A 200 gallon tank initially contains 100 gallons of water with 20 pounds of salt. A salt solution with 1/5pound of salt per gallon is added to the tank at 10 gal/min, and the resulting mixture is drained out at 5gal/min. Let Q(t) denote the quantity (lbs) of salt at time t (min).(a) Write a differential equation for Q(t) which is valid up until the point at which the tank overflows.Q' (t) =(b) Find the quantity of salt in the tank as it's about to overflow.OO✓19W3ERс$4r%5Oll6y&7u*81(90р#1

We are given that in a 200 gallon tank , intially there was 100 gallon of water which contains 20…

Answered: A 200 gallon tank initially contains…

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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Newton's law of cooling says that the rate at which a body cools is proportional to the difference in temperature between the body and an environment into which it is introduced. This leads to an equation where the temperature f(t) of the body at time t after being introduced into an environment having constant temperature To is where C and k are constants. Find the temperature of an object when t=9 if To = 17, C = 7 and f(t)= To + Ce k=0.6. - kt The temperature of the object is (Round to two decimal places as needed.)
A tank is filled with 200 l of salt solution containing Qo kg of salt at time t = 0. Another salt solution with 1/4 kg of salt per liter flows into the tank at a rate of 6 lt / min. By mixing, a homogeneous water-salt mixture is obtained continuously in the tank and the mixture leaves the tank at the same speed. Find the expression Q (t) which gives the amount of salt present in the tank at time t.
H.W1: A 150-L tank initially contains (30 L) of fresh water. At (t = 0), a brine solution containing (0.5 kg) of salt per liter is poured into the tank at the rate of (10 L/min), while the well- stirred mixture leaves the tank at the rate of (4 L/min). Find: (a) The amount of time required for overflow to occur and (b) The amount of salt in the tank at the moment of overflow.
A tank contains 210 liters of fluid in which 50 grams of salt is dissolved. Pure water is then pumped into the tank at a rate of 3 L/min; the well-mixed solution is pumped out at the same rate. Let the A(t) be the number of grams of salt in the tank at time t. Find the rate at which the number of grams of salt in the tank is changing at time t. Find the number A(t) of grams of salt in the tank at time t.
Let y(t) be the height (in meters) after time t (in seconds) of a rover that is landing on some other planet with the help of a parachute. Taking into account gravity and air resistance, physicists suggest that the air resistance is proportional to velocity. Further data suggests that the fall can be modeled by y=-4-3y. If the parachute is released at a height of 600m with an initial velocity of Om/s, what is its height after t seconds? What is its terminal velocity? The terminal velocity is m/s. m/s
When drugs are administered into the bloodstream, the amount of the drug present decreases continuously at a constant rate. The amount of a certain drug, Xanaz, in the bloodstream is modeled by the function, where is the initial dosage, and t is the time (in hours) after the initial dose was given. The following chart shows the relationship between the original dose and how much is sti in the system after so much time. Xanax (3mg) amount still in system after X hours 2.5 1.5 0.5 2 10 12 14 16 18 20 22 24 Number of hours after dose was taken After how many hours will there be approximately 1/2 of the original dose in the body? 3. 2. 1. Amount still in the system in mg's
According to Newton's law of cooling, the temperature of a body changes at a rate proportional to the difference between the temperature of the body and the temperature of the surrounding medium. Thus, if Tm is the temperature of the medium and T = T(t) is the temperature of the body at time t, then T'= -k(T - Tm) where k is a positive constant. In this exercise, you will verify that T = Tm+ (To-Tm)e -kt is a solution to the differential equation. Here To denotes the initial temperature T(0) of the body. (a) First substitute the above expression for T into the left side of the differential equation. In other words, compute T'. Use an underscore "_" to write the subscripts on To and Im T'= (b) Next substitute the above expression for T into the right side of the differential equation. In other words, compute -k(T – Tm). - -k(T - Tm) (c) Are your answers in parts (a) and (b) equal? No Yes
Researchers have found a correlation between respiratory rate and body mass in the first three years of life. This correlation can be expressed by the function log R(w) = 1.85-0.48 log (w), where w is the body weight (in kilograms) and R(w) is the respiratory rate (in breaths per minute). a. Find R'(w) using implicit differentiation. b. Find R'(w) by first solving the equation for R(w). c. Discuss the two procedures. Is there a situation when you would want to use lone method over another? a. R'(w) =[| (Simplify your answer. Use integers or decimals for any numbers in the expression. Round to four decimal places as needed.)

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