(d) Suppose two students are memorizing a list according to the same model dL dt = 0.5(1 − L) where L represents the fraction of
the list that is memorized at any time t. According to the uniqueness theorem, will the student who starts out knowing none of the list ever catch up to the student who knows one-third of the list? Explain.
1 answer:
You might be interested in
Answer:
a) 42.08 ft/sec
b) 3366.33 ft³/sec
c) 0.235
d) 18.225 ft
e) 3.80 ft
Explanation:
Given:
b = 80ft
y1 = 1 ft
y2 = 10ft
a) Let's take the formula:
1 + 8f² = (20+1)²
= 8f² = 440
f² = 55
f = 7.416
For velocity of the faster moving flow, we have :
V1 = 42.08 ft/sec
b) the flow rate will be calculated as
Q = VA
VA = V1 * b *y1
= 42.08 * 80 * 1
= 3366.66 ft³/sec
c) The Froude number of the sub-critical flow.
V2.A2 = 3366.66
Where A2 = 80ft * 10ft
Solving for V2, we have:
= 4.208 ft/sec
Froude number, F2 =
F2 = 0.235
d)
= 18.225ft
e) for critical depth, we use :
= 3.80 ft