Search over 10,000 free study notes

Start by multiplying equation (2) by 4 so both equations contain 4 lots of x: 4x - 12y = 20 Then take away equation 1 from equation 2 to eliminate x -13y = 13 divide by 13 and then reverse the negative si...

To solve this you need to integrate by substitution. You can spot this because the differential of the bottom of the fraction is a multiple of the top part, showing this quickly; if u = x²  + 3...

The equation we use to integrate by parts is

y = uv - ∫ v(du/dx) dx + c

so we separate dy/dx into u=(3x-4) and dv/dx=(2x²+5)

however we still need to find du/dx an...

Water molecules are polar. This means that one end of the molecule is slightly negatively charged (the oxygen atom) and one end of the molecule is slightly positively charges (the hydrogen atoms). The sli...

The chracteristics of perfect competition are: many firms, freedom of entry and exit, all firms produce identical or homogenous products, all firms are price takers(have no influence over the price) and h...