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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 find the x values (and corresponding y values...
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Answered by Anthony H. • Maths tutor
10342 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: sin 2 (x) + cos 2 (x) = 1 1 - cos 2 (x) = sin 2 (x) Substituting this into the e...
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Answered by Andrew B. • Maths tutor
9136 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)
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Answered by Aaquib N. • Maths tutor
13470 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 this, w...
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Answered by Rhiannon T. • Maths tutor
11159 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-(4x1x-2)) / 2 which simplifies to x= 6...
MB
Answered by Molly B. • Maths tutor
14046 Views