The answer is 3x-x :)
You just simplify the expression, (4x^2-x^2) - (x- (-2x))
Well right off the bat, I can see a good reason why it should boggle.
If (x+y)=6 and (x-y)=2, then (x+y)(x-y) would be 12. It can't be 20.
The first 4 lines on the paper are inconsistent, so the question in the 5th line can't be calculated.
Another possible source of uncertainty (for us, anyway) is the remarkable similarity between the way you write ' Y ' and the way you write ' 4 ' . For example, look at the ' Y⁴ ' (I think ...) in the last line.
The left sum would be f0+f1+f2+f3
The right sum would be f1+f2+f3+f4
The trapezoidal rule value is:
(f0+f1)/2 + (f1+f2)/2+(f2+f3)/2 +(f3+f4)/2
This would put the trapezoidal rule in the middle , which makes the answer:
Lower sum < Trapezoidal rule Value < Upper sum
Dan:12/16=3/4=75%
Josh:15/25=3/5=60%
Ryan:14/20=7/10=70%
Scott:10/15=2/3=67%
Answer:Dan
There are 2² butterflies.
Or simply 2²