Answer:
A. No
Step-by-step explanation:
Answer:
a) dx/dt = kx*(M - h/k - x)
Step-by-step explanation:
Given:
- The harvest differential Equation is:
dx/dt = kx*(M-x)
Suppose that we modify our harvesting. That is we will only harvest an amount proportional to current population.In other words we harvest hx per unit of time for some h > 0
Find:
a) Construct the differential equation.
b) Show that if kM > h, then the equation is still logistic.
c) What happens when kM < h?
Solution:
- The logistic equation with harvesting that is proportional to population is:
dx/dt = kx*(M-x) hx
It can be simplified to:
dx/dt = kx*(M - h/k - x)
- If kM > h, then we can introduce M_n=M -h/k >0, so that:
dx/dt = kx*(M_n - x)
Hence, This equation is logistic because M_n >0
- If kM < h, then M_n <0. There are two critical points x= 0 and x = M_n < 0. Since, kx*(M_n - x) < 0 for all x<0 then the population will tend to zero for all initial conditions
Answer:
54
Step-by-step explanation:
216 - 3x = 324 -5x
subtract 216 from both sides
add 5x to both sides
divide both sides by 2x.
Answer:
The required volume, if he wants to fill 75% of the pot's volume, is 11664cm³
Step-by-step explanation:
The volume of a pyramid is given as
Where V is the pot's volume, A is the base area and h is the height.
Our base is a square, so the base area, if s denotes the side length, would be s x s.
s = 36cm, therefore we have A = 36cm X 36cm = 1296cm².
The height is given as 36cm, therefore we have our volume to be:
Since Luis wants to fill 75% of the pot's volume with soil. Then it will take
Thus, the required volume, if he wants to fill 75% of the pot's volume, is 11664cm³