Answer:
The standard form of the equation for the conic section represented by is:
Step-by-step explanation:
We know that:
is the standard equation for an up-down facing Parabola with vertex at (h, k), and focal length |p|.
Given the equation
Rewriting the equation in the standard form
Thus,
The vertex (h, k) = (-5, 12)
Please also check the attached graph.
Therefore, the standard form of the equation for the conic section represented by is:
where
vertex (h, k) = (-5, 12)
The manager already hired 9 people. Let be the number of people he still can hire. Since these people will add to the 9 he already hired, when the hiring campaign will be over he will have hired
people. We know that he can't hire more than 14 people, so the number of people hired must be less than or equal to 14:
If we subtract 9 from both sides, we have
so, the manager can hire at most 5 other people
Let S(t) denote the amount of sugar in the tank at time t. Sugar flows in at a rate of
(0.04 kg/L) * (2 L/min) = 0.08 kg/min = 8/100 kg/min
and flows out at a rate of
(S(t)/1600 kg/L) * (2 L/min) = S(t)/800 kg/min
Then the net flow rate is governed by the differential equation
Solve for S(t):
The left side is the derivative of a product:
Integrate both sides:
There's no sugar in the water at the start, so (a) S(0) = 0, which gives
and so (b) the amount of sugar in the tank at time t is
As , the exponential term vanishes and (c) the tank will eventually contain 64 kg of sugar.