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Prove that √2 is irrational

Prove by contradiction: Assume negation to be true i.e. √2 is rational Then √2 can be written in the form a/b where a and b are integers with no common factor (the fraction cannot be simplified) => a/b = ...
PM
Answered by Paul M. • Maths tutor
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For y = 7x - x^3, find the two stationary points and what type of stationary points they are.

Differentiate y to get: dy/dx = 7-3x^2 , dy/dx = 0 , therefore x=(+/-)sqrt(7/3) d^2y/dx^2 = 6x , substitute x values in to y=7x-x^3 and d^2y/dx^2 to find coordinates and the type of the stationary point.
RS
Answered by Robbie S. • Maths tutor
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expand and simplify (x+3)(x-7)

(x+3)(x-7) = (x x) + (x -7) + (x 3) + (3 -7) = x^2 - 7x + 3x - 21 = x^2 - 4x - 21 Key here is to ensure you multiply each term in one bracket by both in the other, and to keep careful track of the signs.
LP
Answered by Luke P. • Maths tutor
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Find the x co-ordinates of the stationary points of the graph with equation y = cos(x)7e^(x). Give your answer in the form x = a +/- bn where a/b are numbers to be found, and n is the set of integers.

The stationary points on a curve of the form y=f(x) are where dy/dx = 0. To find dy/dx, differentiate using the product rule: dy/dx = 7e^x(d/dx(cosx)) + cosx(d/dx(7e^x)) = -sinx(7e^x) + cosx(7e^x). Now set d...
JS
Answered by Joseph S. • Maths tutor
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How do I use Pythagoras' Theorem to calculate the hypotenuse of a triangle?

[use of board] So, Pythagoras' theorem states that a^2+b^2=c^2. Therefore, we need to mark the triangle with a, b &c. a and b do not matter, c must be the longest edge, that creates the diagonal. Put the...
CT
Answered by Cathy T. • Maths tutor
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