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This curve is a quadratic due to the highest power in the equation being two. Quadratics typically have the shape of a U. Due to the coefficient of the x^2 term being positive, the curve is increasing for...

Equation 1: x-2y=3Equation 2: x²+2y²=27The easiest way to do this is to put one of these equations into the other, by rearranging for either x or y. Because there are no squares to d...

A matrix is a representation of a linear map with respect to any basis of vectors of our choice. We often deal with matrices with respect to the standard cartesian basis, (1,0,0) (0,1,0) (0,0,1), but we c...

The first step is to rearrange for x: we have x=2y-3now we can plug this into the equation of the ellipse: y^2+2(2y-3)^2=39y^2-24y+15 = 0we can use the quadratic formula to solve this equation:y = (24+-sq...

Firstly, by looking at the integral, we see that this will have to be done by parts. There are 2 parts of this expression, the 'x' and the 'e^x'. As we know the formula f...