A function includes ordered pairs (−2, 3), (0, −1), (1, 0), (3, 8), and (5, 24). Which point could not be the part of this funct
1 answer:
A relation or an ordered pair may or may not be a function.
An ordered pair will only be a function when the x and y values are unique
<em>The options are not given, so I will provide a general explanation</em>
For an ordered pair to be a function, all the y values must point to different x values.
Take for instance, the given ordered pair
The above represents a function, because the y-values have different x-values
However, the following ordered pair is not a function
The reason is that:
y-values 9 and 8 have the same x-value (3)
Read more about ordered pairs and functions at:
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1. dy/dt is the net rate of change of salt in the tank over time. As such, it's equal to the difference in the rates at which salt enters and leaves the tank.
The inflow rate is
(0.4 kg/L) (6 L/min) = 2.4 kg/min
and the outflow rate is
(concentration of salt at time t) (4 L/min)
The concentration of salt is the amount of salt (in kg) per unit volume (in L). At any time t > 0, the volume of solution in the tank is
100 L + (6 L/min - 4 L/min) t = 100 L + (2 L/min) t
That is, the tank starts with 100 L of pure water, and every minute 6 L of solution flows in and 4 L is drained, so there's a net inflow of 2 L of solution per minute. The amount of salt at time t is simply y(t). So, the outflow rate is
(y(t)/(100 + 2t) kg/L) (4 L/min) = 2 y(t) / (50 + t) kg/min
and the differential equation for this situation is
There's no salt in the tank at the start, so y(0) = 0.
2. Solve the ODE. It's linear, so you can use the integrating factor method.
The integrating factor is
Multiply both sides of the ODE by µ :
The left side is the derivative of a product:
Integrate both sides with respect to t :
Use the initial condition to solve for C :
Then the amount of salt in the tank at time t is given by the function
so that after t = 50 min, the tank contains
kg of salt.