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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 = 2cosh 2 x - 1. Upon substitution and simplification we get 6cosh 2 x - 29cosh x + 35...
JC
Answered by Jacob C. • Maths tutor
5543 Views

How do you rationalise surds?

Irrational surds occur when a fraction's denominator is a surd, leaving the fraction in a messy way. To rationalise surds, the general rule is that you multiply the both the denominator and the numerator of ...
BM
Answered by Baraka M. • Maths tutor
3781 Views

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 th...
LA
Answered by Luke A. • Maths tutor
5500 Views

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 the v...
TS
Answered by Thomas S. • Maths tutor
3552 Views

Solve algebraically the simultaneous equations: x^2 + y^2 = 25 and y - 3x = 13

Firstly, we need to use one equation to find an expression for one variable in terms of the other. Then we can substitute this expression into the other equation and solve for that variable. Using this numer...
GW
Answered by Gregor W. • Maths tutor
3925 Views