Search over 10,000 free study notes

DNA mutations happen randomly during division by mitosis. Some of these mutations code for antibiotic resistance. When a bacterial colony is exposed to antibiotics most bacteria without the resistance mut...

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...