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To find the values for 45 degrees, we construct a right angled isosceles triangle, which has two sides of equal length. We can say that these sides are 1 unit long, and so we can figure out the value of t...

We know that the number of undecayed nuclei, N, is given by N=N₀e^{-lambda t}. From this, by setting N=N₀/2 we know at this point that t= T_0.5 (the half life) and ...

The number has been decreased by 26%, this means that the original number is 100-26=74% of the original value. 

Therefore 9 x 10^-7 = 0.74 x N, where N is the original number.

Henc...

To integrate the volume of revolution first imagine a thin disk around the x-axis which we want to know the volume of: Volume=area x height. The area of a circle is given by pi r^2 and in our case let us ...

Factorise the equation and then equate each set of brackets to 0 to obtain both possible solutions. 

By factorising: (x-6)(x-1)=0 

Therefore: x=6 or x=1