Borbin the 🐱

Here is the third one:

Option c) leads to the solution. The expression
f(x) + f(y) + x²y + xy²
is part of the expansion of the binomial
(x+y)³
If f(x) corresponds to the first or last term of the binomial expansion, the equation can be solved.

Here is the second one:

Start by moving the x term to the right-hand side and setting x=0. This is the first equation for b.
Then with b in place, get the second equation. Isolate a and substitute 0 for x. This gets

I've been helping out with high school math lately, and some of the questions are quite interesting.
Check this one out:

The key is to derive two equations from the derivative. With a fourth-degree polynomial, we get three points where the slope is the same, but only two of them share a common tangent line.
After that, everything falls into place.

The custom airfilter box needed an update. Too much air flow caused a lean mixture.
The solution is an adjustable air flow.

The tubes were made out of stainless steel, grade 304.

Changed the filter from 6" length to 5" length (K&N Filter RD-0610) to cover for the air adjustment lever.

The current airfilter box of my motorcycle is undersized. Way too small and has the wrong connection tubes to the carbs which are not symmetrical. Note the diameter getting larger towards the carbs!
The restricted airflow makes it also very difficult to dial in the correct fuel-air-ratio.

To change this, I designed a new airfilter box that takes care of all the shortcomings:

Here are some pictures of the 'making of':