Alan

If only it were that simple; unfortunately a^x - b^x doesn't equal (a-b)^x in general!

4.466^x - 2*2.331^x + 1 = 0 has one immediately obvious solution; namely x = 0, because:

4.466⁰ - 2*2.331⁰ + 1 = 1 - 2*1 + 1 = 0.

I can't see any way of getting another (real number) solution except by a numerical method.  A straightforward, though rather inefficient way is just to rearrange the equation as shown below, guess an initial value and then iterate until the iterates converge.  It takes about 100 iterations to get 5 decimal places!

There are an infinite number of common multiples of any three numbers.  However, the simplest to find is often obtained just by multiplying the three together.  In this case that would be 20*22*23 = 10120.

Sometimes it is more convenient to work with the least (or lowest) common multiple.  This can be obtained by finding the prime factors of each number and multiplying together the highest power of each that occurs in any of them.  Here we have 20 = 2²*5, 22 = 2*11, 23 = 23, so the least common denominator is 2²*5*11*23 = 5060.

Chris beat me to it!

At the risk of confusing you still further, I've written a more detailed explanation of 3-d vectors below:

There is no direct, one-step function as far as I can tell.  However, you can use the abs() and atan() functions.

x + iy = abs(x+iy)*e^i*atan(y/x) 

What is it that you want to know about this expression? 

Volume of a cylinder is given by pi*radius²*height.  You can use the calculator on the Home page here to plug in the numbers.

(3^2)^2 = 9^2 = 81

or (3^2)^2 = 3^4 = 81

Yes, though you can take it a little further to get:  4x^2(4x+1)(4x-1)

So the factors are: 4, x^2, 4x+1 and 4x-1 (and various combinations of these).

In the second quadrant cosine is also negative so cos σ = -7/√(4² + 7²) = -7/√65

This is in the second quadrant where tan is negative, so tanx = -2/√(5²-2²) = -2/√21