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I. 3x + 5y = 19 II. 8x - 2y = -18 . We see that we can simplify the second equation, and we do so: II. x - y = -9. Now, we check to see which variable i...

Recall that all straight lines have the general equation y = mx + c, where m is the gradient of the line and c is the y intercept. First work out the gradient, m, of the line: Gradient = rise/run = (chang...

Firstly, recognise the relevant equations. The two functions are y = mx and y = ln(x). As the straight line is a tangent, we know that at a certain point x₀, the functions and ...

No, and we may take a counterexample to see why. If y=x^5+5/3x^4, dy/dx=5x^4+20/3x^3, d2y/dx2=20x^3+20x*2=20x^2(x+1). Setting this to 0 will give us the candidates for a POI, but not all these numbers wil...

This is a compound interest problem. Here we have to put 18 months in terms of years. There are 12 months in a year, so 18 months is a year and 6 months.
6 months is half a year, so 18 months repres...