Concept explainers
Repeat Example 5 if water is released from the tank at the rate of 75 gallons per hour.
Pollution Control A company has a 1,000-gallon holding tank that is used to control the release of pollutants into a sewage system. Initially, the tank contains 500 gallons of water. Each gallon of water contains 2 pounds of pollutants. Additional polluted water containing 5 pounds of pollutants per gallon is pumped into the tank at the rate of 100 gallons per hour and is thoroughly mixed with the water already present in the tank. At the same time, the uniformly mixed water in the tank is released into the sewage system at a rate of 50 gallons per hour (Fig. 2). This process continues for 5 hours. At the end of this 5-hour period, determine
(A) The total amount of pollutants in the tank
(B) The rate (in pounds per gallon) at which pollutants are being released into the sewage system
Want to see the full answer?
Check out a sample textbook solutionChapter 9 Solutions
Pearson eText for Calculus for Business, Economics, Life Sciences, and Social Sciences, Brief Version -- Instant Access (Pearson+)
- What operations can be performed on a linear system to arrive at an equivalent system?arrow_forwardHeart Disease In a certain country, the number of deaths due to heart disease decreased from 235 in one year to 221 in the next year. What percentage decrease in deaths due to heart disease does this represent?arrow_forwardFind the constant of proportionality. y is directly proportional to x. If x=30, then y=15.arrow_forward
- Asaparrow_forward→ Consider a large vat containing sugar water that is to be made into soft drinks (see figure below). A B Suppose: • The vat contains 260 gallons of liquid, which never changes. • Sugar water with a concentration of 5 tablespoons/gallon flows through pipe A into the vat at the rate of 5 gallons/minute. Su water with a concentration of 4 tablespoons/gallon flows through pipe B into the vat at the rate of 20 gallons/minute. • The liquid in the vat is kept well-mixed. • Sugar water leaves the vat through pipe C at the rate of 25 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 M # $ 2 Oll O %arrow_forward3. A tank originally contains 160 gal of fresh water. Then water containing lb of salt per gallon is poured into the tank at a rate of 4 gal / min, and the mixture is allowed to leave at the same rate. After 8 min the process is stopped, and fresh water is poured into the tank at a rate of 6 gal / min, with the mixture again leaving at the same rate. Find the amount of salt in the tank at the end of an additional 8 min.arrow_forward
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningFunctions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage LearningGlencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageAlgebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningCollege AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning