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First, recall that the formula for finding such a volume is pi times the integral from 0 to pi/2 of y^2 with respect to x. This leads to pi times the integral from 0 to pi/2 of 4sin^2(2x) + 4sin(2x) + 1 (...

First rewrite right hand side in terms of sinθ and cosθ, because those are the terms we'll be dealing with on the left hand side: sec2θ+tan2θ = 1/cos2θ + sin2θ/cos2θ, so RHS = (1+sin2θ)/cos2θNow look at t...

x = −b ± √(b² − 4ac) / 2a
x = −20 ± √(20² − 4(3)(-500)) / 2(3)
x = (3x + 50) (x - 10)

First of all, you want to try and get rid of the brackets so the equation is easier to simplify in the next steps. So you multiply the whole bracket by 3. So it is 3x-6 = x+7. Secondly, in order to solve ...