Math B)

you can use your hand, but i just memorized the circle when i learned it. you’ll see after a while that the sin, cos, and tan values only take on a set number of values. they just change signs and angles each quadrant

https://math.stackexchange.com/questions/2429089/cusp-vs-corner-or-both

dy/dx(4) = -2/sqrt(4) = -2/2 = -1

5*1 = 5

= (1/2)*(25x^2+16)^(-1/2)*(2)*(25x) = 25x/(sqrt(25x^2+16))

thanks! ik i havent really been helping out a lot recently so im sorry for that. i stopped taking math courses as part of my curriculum (im an engineer) and im really focused on research lately. hope the blog still helps ppl!

Perimeter = PQ + QR + PR = (3x+y) + (5y-x) + (5y-x) = (11y+x) cm

yep it’s correct! good job!

@sempre-felice Your process is right, but you messed up the integral a little bit. Yes, I would expand the integral and separate it out, but you don't need u substitution and (e^x)^2 = (e^x)(e^x) = e ^(x+x) = e^(2x) not e^(x^2) So integral (e^x + 1)^2 dx = integral (e^(2x) + 2e^(x) + 1) dx = integral (e^(2x))dx + integral (2e^(x))dx + integral 1 dx = (e^(2x)/2) + (2e^(x)) + x + C