Alan

Well, if the total length is (174+336)ft = 510ft you need to divide this by 6ft to find how many sections.  You can calculate what 510/6 is (use the calculator on this site if necessary).

Do you just want to simplify this?

(2x-5)² - (1-x)(1+x)  = 4x² - 20x +25 -(1+x-x-x²)  =  4x² - 20x +25 - 1 +x²  = 5x²-20x +24

The prime factors are 2, 3 and 7.  Non-prime factors are 6, 14 and 21.

This would mean the angle whose cosine is -3.2257; but the limits of cosine lie between +1 and -1 (inclusive).

Let E be the number Eugene has and J be the number Jason has. There are two conditions given:

(E-70)/(J+70) = 1/5

(E-80)/(J+80) = 1/8

Cross-multiply each of these to get:

5*(E-70) = J+70

8*(E-80) = J+80

or

5E - 350 = J + 70

8E - 640 = J + 80 

Subtract the first from the second to get:

3E - 290 = 10

Add 290 to each side

3E = 300

Divide both sides by 3

E = 100

You can also find how many Jason has, but I'll leave you to do that.

I assume you mean log(b^x) = (1/2)log(b⁴) +(2/3)log(b²⁷) - log(b⁶) and you want to find x.

Using the properties of logs (see the Formulary) we can write the right-hand side as log(b^4*(1/2)) + log(b^27*(2/3)) - log(b⁶), which is log(b²)+log(b¹⁸)-log(b⁶), which is log(b^2+18-6), which is log(b¹⁴).  Comparing this with log(b^x) we can see that x is 14.

You would first need to use the cosine rule [ cos(A) = (b² + c² - a²)/(2bc) ] to find one angle, then you could use the sine rule [ sin(B)/b = sin(A)/a ] to find the other angles. 

a²b(3a² + 4ab²) = 3a⁴b + 4a³b³

Hmm!  Chris, suppose there are 4 volunteers where each subgroup consists of 1 participant. 

If there is one subgroup then clearly there are 4 possible choices.

However, if there are 4 subgroups, it seems to me there is only one way to do this; but your method would give nCr(4,1)*nCr(3,1)*nCr(2,1) = 24 ways!!  This would only be correct if each subgroup were given a different label and it was the number of combinations of label and participant that was required.  Perhaps the subgroups are given labels - this would be quite sensible. However, it isn't clear to me that that was what was intended here.