Search over 10,000 free study notes

3/12, 2/8. To identify fractions which are equivalent to one another, you need to identify the common multiple of both the denominator and numerator and then simplify. When a fraction is equivalent to one...

first equation: 6a + b = 16     second equation: 5a - 2b = 19    from 2 times first equation + second equation 17a = 51 meaning a = 3

.... from the first equation 6(3) + b = 16 therefore b = - 2

putting in the conditions: 18000 = 2000e^3k ..  ln(9) = 3k .. k=(1/3)ln(9)

Rearrange the equation so that the x terms and y terms bracketed together, like so: (x^2 - 4x) + (y^2 + 10y) - 115 = 0. Complete the square on both sets of brackets, giving (x - 2)^2 - 4 + (y + 5)^2 - 25 ...

Divide 160 by 2 as many times as you can to get 80x2, 40x2x2, 20x2x2x2, 10x2x2x2x2, 5x2x2x2x2x2. Then re-write your answer so that it is 5x2^5. If you're struggling to divide by 2 and keep track of how ma...