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Given that y=π/6 at x=0 solve the differential equation,dy/dx=(e^x)cosec2ycosecy

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 mult...
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Answered by Oliver L. • Maths tutor
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Find the area enclosed between C, the curve y=6x-x^2, L, the line y=16-2x and the y axis.

First we need to find the intersection point(s) of L and C so set 6x-x 2 =16-2x and rearrange to get x 2 -8x+16=0 so (x-4) 2 =0.Repeated root so line is tangent to the curve at x=4, y=16-2(4)=8 that is the p...
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Answered by David M. • Maths tutor
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Express 9^3x + 1 in the form3^y ?

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 fr...
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Answered by Polly M. • Maths tutor
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A mass of 3kg rests on a rough plane inclined at 60 degrees to the horizontal. The coefficient of friction is 1/5. Find the force P acting parallel to the plane applied to the mass, in order to just prevent motion down the plane.

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 = 3g...
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Answered by Jonathan M. • Maths tutor
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Differentiate x^3⋅cos(5⋅x) with respect to x.

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(5 x)+(x^3)⋅[d/dx[cos(5 x)]]=(3⋅x^2)⋅cos(5⋅x)+(x^3)⋅−5⋅sin(5⋅x )=3⋅x^2⋅cos(5⋅x)−5⋅x^3⋅sin(5⋅x)
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Answered by Tianyu L. • Maths tutor
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