Question

In: Advanced Math

Your swimming pool containing 84,000 gal of water has been contaminated by 6 kg of a...

Your swimming pool containing 84,000 gal of water has been contaminated by 6 kg of a nontoxic dye that leaves a swimmer's skin an unattractive green. The pool's filtering system can take water from the pool, remove the dye, and return the water to the pool at a flow rate of 250 gal/min.

(a) What is the initial value problem for the filtering process? Let q be the amount of dye in grams in the pool at any time t. dq dt = − 250q/84000​ Correct: Your answer is correct. g/min, q(0) = Correct: Your answer is correct. grams

(b) Solve the problem in part (a).

(d) Find the time T at which the concentration of the dye first reaches the value of 0.03 g/gal. (Round your answer to two decimal places.) T = hr

(e) Find the flow rate r that is sufficient to achieve the concentration 0.03 g/gal within 4 h. (Round your answer to the nearest integer.) r = gal/min

Solutions

Expert Solution

Colby Messinger answered 4 months ago
Next > < Previous

Related Solutions

A swimming pool whose volume is 10,000 gal contains water that is 0.02% chlorine. Starting at...
A swimming pool whose volume is 10,000 gal contains water that is 0.02% chlorine. Starting at t = 0, city water containing 0.001% chlorine is pumped into the pool at a rate of 4 gal/min. The pool water flows out at the same rate. What is the percentage of chlorine in the pool after 1 hour? When will the pool water be 0.002% chlorine?
A tank contains 200 gal of water and 50oz of salt. Water containing a salt concentration...
A tank contains 200 gal of water and 50oz of salt. Water containing a salt concentration of 1/8(1+1/2 sint) oz/gal flows into the tank at a rate of 4 gal/min, the mixture flows out at the same rate. A) find the amount of salt in the tank at any moment. Q(t) = B) the amplitude of oscillation is C) level of the amplitude is
A swimming pool, 10.0 m by 4.0 m, is filled with water to a depth of...
A swimming pool, 10.0 m by 4.0 m, is filled with water to a depth of 3.0 m at a temperature of 20.2°C. If the energy needed to raise the temperature of the water to 26.1°C is obtained from the combustion of methane (CH4), what volume of methane, measured at STP, must be burned? ∆Hcombustion for CH4 = -891 kJ/mol volume CH4 needed
Pythagoras is at it again. He is pumping into my backyard pool 3 gal/min of water...
Pythagoras is at it again. He is pumping into my backyard pool 3 gal/min of water in one hose that contains a concentration of 2 g/gal of liquid catnip and 4 gal/min of water in another hose that is clean. The pool has a capacity of 200 gallons, but is initially only half full and is initially clean. Let’s assume that there is a benevolent mathematical higher spirit that is using his or her supernatural large spoon to constantly stir...
A tank originally contains 100 gal of fresh water. Then water containing 1 2 lb of...
A tank originally contains 100 gal of fresh water. Then water containing 1 2 lb of salt per gallon is poured into the tank at a rate of 2 gal/min, and the mixture is allowed to leave at the same rate. After 10 min the process is stopped, and fresh water is poured into the tank at a rate of 4 gal/min, with the mixture again leaving at the same rate. Find the amount of salt in the tank at...
A tank originally contains 100 gal of fresh water. Then water containing 1 2 lb of...
A tank originally contains 100 gal of fresh water. Then water containing 1 2 lb of salt per gallon is poured into the tank at a rate of 2 gal/min, and the mixture is allowed to leave at the same rate. After 10 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 function f(t) represents water going into a swimming pool with respect to the number of...
The function f(t) represents water going into a swimming pool with respect to the number of hours(t) water is flowing in where(t) represents time.f(t)=t squared +8t+9 There is a leak in the pool and it’s losing water at a rate represented by d(t) d(t)=t squared +11t+4 a. Write a function to represent the amount of water in the pool using the two functions. b. Use the new function w(t) to determine if the pool will leak all of the water....
A tank originally contains 120 gal of fresh water. Then water containing 1/2 lb of salt...
A tank originally contains 120 gal of fresh water. Then water containing 1/2 lb of salt per gallon is poured into the tank at a rate of 2 gal/min, and the mixture is allowed to leave at the same rate. After 11 min the process is stopped, and fresh water is poured into the tank at a rate of 2 gal/min, with the mixture again leaving at the same rate. Find the amount of salt Q(11) in the tank at...
Miller Toy Company manufactures a plastic swimming pool at its Westwood Plant. The plant has been...
Miller Toy Company manufactures a plastic swimming pool at its Westwood Plant. The plant has been experiencing problems as shown by its June contribution format income statement below: Flexible Budget Actual Sales (3,000 pools) $ 179,000 $ 179,000 Variable expenses: Variable cost of goods sold* 33,390 44,540 Variable selling expenses 11,000 11,000 Total variable expenses 44,390 55,540 Contribution margin 134,610 123,460 Fixed expenses: Manufacturing overhead 50,000 50,000 Selling and administrative 75,000 75,000 Total fixed expenses 125,000 125,000 Net operating income...
Miller Toy Company manufactures a plastic swimming pool at its Westwood Plant. The plant has been...
Miller Toy Company manufactures a plastic swimming pool at its Westwood Plant. The plant has been experiencing problems as shown by its June contribution format income statement below: Flexible Budget Actual Sales (6,000 pools) $ 265,000 $ 265,000 Variable expenses: Variable cost of goods sold* 95,580 112,700 Variable selling expenses 14,000 14,000 Total variable expenses 109,580 126,700 Contribution margin 155,420 138,300 Fixed expenses: Manufacturing overhead 63,000 63,000 Selling and administrative 78,000 78,000 Total fixed expenses 141,000 141,000 Net operating income...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT