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A curve is described by the equation x^3 - 4y^2 = 12xy. a) Find the points on the curve where x = -8. b) Find the gradient at these points.

a) The first part of this question is asking us to find points, (x,y), such that x = -8. By taking the equation and substituting in x = -8, we should find values, y, such that the points given are (-8,y). (-...
BC
Answered by Ben C. • Maths tutor
16794 Views

How do you solve the following simultaneous equation?

2x - 6y = 18 4x + 3y = 6 First, make either the x or y the same value by multiplying the equations. Let's choose x. 2x - 6y = 18 x2 4x + 3y = 6 x1 (+)4x - 12y = 36 (+)4x + 3y = 6 Now, we use the rule of 'sam...
JE
Answered by Jason E. • Maths tutor
6342 Views

How do I find the nth term of a sequence?

For any sequence where there is a common difference (it increases or decreases with the same amount, n, each time) you can find the nth term using the formula: dn+(a-d) "a" is the value of the firs...
LM
Answered by Laura M. • Maths tutor
32285 Views

What is integration by parts, and how is it useful?

"Integration by parts" is one of several methods in our arsenal that we can use to integrate a function f ( x ). It involves expressing f ( x ) as the product of two other functions, which I will c...
AJ
Answered by Alexander J. • Maths tutor
3751 Views

What are the roots of 3x^2 + 13x + 4 ?

To find the roots, we solve the equation 3 x 2 + 13x + 4 = 0. We could try factorising the equation, which gives us (3x + 1)(x + 4) = 0 So the roots are x = -1/3 and x = -4. Alternatively, we could use the q...
NB
Answered by Nicholas B. • Maths tutor
11350 Views