Math Quiz 5

[Ether]

Originally Posted by Bryce Paputa

Nope, it was wrong. Correct area, a and b are
a=.285, b=3.34, area = 15.2

Nice job.

Want some reps? Please post your work and explain each step.

[Bryce Paputa]

Here's how I did it: https://docs.google.com/document/d/1...it?usp=sharing

[Ether]

Originally Posted by Bryce Paputa

Here's how I did it: https://docs.google.com/document/d/1...it?usp=sharing

Very interesting approach.

On page2 of the Google doc you say "Assume dR/dc=0, Solve for c"... But I don't see dR/dc anywhere, and I don't see you setting dR/dc=0 and solving analytically for c.

It looks like you gave a(c), b(c), and R(c) to desmos, and let it figure out dR/dc (numerically?) and find the zero crossing to get the desired value of c. Yes? I'm not familiar with the desmos calculator so I'm guessing.

If you would add just a bit more explanation to the Google doc for the benefit of future readers that would be most helpful.

[Bryce Paputa]

Originally Posted by Ether

Very interesting approach.

On page2 of the Google doc you say "Assume dR/dc=0, Solve for c"... But I don't see dR/dc anywhere, and I don't see you setting dR/dc=0 and solving analytically for c.

It looks like you gave a(c), b(c), and R(c) to desmos, and let it figure out dR/dc (numerically?) and find the zero crossing to get the desired value of c. Yes? I'm not familiar with the desmos calculator so I'm guessing.

If you would add just a bit more explanation to the Google doc for the benefit of future readers that would be most helpful.

That's correct, I did it numerically with the calculator. The Google doc now clarifies this. I'll look into an analytic solution.

[Ether]

Originally Posted by Bryce Paputa

I'll look into an analytic solution.

It may not exist. My CAS choked on it.

[Ether]

Originally Posted by Ether

It may not exist. My CAS choked on it.

Using your R(c) method, a numerical root finder quickly converges to a precise value for c.

But you can get the same result without differentiating R(c), by simply plotting R(c) and locating the extremum.

[Bryce Paputa]

I get 3 arcsinh(2 sqrt(c)) * sqrt(4c^2+c) = 2c+8c^2. I doubt there is a nice closed form of this.

[Ether]

For completeness, here's how to solve the problem using constrained nonlinear optimization.

It's a bit easier to set up. All you need is the length and area as a function of a and b.

The area is the objective (to be maximized), and the length is a constraint on the values of a and b.

[Ether]

Extra credit:

What is wrong with this method?

[Ether]

Originally Posted by Ether

Extra credit:

What is wrong with this method?

It gives the correct answer... but what are the pros and cons compared to this method?

[Ether]

Originally Posted by Ether

It gives the correct answer... but what are the pros and cons compared to this method?

Any college students out there taking a course in numerical methods?

[Ether]

Originally Posted by Ether

Any college students out there taking a course in numerical methods?

... or multivariate calculus?