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In order to integrate (cosx)^3, there is no given rule (by-parts, 'try' method, chain rule) which we can follow. We would need to split it into (cosx)^2 and cosx. Then use the identity: (sinx)^2 + (cosx)^...

We can think of any solution of this equation as a string of twelve 1's and two 0's. For example, one such solution could be a=6, b=2 and c=4. In this case we would write the solution as 11111101101111. W...

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 ...