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**sirsosay**- Replies: 4

There is a competition where you have to "guess" how many gumballs are in the gumball machine.

There gumball machine is spherical so I want to calculate a thoretical amount of gumballs inside.

I wan to keep away from subtracting volume from volume and figure out a more precise calculation that takes into account wasted space.

If someone could help me figure this out that would be great. Thanks

**sirsosay**- Replies: 0

I missed the second half of my lecture due to an interview so it isn't that I'm not trying but that I don't have the notes and this math textbook only had 2 examples

First Problem:

Suppose a population is growing according to the logistic equation,

dP/dt = rP(1-P/K)

Prove that the rate at which the population is increasing is at its greatest when the population is at one-half of its carrying capacity. Hint: Consider the second derivative of P.

Second Problem:

Consider a lake that is stocked with walleye pike and that the population of pike is governed by the logistic equation

P' = 0.1P(1-P/10)

where time is measured in days and P in thousands of fish. Suppose that fishing is started in this lake and that 100 fish are removed each day.

(a) Modify the logistic model to account for the fishing

(b) Find and classify the equilibrium points for you model.

(c) Use quantitative analysis to completely discuss the fate of the fish population with this model. In particular, if the initial fish population is 1000, what happens to the fish as time passes? What will happen to an initial population having 2000 fish?

***Any Help Is Greatly Appreciated

***I'll do my part and help others as well

Last equation was the derivative after being simplified.

The derivative of...

would use the product rule.

f'g+g'f

+ J*(-1/(x+1)^2)

I don't know how to use th math script..

(x^2+2x+2)/(x+1)^2

Wow thats really ingenious. Thats cool.

I'll show my teacher your method.

I think what he may have done is made a triangle by drawing a line from the origin to the point and making a right triangle.

What I'm most curious is if this congruency is true at all points.

**sirsosay**- Replies: 3

I don't know if there is a limit to the amount of questions you can ask here, but so far the help has been really great.

The sum of the squares of two positive numbers is 200. The minimum product of these two numbers is?

So I set up an equaiton...

a²+b²=200

So do I need to substitute one variable in for the other and solve the derivative of ab?

Thank you both for helping.

**sirsosay**- Replies: 15

A line passes through the point (1,2). What's the slope of the line passing through this point that would create a triangle of the least area. The x and y axis being the legs of a right triangle.

I went through what has to be done in my head but I don't know how to do it on paper.

I need to make a function that gives the area of the traingles based off m, find when the derivative equals 0 and find which gives a smaller output.

Thank you!

**sirsosay**- Replies: 4

xy=2 and x²-y²=3

I got y by itself then I got...

2/x = ±√(x²-3)

I'm stuck at 4 = x^4-3x²

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