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Polar coordinates are expressed in the form (r,θ), where r is the distance of the point, P, from the origin, and θ (usually expressed in radians) is the angle between the line joining the point to the ori...

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...

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 ...