Answer: D.
Step-by-step explanation:
For an absolute value function, the vertex of is defined as the point (-h, k) for the coordinate (x, y).
When x is equal to negative h, the value for x and value for h effectively cancel out, and only the positive k remains, hence the vertex being (-h, k).
The function given has a vertex at (2, 3). We know that the vertex of an absolute function is (-h, k), so h must equal -2 and k must equal 3.
The equation:
Answer:
Step-by-step explanation:
This is a differential equation problem most easily solved with an exponential decay equation of the form
. We know that the initial amount of salt in the tank is 28 pounds, so
C = 28. Now we just need to find k.
The concentration of salt changes as the pure water flows in and the salt water flows out. So the change in concentration, where y is the concentration of salt in the tank, is . Thus, the change in the concentration of salt is found in
inflow of salt - outflow of salt
Pure water, what is flowing into the tank, has no salt in it at all; and since we don't know how much salt is leaving (our unknown, basically), the outflow at 3 gal/min is 3 times the amount of salt leaving out of the 400 gallons of salt water at time t:
Therefore,
or just
and in terms of time,
Thus, our equation is
and filling in 16 for the number of minutes in t:
y = 24.834 pounds of salt