Alarge mixing tank currently contains 350 gallons of water, into which 10 pounds of sugar have been mixed. a tap will open, pouring 20 gallons of water per minute into the tank at the same time sugar is poured into the tank at a rate of 3 pounds per minute. find the concentraion (pounds per gallon) of sugar in the tank after 15 minutes. is that a greater concentration than at the beginning?

Answer

Let t be number of minutes since tap is opened

water is increased by 20 gallons of water per minute.

sugar increase rate of 3 pounds per minute

water :- W(t) = 350 + 10 t

sugar :- S(t) = 10 + 3 t

concentration

C(t) =

at t = 15 minutes

C(15) =

C(15) =

C(15) = 0.11

at beginning t = 0 minutes

C(0) =

C(0) =

C(0) = 0.0286

C(15) > C(0)

hence, concentration is increasing as time is passing.

1)is not similar since corresponding sides are not in the same ratio

2)are similar since corresponding sides are in the same ratio and corresponding angles are equal

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