Melody

\(6tan^2(5x-3)=2\\ tan(5x-3)=\frac{1}{\sqrt3}\\ \quad \text { you should recognise that } \quad tan \frac{\pi}{6} =\frac{1}{\sqrt3}\\ 5x-3=\frac{\pi}{6}\\ \)

And you can finish it.

\(y=\sqrt x\\ so\\ x=y^2\)

\(If\;\;\;  y=\sqrt2 \;\; then \;\;x = (\sqrt2)^2=2\\ If\;\;\;  y=-\sqrt3 \qquad \text{then what will x equal?} \)

\(y=\sqrt x\)

If x=9 then  y= sqrt9 = 3

etc

if order does not matter then  13C5

If order does matter then   13P5

I do not know Straight.  I actually do not understand what you are trying to describe.

I use Chrome and have not had any recent problems.

I will assume that they cannot be repeated.

there are (47-1)/2 = 23 odd positive numbers less than 47

43+4         1,3

41+6         1,5       

39+8          1,7         3,5

37+10        1,9         3,7        

35+12         1,11       3,9        5,7

33+14          1,13      3,11      5,9    

31+16          1,15      3,13      5,11      7,9

29+18           1,17     3,15      5,13     7,11       

27+20           1,19     3,17      5,15      7,13      9,11

25+22           1,21                                            9,13

------------------------------------------------------------------------------------

23+24          21, 3     19,5       17,7    15,9    13,11  

21+26          19,7      17,9       15,11    

19+28          17,11     15,13     

1+1+2+2+3+3+4+4+5+5     5+3+2  = 1+1+2+2+3+3+4+4+5+5+5+3+2 = 40

I get 40 odd triples with no repeats.    

Edit: I have changed this from 39 to 40 as there was an addition error at the very end.

Little numbers always get the best of me  

x^2 - 2x + 1 - 15x + 4 = 0

x^2 - 17x + 5=0

solve using the quadratic formula

I am pretty sure I saw this question answered yesterday.  Go see if you can find it.

Hint:

cos(2x)=cos^2x-sin^2x

and

sin^2x=1-cos^2x

simplify then sub   y=cos(theta)

then solve as a quadratic

8C3  

nCr(8, 3) = 56