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How do I show two vectors are perpendicular?

Vectors can describe a line of particular length ("magnitude") and direction. The angle x between two vectors a and b can be found using the formula a.b = | a | | b | cosx. For the vectors to be pe...
SA
Answered by Sarah A. • Maths tutor
132675 Views

Differentiate 2x^3 - xy^2 - 4

Differentiate the first term 2x3 as normal by multiplying the coefficient of x by the power and subtracting the power by 1 to get 6x 2 . For the next term you have to use the product rule as you have two var...
EV
Answered by Elena V. • Maths tutor
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Express 4x/(x^2-9)-2/(x+3) as a single fraction in its simplest form

4x/(x 2 -9)-2/(x+3) = 4x/((x+3)(x-3))-2/(x+3) = 4x/((x+3)(x-3))-2(x-3)/((x+3)(x-3)) = (4x-2(x-3))/((x+3)(x-3)) = (2x+6)/((x+3)(x-3) = (2(x+3))/((x+3)(x-3)) = 2/(x-3)
CS
Answered by Charles S. • Maths tutor
9168 Views

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 of t...
ML
Answered by Maddy L. • Maths tutor
10219 Views

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...
OL
Answered by Oliver L. • Maths tutor
13735 Views