Alan

Four positive integers A, B, C and D have a sum of 36. If A + 2 = B - 2 = C*2 = D*2, what is the value of the product ABCD?

Unfortunately, some of their answers were wrong!  See https://web2.0calc.com/questions/help_74185#r2

See the following plot:

The first equation allows you to calculate $\theta$

Then you can calculate $\beta$ from the second equation

Then you can calculate $\alpha$ from the third equation

Then you can calculate $\sin \alpha$

Yes, it's right (though it's better to write pi, not pie!).

Use the fact that $cos(x)=2cos^2(x/2)-1$

Like so:

Here are some useful equations:

I'll let you fill in the numbers.

As follows:

"Find the minimum value of  2x^2 + 2xy + y^2 - 2x + 12y + 4  over all real numbers x and y."