Recent content by pjallen58

I am trying to figure out how to prove the 2:1 ratio of a triangle's medians at the centroid using vectors. Example if I had a triangle ABC with midpoints D of BC, E of AC and F of AB. I know G is where the medians intersect. I have seen many proofs and understand the process that proves the...

I am trying to shorten and generalize the the definition of a vector space to redefine it in such a way that only four axioms are required. The axioms must hold for all vectors u, v and w are in V and all scalars c and d. I believe the four would be: 1. u + v is in V, 2. u + 0 = u 3. u...

I am working on a population model using US population data. I have done a scatter plot, linear regression and now need to complete. This is what I have: y = .0287 - .0000917x (1/P) (dP/dt) = b + aP I have set this up to integrate and by keeping the variables a and b in the equation...

Just a little more help would be appreciated. Thanks.

I thought that didn't look right. Here is what I get: (1/P(.0287-.0000917P)dp = dt Integrate using partial fractions 1/.0287 ln|P/.0287-.0000917P| + C = t + C ln|P/.0287-.0000917P| = .0287t + C If t = 0, P = 3.9 so C = ln 137.6 Now I think I should take the exponential of each...

Any suggestions or advice would be appreciated. Thanks.

Use P0 = 3.9 (1790 population) as your initial condition to find the particular solution for this differential equation. Note: You may find it easier to solve in terms of the constants a and b. Show all the steps in your solution. This is the last step to a multi-part problem. I basically did...

Here is what I calculated: Use P0 = 3.9 as your initial condition to find the particular solution for this differential equation. (1/P)(dP/dt) = b + at y = -.0001t + .0338 dP/P = (.0338 - .0001t)dt ln P = .0338t - (.0001t^2/2) + C At t = 0, P0 = 3.9 so then C = ln 3.9 ln P =...

Thanks. After I sent the last reply it clicked that I understood what you ment by solve for P as the variable. Thanks again.

Thanks for the reply. I already have all the P's. If you could give a little more information to clear things up it would be appreciated. Thanks.

Use P0 = 3.9 (1790 population) as your initial condition to find the particular solution for this differential equation. Note: You may find it easier to solve in terms of the constants a and b. Show all the steps in your solution. This is the last step to a multi-part problem. I basically...

I think I understand the process shown for the above proof but if someone could provide the second part it would improve my understanding. Given that lim f(x)=L as x approaches a , prove that lim x*f(x)=aL as x approaches a using the delta epsilon definition of a limit. This would be much...