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Solve x^2=3(x-1)^2

To start with, we want to put this into quadratic form, where we have ax^2+bx+c=0. We notice that there are terms on both sides of the equation. So we can expand the right hand side and then bring all th...

Answered by Joshua U. • Maths tutor

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Solve 29cosh x – 3cosh 2x = 38 for x, giving answers in terms of natural logarithms

Firstly, we need the equation to be in terms of one cosh argument if possible, which can be done by the identity cosh 2x = 2cosh²x - 1. Upon substitution and simplification we get 6cosh²

Answered by Jacob C. • Maths tutor

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Find the gradient of the tangent to the curve y=4x^2 - 7x at x = 2

First, we differentiate our equation using the power rule:dy/dx = 8x - 7This is the gradient of our tangent, to the original equation, at any point x. So, to calculate the gradient at x = 2, we substitute...

Answered by Luke A. • Maths tutor

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a typical question would be a setof parametric equations y(t) and x(t), asking you to find dy/dx and then the tangent/normal to the curve at a certain point (ie t = 2)

this question is a great example as we have many different aspects of a level maths workng together into one.initialy you will use use chain rule to find dy/dx = dy/du * du/dx.then you will either keep th...

Answered by Thomas S. • Maths tutor

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