Start with the logistic equation 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 (similar to earlier example with h replaced with hx).

a) construct the differential equation.
b) show that if km > h, then the equation is still logistic.
c) what happens when km < h?

a)

b)

Let's say that

If we multiply the woule equation by k we got:

So then we satisfy that the equation is also logistic since the parameter

c) If we assume that then we have that

And then [tec] kx (a -x) <0[/tex] for any value of

And if that hhapens then the population will tend to 0 for any initial condition established/

Step-by-step explanation:

For this case we have the following logistic equation

Part a

We want to modify our harvesting for this case, so we harvest hx per unit of time for some

So then the model with harvesting who is proportional is given by:

And we can write like this:

Part b

For this case we assume that and we need to show that the equation is still logistic. So we need that the sollowing quantity higher than 0

Let's say that

If we multiply the woule equation by k we got:

So then we satisfy that the equation is also logistic since the parameter

Part c

If we assume that then we have that

And then [tec] kx (a -x) <0[/tex] for any value of

And if that hhapens then the population will tend to 0 for any initial condition established/

80π/3 or about 83.775

step-by-step explanation:

since a cone is 1/3 of a cylinder, we need to find the base's area. since area = πr^2, we get 16π. then, multiplying this by 5, we get 80π. dividing by 3, since the cone's volume is 1/3 of that of a cylinder's, we get 80π/3.

hope this !

there has been genes found in the x chromosome of males that have been linked to [homo/hetero]sexuality. in addition to the reign of the x chromosome, a section of chromosome 8 has also been link to, "alot of ppl are so " these facts were proven true after a 2014 study of a gay male and his strait brother. according to newscientist.com,"chromosome 14 and is mainly active in the thyroid, but also the brain. called tshr, it makes a type of receptor protein that recognises and binds to a hormone that stimulates the thyroid. in this way, the gene plays an important role in controlling thyroid function. the fact that tshr seems to be involved in sexual orientation fits with evidence that thyroid function seems to be linked to sexuality."

in conclusion, "ppl are so gay" due to their genetics.