What is — 2х + y = 0 — 7х + Зу = 2 added together? HELPPP
1 answer:
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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
Answer:
See attachment
Step-by-step explanation:
We want to graph on the interval -10 to 10.
Let be the parent absolute value function.
We can easily graph , if we use translation.
When the parent function is shifted downwards by 12 units, we obtain the graph of .
The parent function is a v-shaped graph with vertex at the origin.
We shift the parent function down so that its vertex is now at (0,-12) to get the graph of .
See attachment for the graph of on the specified interval.
