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This question challenges a students skills with integration and trigonometry a very common question on Core 4 papers that can leave students struggling. First we use our knowledge that cosecy=1/siny and m...

First we need to find the intersection point(s) of L and C so set 6x-x²=16-2x and rearrange to get x²-8x+16=0 so (x-4)²=0.Repeated root so line is tangent to the curve at ...

In these types of question, you need to find out how the integer relates to the new integer - it will be by integrals. We can see that 9 is just 3 x 3 which is 3^2. Thus we now have 3^2(3x +1). As we know...

Firstly draw a diagram of the problem.Then resolve the forces into their components parallel and perpendicular to the plane.Resolving parallel: P + Fmax = 3gsin(60) equation 1.Resolving perpendicular: R =...

In order to solve this problem we will have to use the product rule as follows: d/dx[x^3⋅cos(5⋅x)]=[d/dx(x^3)]⋅cos(5x)+(x^3)⋅[d/dx[cos(5x)]]=(3⋅x^2)⋅cos(5⋅x)+(x^3)⋅−5⋅sin(5⋅x)=3⋅x^2⋅cos(5⋅x)−5⋅x...