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We know to find roots of any quadratic equation we use the quadratic formula, [-b +- (b^2 - 4ac)^(1/2)]/2a where a=2, b=6, and c=7.

Plug these values in and we obtain, [-6 +- (-20)^(1/2)]/4. [Remem...

We first find the complementary function by guessing y=e^(kx). Substituting this into the equation d^2y/dx^2 + (3/2)dy/dx + y = 0. we find k^2 + (3/2)k + 1 = 0 which factorises into (k+2)(k+1/2). So our c...

tan^2(x)=1/(cos^2(x))-1 Left hand side of the equation (LHS)=tan^2(x) Use the identity tan(x)=sin(x)/cos(x) and substitute it into the LHS LHS=sin^2(x)/cos^2(x) Use the identity sin^2(x)+cos^2(x)=1 and re...

The first step is to write sinhx in its exponential form and set it equal to y, this will make rearranging easier. Then multiply everything by e^x and rearrange to form a quadratic, in terms of e^x. Expre...

The volume of revolution, V, is given as 2π∫ydx Substituting in the equation and limits gives as follows: V = 2π∫2e^2x dx between 0 and 1 Integrating this gives V = 2π[e^2x] between 0 and 1 Applying the ...