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."