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Answer:
50
Step-by-step explanation:
Its initial size was 50, because that is the y-intercept. From 50, it increases, so it can't be anything above 50.
13, start with 24, right? 24 plus 6 is 30. 30 minus 12 is 18. 18 minus 5 is 13.
Answer:
6 =k
Step-by-step explanation:
Given the equation for inverse variation
xy = k
We know x=-3 and y = -2
Substituting these values in
(-3) (-2) = k
6 =k
Let y(t) represent the level of water in inches at time t in hours. Then we are given ...
y'(t) = k√(y(t)) . . . . for some proportionality constant k
y(0) = 30
y(1) = 29
We observe that a function of the form
y(t) = a(t - b)²
will have a derivative that is proportional to y:
y'(t) = 2a(t -b)
We can find the constants "a" and "b" from the given boundary conditions.
At t=0
30 = a(0 -b)²
a = 30/b²
At t=1
29 = a(1 - b)² . . . . . . . . . substitute for t
29 = 30(1 - b)²/b² . . . . . substitute for a
29/30 = (1/b -1)² . . . . . . divide by 30
1 -√(29/30) = 1/b . . . . . . square root, then add 1 (positive root yields extraneous solution)
b = 30 +√870 . . . . . . . . simplify
The value of b is the time it takes for the height of water in the tank to become 0. It is 30+√870 hours ≈ 59 hours 29 minutes 45 seconds
