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Let n be an integer greater than 1. Prove that n^2 - 2 - (n-2)^2 is an even number.

To show a number N is even, we must be able to express it in the form N = 2x for some other whole number x. Let's try to manipulate the given expression to see if we can put it in this form. By expanding ...

SL
Answered by Sam L. Maths tutor
17659 Views

The equation of line A is y = 6x -4. The equation of line B is 2y - 12x + 14 = 0. Are these two lines parallel?

Line A has a gradient of 6, because it is in the form y = mx + c, where m=6.
Line B can be rearranged to y= 6x - 7, so the gradient is also 6.
The gradient of both lines is the same, so they are...

ML
Answered by Matthew L. Maths tutor
3381 Views

Find, using calculus, the x coordinate of the turning point of the curve with equation y=e^3x cos 4

1st step: find the derivative dy/dx of the given equation2nd step: now equate the obtained derivative to 0 because this is precisely the situation in which the graph changes direction (the derivative dy/d...

UW
Answered by Urszula W. Maths tutor
4201 Views

Express x^2 +10x -3 in the form (x + p)^2 + q


x2 +10x-3=(x+5)2-25-3= (x+5)2 -28

CT
Answered by Carmen T. Maths tutor
6767 Views

3/5 of a number is 162. Work out the number.

If we call the unknown number 'x' we can put it in to an equation to work it out as we known 5/3 of the number is 162.5x/3 = 162then times each side of the equals symbol by 5 to get (3x/5) 5 = 162

LM
Answered by Lucy M. Maths tutor
13676 Views

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