Answer:
5.243 is less than 5.4....
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:
x + y = 14
Step-by-step explanation:
Parallel lines have the same slope, so the line's slope will be -1.
Plug this slope and the given point into y = mx + b to find b:
y = mx + b
4 = -1(10) + b
4 = -10 + b
14 = b
Then, plug this and the slope into y = mx + b
y = -x + 14
Then, put this into standard form by moving the x to the other side:
x + y = 14 is the equation in standard form
First, we must know what the two variables in the equation y=mx+b really means.
The M represents slope while the B represents the Y-intercept.
With that out of the way, take a look at your top equation, y = 3/2x + ?. If you noticed the question mark is in the spot of the B (Y-intercept), we can simply find this by finding where on the graph does the line intercept the Y-axis.
Triangle B shows the Y-intercept to be -7, this means that the hypotenuse intercepts the Y-axis at (0 , -7).
If we were to find the (what I like to call) the interception point of triangle A's hypotenuse and the Y-axis, we find our missing variable.
Just looking at the graph, we can count and visually determine that the Y-intercept of the hypotenuse is (0 , 1).
Therefore, we can say: The equation of A's hypotenuse is:
y = 3/2x + 1
Hope I could help you out!
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