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Moving Ln to one side ln(2x^2 +9x-5) -  ln( x^2+2x-15) =1 Subtracting Ln is the same as dividing ln(((2x^2 +9x-5)/( x^2+2x-15)) ln((2x-1)/(x-3))=1 Taking e to both sides (2x-1)/(x-3)=e x=(1-3e)/(2-e)

Profit is (New price-Original price)/Original price . As a fraction it is percentage Profit/100. Equate (New price-Original price)/Old Profit to the fraction of Profit in %/100. Cross multiply and come up...

To find a) just plug in the number two to all places where n appears. In this case 8(2^2 + 2^(6 * 2 - 7))  and then number crunch. 8(4+2^5) -> 8 * (4 + 32) -> 8 * 36= 288.

To find part b, we ...

This one is quite complicated to answer typed up like this and i would definitley use a white board Show that 7x^2 - 21x can be come x(7x-21) which can in turn become 7x(x-3) Show that x^2 + 2x - 15 can b...

This is a typical C4 differential equation question. The same algorithm could be used for a lot of other problems.

First of all, from the hint we have that dH/dt = -kH (1).

We need to separa...