Alan

Thank you GingerAle, I like to plot graphs where possible - they often make it easier to see what is going on.

The integral Lancelot link gives after "V = " is the one I've written below my 3D graph. Lancelot provided more explicit steps to the solution than I did (I skipped over a few!).

It is sad that this forum has such a poor search facility.  An alternative way of searching it is to use your browser's search facility.  From outside the forum enter something like: "web2.0calc Badinage xxx" where you replace xxx with a key word or two from the question you are trying to find. Not ideal, but with luck you might have more success than with the forum search engine.

To clarify the above a little:

The black triangle is a right-angled triangle lying in the x-y plane, with vertices (1,1), (4,1) and (1,2).  Its hypotenuse has the equation y = -x/3 + 7/3.  

I should really have just said that as x goes from 1 to 4, y goes from 1 to -x/3 + 7/3.

I assume this means 

A = k/3,  B = k/5 and C = k/2  where k is a constant.

A+B+C = 180°  so  k/3 + k/5 + k/2 = 180 or 31k/30 = 180 so that k = 5400/31

Hence A = 1800/31 ≈ 58.1°,  B = 1080/31 ≈ 34.8° and C = 2700/31 ≈ 87.1°

.

"Find the volume of the solid under the surface z=xy and above the triangle with verticies (1,1) (4,1) and (1,2)."

The following should help:

.

This graph should help:

I think this is intended to be a mean of 21.3

a standard deviation of 6

and the top 4%

(I've noticed in the past that numbers are sometimes doubled up here - no idea why!)

The top 4% occur above about 1.75 standard deviations, so the minimum score is 

21.3 + 1.75*6

I don'tknow why there are so many brackets (there aren't any in the solution displayed above the calculator), but, since you have only one equation for two unknowns there are an infinite number of possible values of x and y that satisfy the equation.  You need two independent equations if you expect a unique solution.

First divide through by 200:

2^(x/9) - 8*2^(x/18) = 0

Divide through by 2^(x/18)

2^(x/18) - 8 = 0

Rewrite this as

2^(x/18) = 2^3

So we must have 

x/18 = 3

Multiply through by 18

x = 54

.

Number       Prime Factors

28               2^2, 7

35               5, 7

42               2, 3, 7

45               3^2, 5

60               2^2, 3, 5

72               2^3, 3^2

The only two with no factors in common are 35 and 72.