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The line L has equation y=5-2x. Find an equation of the line perpendicular to L, which passes through the point P (3,-1).

The gradient of the line L is -2 so the gradient of the line perpendicular to L will be the negative reciprocal of -2 which is 1/2.The equation of the line perpendicular to L will be y=mx+c where m is the gr...
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Answered by Katie N. • Maths tutor
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What is product rule differentiation?

Product rule differentiation, is a form of differentiation which is used to calculate the derivative, i.e. the gradient of the function, of a function f(x) which is made up of one function g(x) multiplied by...
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Answered by Thomas F. • Maths tutor
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What are differences between speed and velocity, velocity and speed and acceleration?

Firstly, it is important to know the difference between scalars and vectors. Scalars are just a number associated with a measured quantity, while vectors are a number AND a direction associated with a quanti...
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Answered by Felix P. • Maths tutor
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The curve C has equation 4x^2 – y^3 – 4xy + 2^y = 0 The point P with coordinates (–2, 4) lies on C . Find the exact value of dy/dx at the point P .

Since we need to find dy/dx, we must first differentiate the equation implicitly which gives us: 8x - 3y 2 dy/dx - 4y - 4xdy/dx + 2 y ln(2)dy/dx = 0. Because we are given a point, we can substitute in the x ...
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Answered by Samuel N. • Maths tutor
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At what point(s) do lines y = x^2 - 5x - 14 and y = 3x + 2 intersect? Write your answer in surd form

To find the point(s) where these two lines intersect we will first find the x coordinate of the point(s) where they intersect snd use this to find the corresponding y coordinate by substituting the x value i...
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Answered by Kieran J. • Maths tutor
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