Alan

There's a scientific calculator on the home page on this site.

I suspect someone is just trying to sell their xerox copying machine and looking to see if any interest is being shown in it!  (Alternatively, they are looking to buy one?!) 

It's easy enough to draw a graph with 4 straight lines, 2 of which are parallel to each other and the other two of which are perpendicular to the first two.  However, where does the "random" part come in and what's the significance of the "5"?

A tenth is 0.1, so divide 89.5 by 0.1.

 89.5/0.1  multiply top and bottom by 10 to get 895/1 or just 895.

If you take the first and the third equation you have 2 simultaneous equations in the 2 unknowns, Q and T2, so you could solve for them, then insert the values into the middle equation to get T3.  Perhaps that is what your lecturer wants you to do.

We could still interpret this as a question about the cross-product of 3-d vectors.  Each of u, v and w lie in the x-y plane, so the cross-product result would point in the z-direction.

You would expect to get 1/4 of the 20 and 1/5 of the 10; so expected number = 20/4 + 10/5 = 5+2 = 7

Spot on Chris!

For the exact answer use the fact that cos(a-b) = cos(a)cos(b)+sin(a)sin(b)

With a = sin^-1(1/3)  we have cos(a) = (2√2)/3  and sin(a) = 1/3  because if opposite = 1 and hypotenuse = 3 then adjacent = √(3²-1²) = √8 = 2√2

With b = tan^-1(1/2) we have cos(b) = (2√5)/5 and sin(b) = (√5)/5 because if opposite = 1 and adjacent = 2 then hypotenuse = √(1²+2²) = √5  (and 1/√5 = (√5)/5).

I'll leave you to combine the above values to get the final expression.