Question Solved1 Answer Problem begins here: A tank with a capacity of 74 liters, initially contains 20 kilograms of salt dissolved in 50 liters of water. Another solution, containing 3 kilograms of dissolved salt per liter, runs into the tank at 4 liters every minute and that the mixture (kept uniform by stirring runs out of the tank at the rate of 1 liter per minute. What is the concentration of the solution in the tank at point of overflow? Intermediate values should be rounded only to two decimal places. Round off the final answer to two decimal places. Choose the correct answer from among the given choices.

GHPDCG The Asker · Calculus

Transcribed Image Text: Problem begins here: A tank with a capacity of 74 liters, initially contains 20 kilograms of salt dissolved in 50 liters of water. Another solution, containing 3 kilograms of dissolved salt per liter, runs into the tank at 4 liters every minute and that the mixture (kept uniform by stirring runs out of the tank at the rate of 1 liter per minute. What is the concentration of the solution in the tank at point of overflow? Intermediate values should be rounded only to two decimal places. Round off the final answer to two decimal places. Choose the correct answer from among the given choices.
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Transcribed Image Text: Problem begins here: A tank with a capacity of 74 liters, initially contains 20 kilograms of salt dissolved in 50 liters of water. Another solution, containing 3 kilograms of dissolved salt per liter, runs into the tank at 4 liters every minute and that the mixture (kept uniform by stirring runs out of the tank at the rate of 1 liter per minute. What is the concentration of the solution in the tank at point of overflow? Intermediate values should be rounded only to two decimal places. Round off the final answer to two decimal places. Choose the correct answer from among the given choices.
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let y(t) be the amount of Salt af ary tinie t:.(dy)/(dt)= (rete of Sat flowing into tenk) -(vete of Salt out of tank)(dy^('))/(dt)=(3(kg)//urxx4inim//wi^('))-((y)/(v(t))*1" wirf/in ")Hene V(t)= ehaying velune of Solution{:[v(t)=50+(4-1)t],[v(t)=" So "+3t quad A+0" verflow "quad" So "+3t=74],[3t=74-50],[" overflow at "t=8" min "]:}:.(dy)/(dt)=12-(y)/((50+3t))ov (dy)/(dt)+(y)/(50+3t)=12 rarr1 let mu(t)=e^(int(1)/((50+3t))dt)Mutiply eqn (c) on b/s by mu(t){:[root(3)(50+3t)(dy)/(dt)+(y(t))/(sqrt(3t+50)(50+3t))=12root(3)(50+3t)],[root(3)(50+3t)(dy)/(dt)+(y(t))/((50+3t)^(2//3))=12^(3)sqrt(50+3t)]:}Apply reverse product nuee f(dg)/(dt)+g(df)/(dt)=(d)/(dt)fga ... See the full answer