Differentiate:x^2 + y^2 = 4
You get this:2x + 2yy' = 0
bring the x variable on the other side:2yy' = -2x
Now divide 2y to leave y' by itself:y' = -2x/2y
Answer: y' = -x/y
The given relation is not a implicit solution to the given differential equation.
Answer:
watts
Step-by-step explanation:
I think your asking how much the school will have left over. If so:
125 ( not including the tickets)
It depends on how many kids are coming to the dance in order to fully solve this problem.
You didn't word this properly so that what I got with what I had:)
If you have anymore questions, ask me them on my profile so I'll be sure to get them:)
I hope this helps:)
Step-by-step explanation:
(a) dP/dt = kP (1 − P/L)
L is the carrying capacity (20 billion = 20,000 million).
Since P₀ is small compared to L, we can approximate the initial rate as:
(dP/dt)₀ ≈ kP₀
Using the maximum birth rate and death rate, the initial growth rate is 40 mil/year − 20 mil/year = 20 mil/year.
20 = k (6,100)
k = 1/305
dP/dt = 1/305 P (1 − (P/20,000))
(b) P(t) = 20,000 / (1 + Ce^(-t/305))
6,100 = 20,000 / (1 + C)
C = 2.279
P(t) = 20,000 / (1 + 2.279e^(-t/305))
P(10) = 20,000 / (1 + 2.279e^(-10/305))
P(10) = 6240 million
P(10) = 6.24 billion
This is less than the actual population of 6.9 billion.
(c) P(100) = 20,000 / (1 + 2.279e^(-100/305))
P(100) = 7570 million = 7.57 billion
P(600) = 20,000 / (1 + 2.279e^(-600/305))
P(600) = 15170 million = 15.17 billion
