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Find the equation of the normal to the curve y=2x^3 at the point on the curve where x=2. Write in the form of ax+by=c.

For x = 2, y = 16. Calculate the gradient of the curve at y = 2, dy/dx = 6x^2, dy/dx = 24. This is also the gradient of the tangent to the curve at x = 2. It is a rule that the products of the gradients o...

Answered by Maddy L. • Maths tutor

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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 m...

Answered by Oliver L. • Maths tutor

11982 Views

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-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 ...

Answered by David M. • Maths tutor

3366 Views

find the coordinates of the single stationary point of the curve with equation y=8x^2 + 2/x

rewrite the equation in a more helpful way:y=8x² + 2x^-1 differentiate:dy/dx = 16x -2x^-2set equal to 0 and solve for x16x -2x^-2= 016x -2/ x²=016x= 2/...

Answered by Pavan R. • Maths tutor

8969 Views

There are 720 boys and 700 girls in a school. The probability that a boy chosen at random studies French is 2/3 The probability that a girl chosen at random studies French is 3/5 . Work out the number of students in the school who study French.

To find out how many students take French, start by finding out how many boys take it, and then how many girls, and the sum of these will be the total number of students taking French.There are 720 boys, ...

Answered by Isabelle S. • Maths tutor

6895 Views