Rob works part time at the fallbrook riding stable. he makes $5 an hour exercising horses and $10 hour cleaning stalls. because rob is a full time student he can work no more than 12 hours per week. however he must make $60 per week. write a system of inequalitites

Let x be the number of hours exercising horses.
Let y be the number of hours cleaning stalls.

x + y <= 12
5x + 10y >= 60
x + 2y >= 12

At this point you might do well to graph this set of equations on Wolframalpha.com

In the meantime solve this system this way.

12 - x > y > 6 - x/2
When y =0 the x = 12.

-2+sqrt(3)

Step-by-step explanation:

When cos(angle)=sqrt(3)/2

then sin(of that angle)= + or - 1/2 depending on the quadrant

Anyways 330 degrees is in the 4 quadrant.  Cosine is positive there while sine is negative.

so sin(330)=-1/2

Formula for tan(x/2)=(1-cos(x))/sin(x)

Therefore  tan(165)=tan(330/2)=(1-cos(330))/sin(330)=(1-sqrt(3)/2)/(-1/2)

Multiply top and bottom by 2 to get

tan(165)=(2-sqrt(3))/-1

tan(165)=-2+sqrt(3)