B. Abigail used less than Carly and the total was 109.
Circumference: 2πr C=18 so r= 18/2π= 9π
Arc length = rθ 6=(9π)θ θ=6/9π
Convert to degrees by multiplying by 180/π
6/9π x 180/π = 120 degrees
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:
![\dfrac{\mathrm d}{\mathrm dt}\left[e^{t/800}S(t)\right]=\dfrac8{100}e^{t/800}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dt%7D%5Cleft%5Be%5E%7Bt%2F800%7DS%28t%29%5Cright%5D%3D%5Cdfrac8%7B100%7De%5E%7Bt%2F800%7D)
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.
The relation t relates x to y. To determine if it is a function, see if one x value can give two different y values. Since each x value only has one y value, the relation is a function. To check if the inverse is a function, see if any one y value will give multiple x values. By inversing t, there are two values of x for the value of y = -4 (x = 4 and x = 6), so this is NOT a function.
Answer: Relation t is a function. The inverse of relation t is NOT a function.
