Alan

NinjaDevo sent me a message about this.  Here's a copy of the reply I sent him:

The default for the LaTeX box on the site is to be in "Display" math mode. I often switch this off to begin with by inserting $$ right at the start. If I then type words it comes out as text. 

In the "average slope" case I wanted to start with some "Inline" math, which requires a single $ immediately before and immediately after the math (so it looks like I started the whole thing with 3 dollar signs - 2 to switch off the default "Display" mode and 1 to switch on the "Inline" mode). 

Putting $$ immediately before and after the math produces "Display" mode math, where the math appears centred on a new line. 

You switch off math mode and enter text mode by using either $ (for "Inline" math) or $$ (for "Display" math). 

Hope this helps. 
PS I'm no LaTeX expert - I just use trial and error and see what results!

What I'm really trying to do in the denominator is to find the x-axis distance between two limits. If I integrate a constant (k, say) with respect to x, I just get kx, which, if my limits are hi and lo gives me k(hi - lo).  If I set k to 1 then I just get hi - lo, the distance between the two limits.  (In the case of $$$\int dx$$$ the 1 is implicit).

Perhaps better to ignore some of the calculus and just think in terms of  average x distance = area.  The area can be found using calculus, and the distance using common sense! 

Melody,

$$$\int1dx$ is really just $\int dx$\\\\
Had I done this in LaTeX I would probably just have written $\int dx$, but I did it using Mathcad, which requires an argument to be specified.$$

$$$\int_{lo}^{hi}dx$ is just the distance along the x-axis from x=lo to x=hi.$$

I think you've got it!

Melody, does this help

 average x distance = area  so average = area/distance.

I guess you're meant to equate clockwise and anticlockwise moments:

So d ≈ 1.663 m

note that cos(30°) = (√3)/2

You should double check that the moments given above are correct - I did this rather quickly!

Using the calculator on the home page here you can enter x then press the ^y√x key then type 4 and hit the enter key. 

Or enter x then press the square root key (√x) twice.   

You want the difference between 1/2 and 1/5.  To find this express each fraction in terms of a common denominator.  Here 10 is the least common denominator and 1/2 = 5/10 and 1/5 = 2/10, so the difference is 5/10 - 2/10 = 3/10. So she has to finish 3/10 by Friday.

The slope at any point x is given by s(x) = 4x - 2.  The average of this depends on the interval over which you want to calculate it.  If you want it from x = lo to x = hi, say then the average is given by $$\frac{\int_{lo}^{hi}{s(x)dx}}{hi-lo} = 2(hi+lo-1)$$

If lo = -hi then the average is just -2.

As written it doesn't make much sense!

If the decimal point were one place too far to the left it would have been £13,231.72 which would make more sense as money because you would expect only two decimal places for the pennies.