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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

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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

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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

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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

12731 Views

Use logarithms to solve 9^x=15

According to the rules of logarithms, when you take a log of something to the power of something, you multiply the log of the base by the power, so in this case, taking logs of both sides would give us...

Answered by Molly B. • Maths tutor

6711 Views