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A triangle number is a number such that it is the sum of n consecutive integers, starting from 0. Eg 1, 1+2, 1+2+3... are the first 3 triangle numbers. The formula for the nth triangle number is well-know...

We have that x² + y² + 6x - 2y - 10 = (x+3)² + (y-1)² - 20 = 0 (step was motivated by the equation of a general circle (x-a)² + (y-b)² = ...

First we need to find the cost of one arc from the information we already have about the arc (20 straight lines cost £12). To do this divide the £12 total cost by the number of lines 20.12 ÷ 20 = £0.60 ea...

(x+6)(x+5)=20. x² + 11x +30=20. x²+ 11x + 10 = 0. (x+10)(x+1)=0 . x=-1 and x=-10. width= -10+5=-5 (invalid solution). width =-1+5= 4. Checking through: (-1+6)*(-1+5)=20.

To find the equation of a line, we need; the gradient of that line and a point on that line. To find the gradient of a line, we require two points on the line which have been prov...