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rscott400
11.12.2020 •
Mathematics
Samantha wants to treat her friends to a movie. Tickets cost $6 each and popcorn and drinks will cost $30. She can spend no more than $150 so how many friends can she take?
a) Write an inequality to represent the situation. Be sure to define your variable.
b) Solve the inequality to find the maximum number of friends she can take?
HELP ASAP
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Ответ:
Step-by-step explanation:
Given that a tank contains 350 liters of fluid in which 10 grams of salt is dissolved. Pure water is then pumped into the tank at a rate of 5 L/min
the well-mixed solution is pumped out at the same rate.
Let A(t) be the grams of salt at time t.
Then A(0) = 10 gm
Inflow of fluid = outflow of fluid = 5l/min
So volume of tank at time t = 350 litres
Rate of change of salt = A'(t) = incoming rate - outgoing rate
= 0-![A(t)/350](/tpl/images/0511/0396/972c1.png)
i.e.![\frac{dA}{dt} =\frac{-A}{350} \\ln A = -t/350 +C\\A = Pe^{\frac{-t}{350} }](/tpl/images/0511/0396/41e2b.png)
Use the fact that when t =0, A = 10
P = 10
So we get