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First, we want to find the gradient of L1 using (4,6) and (12,2)m= (2-6)/ (12-4) = -1/2 then we can find the equation of L1 using y=mx+c rearrange for c as the subject, c= y-mx and substitute the gradient...

You need to work out how many animals there are in total first. Mary sells 8 of her sheep so 12-8 = 4 sheep In total she'll have 4+ 16 + 24 + 6 = 50 animals 4/50 = 0.08 0.08 x 100 = 8% - to get a percent...

For the first 24 games, heads = 24 x (2/3) = 16. For the next 6 games, heads = 6. Total number of heads = 22. 30 - 22 = 8 therefore tales = 8. Therefore, ratio = 22:8 = 11:4, heads:tales.

There are to parts involving x in this expression, so we need to use the product rule. Let u=x and v=sin2x.So we find u'=1, and v'=2sin2x. Then the formula for the product rule gives us that d/dx(uv)= uv'...

{} = integral sign for purpose of this solutioncos²x = 1 - sin²x (1)cos 2x = cos²x - sin²x (2)cos²x = 1 - (cos²x - cos 2x)cos²x...