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We want to rearrange the expression to the form (1+y)^n so we can use the general result: (1+y)^n=1+ny+[n(n-1)/2]y^2+[n(n-1)(n-2)/3!]y^3+... 1/(2+5x)^3 = (2+5x)^-3 = [2(1+5x/2)]^-3 = (2^-3)(1+5x/2)^-3 usi...

Amount of paint needed:

White paint = (18 ÷ 5) × 3 = 10.8 litres

Blue paint = (18 ÷ 5) × 2 = 7.2 litres 

Cost of white paint = 10.8 x £2.80 = £30.24

Cost of blue paint = 7.2 x ...

25(5x-2)^4

Information from question

Initial population: 170

Increase: 3% (=x1.03)

Years: 5

Method

Formula: initial...

First of all differentiate the equation of the curve implicitly, giving:

3x²-8y(dy/dx)=12y+12x(dy/dx)

=> (dy/dx)(12x+8y)=3x²-12y

=> dy/dx=(3x²-1...