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question 10 only Test 2 2014 Answers.pd. × t 4 of 7 10. A 98 L tank is filled wi

ID: 2889098 • Letter: Q

Question

question 10 only

Test 2 2014 Answers.pd. × t 4 of 7 10. A 98 L tank is filled with pure water. Water which has a concentration of 4g of salt per litre flows into the tank at a rate of 7 L/min, and the mixture is stirred to a uniform concentration Water also leaks from the tank at the same rate, 7 L/min. Let y(t) be the amount of salt (in grams) in the tank at time t. Find a differential equation describing the rate of change of salt in the tank dy=--y(t) dt 49 98 (b) dy = 4-y(t) (c) dy dt = 28-y(1) y = 2-y(t) (d) dt 7 98 98 dt 49 14 (e) -28- t dt 11. Which of the below integrals represents the area of the surface obtained by rotating the curve y e", 0

Explanation / Answer

As stated in the problem, tank contains pure water which means
y(0) = 0 kg.

Let y(t) = salt in gm in the tank at time t

Since the rate of solution entering the tank and leaving are the same,

volume of solution remains the same in the tank neglecting variation of density.

In a small time interval dt (minute), change in salt quantity in the tank,

dy(t) = (4) * 7 * dt - [y(t)/98) * 7 * ] dt

dy = 28 dt - [y(t)/14] dt

dy = dt [ 28 - y(t)/14 ]

dy/dt = 28 - y(t)/14