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There are three methods to solve these types of silmultaneous equation questions, substitutution, elimination and matrices. In this example we use substitution and elimination.Elimination example.Eq1). 7x...

Start by using the formula d = sqrt((x₂-x₁)²+(y₂-y₁)²)Therefore, substituting in our coordinates from P and Q:Length PQ = sqrt((-8-4)^...

2cot2x= 2(1/tan2x)= 2(1/(2tanx/1-tan²x))=2(1-tan²x)/2tanx= (1-tan²x)/tanx(1-tan²x)/tanx +tanx=(1-tan²x)/tanx +tan²x/tanx=1/tanx=cotx

f^-1(x)=(e^x-1)/3 g(x)=3/(3x+1)

The product rule is used to differentiate this since we are trying to differentiate the product of 2 parts--x and ln(x)So using the product rule which is d/dx=u.(dv/dx) +v.(du/dx)let u=x and v=ln(x)then d...