solution of salt flows at a constant rate of 5 L/min into a large tank that initially held 100 L of brine solution in which was dissolved 0.15 kg of salt. The solution inside the tank is kept well stirred and flows out of the tank at the same rate. If the concentration of salt in the brine entering the tank is 0.03 kg/L, determine the mass of salt in the tank after t min. When will the concentration of salt in the tank reach 0.01 kg/L? Determine the mass of salt in the tank after t min. mass= kg
A brine solution of salt flows at a constant rate of 6 L/min into a large tank that initially held 100 L of brine solution in which was dissolved 0.1 kg of salt. The solution inside the tank is kept well stirred and flows out of the tank at the same rate. If the concentration of salt in the brine entering the tank is 0.02 kg/L, determine the mass of salt in the tank after t min. When will the concentration of salt in the tank reach 0.01 kg/L?
Initially 9 grams of salt are dissolved into 7 liters of water. Brine with concentration of salt 8 grams per liter is added at a rate of 5 liters per minute. The tank is well mixed and drained at 5 liters per minute. a) Let x be the amount of salt, in grams, in the solution after t minutes have elapsed. Find a formula for the rate of change in the amount of salt, dx/dt, in terms of the amount of salt in the solution x. dx dt b) Find a formula for the amount of salt, in grams, after t minutes have elapsed. x(t) = c) How long must the process continue until there are exactly 40 grams of salt in the tank?
A brine solution of salt flows at a constant rate of 8 L/min into a large tank that initially held 100 L of brine solution in which was dissolved 0.2 kg of salt. The solution inside the tank is kept well stirred and flows out of the tank at the same rate. If the concentration of salt in the brine entering the tank is 0.04 kg/L, determine the mass of salt in the tank after t min. When will the concentration of salt in the tank reach 0.01 kg/L? Determine the mass of salt in the tank after t min. mass 4-4e 2t 25 kg
A brine solution of salt flows at a constant rate of 8 L/min into a large tank that initially held 100 L of brine solution in which was dissolved 0.1 kg of salt. The solution inside the tank is kept well stirred and flows out of the tank at the same rate. If the concentration of salt in the brine entering the tank is 0.02 kg/L, determine the mass of salt in the tank after t min. When will the concentration of salt in the tank reach 0.01 kg/L? Determine the mass of salt in the tank after t min. mass = kg When will the concentration of salt in the tank reach 0.01 kg/L? The concentration of salt in the tank will reach 0.01 kg/L after minutes. (Round to two decimal places as needed.)

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If a tank holds 6000 gallons of water, which drains from the bottom of the tank in 40 minutes, then Torricelli's Law gives the volume V of water remaining in the tank after t minutes as V = 6000 [ 1 0