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1 answer:
Answer:
F(x) < 0 , over the intervals (-∞, -0.7) and (0.76 , 2.5)
Step-by-step explanation:
The correct answer is the first option
F(x) < 0 , over the intervals (-∞, -0.7) and (0.76 , 2.5)
We can see that over those intervals, the function becomes negative.
That is, it becomes less than zero.
We can see the graph in the image below.
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Answer:
x(t) = 581.66 lb
Step-by-step explanation:
From the given information:
Consider the salt quantity in the tank at time t be x(t) lb.
∴ the rate of change of salt content in the tank is
where:
the rate of inflow = salt conc. × flow rate = 3 lb/gallon × 7 gallons
=21 lb/s
rate of outflow = salt conc. in the tank × flow rate
= x/250 × 9
= 9x/250 lb/s
∴
This is a 1st order linear differentiation,
The integrating factor if
∴
at t = (0) and x(0) = 100 lb
Hence;
∴
after time t = 1 minute i.e 60 s
x(t) = 581.66 lb