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
4 1/5 - 2 9/10 = 4 2/10 - 2 9/10 = 3 12/12 - 2 9/10 = 1 3/10. Hope this helped
Answer:
3,4
Step-by-step explanation:
You just reflect
P(Reggae) = 1/4
P(Rock) = 1/4
Probability of one after the other is 1/4 × 1/4 = 1/16
Answer:
22
Step-by-step explanation:
11-(-8)-(-3)
19-(3)
19+3
22
hope i helped:)
