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Solve the simultaneous equations y = x + 3, y^2 - x^2 + 3 = -6x

Here, we have two equations involving two variables, x and y.

The question asks us to 'solve' the set of simultaneous equations.

Equivalently, it is asking us to

Answered by Anthony H. • Maths tutor

8608 Views

Given that 5cos^2(x) - cos(x) = sin^2(x), find the possible values of cos(x) using a suitable quadratic equation.

First, need to get all the terms in the equation to be the same. Using the following identity, it is possible to achieve this:

sin²(x) + cos²(x) = 1

1 ...

Answered by Andrew B. • Maths tutor

7542 Views

Line AB has the equation 3x + 5y = 7. Find the gradient of Line AB.

Rearrange equation into the form: y = mx + c

m = gradient

3x + 5y = 7

5y = -3x + 7

y = (-3/5)x + (7/5)

gradient = (-3/5)

Answered by Aaquib N. • Maths tutor

12184 Views

Find the equation of the tangent to the curve y = 2 ln(2e - x) at the point on the curve where x = e.

The first step is to find the y coordinate at the point on the curve where x = e. To do this we subsitute x = e into the equation of the curve, so y = 2ln(2e - x) becomes y = 2ln(2e - e). Simplifying t...

Answered by Rhiannon T. • Maths tutor

9522 Views

Solve x^2 - 6x - 2=0 giving your answer in simplified surd form.

SInce the question requires simplified surd form, it makes sense to use the quadratic formula immediately for this question.

This would give us

x = 6 [+-] squareroot(36-(4x1...

Answered by Molly B. • Maths tutor

12138 Views

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