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Via inspection, one can factorise this via the difference of squares; since a^2-b^2 = (a+b)(a-b), therefore:100-x^2 = (10-x)(10+x)

SInce, for y = uv, dy/dx = uv' + vu', where u' = du/dx, therefore:dy/dx = (1sin(x)) + (xcos(x)) = sin(x) + xcos(x)

The first step whenever you are given an equation is to group like terms. By this I mean put all the terms with the same letter next to it together and, in this case, the numbers without a letter. For the...

First, let's see how the plot of the functions looks like (draw on whiteboard). Next, let's calculate where the functions intersect by setting x² = sqrt(x) and solving for x (manipulate by squa...

First we can plug in the values we already know into the equation
we would get:
V² = 12² + (2 x -3 x 18)
then we would seperate the two multiplications on the right ...