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Say I have a fraction with 2 surds, such as √10 / √6. To rationalise this, we need to get the dominator (bottom fraction) to be an integer. As √10 / √6 x 1 still gives √10 / √6, and we can write 1 as √6 /...

Ian had a 5% rise, so £420 = 105% of his original pay 

To find 1% of his original earnings, divide £420 by 105.

Multiply this by 100 to find his old pay: 
1% of his original earnings =...

5sin(x)-3cos(x)=2

Express in the form Rsin(x-@) = Rsin(x)cos@ - Rcos(x)sin@

Rcos@ =5

Rsin@ = 3    

tan@ = 3/5           @=tan^-1(3/5)= 0.540

R = sqrt(5^{2 <...}

Tackle this problem one part at a time: First differentiate 2x²y using the product rule, showing dy/dx(2x²y) = 4xy + 2x²(dy/dx). After this, the remainder of the question ...