The exact value of tan5pi/12 is

Step-by-step explanation:

This is the sum identity for tangent(x + y), where x and y are angles measured in radians.  The formula for tan(x + y) is  

The first order of business is to find which 2 angles, when expressed in terms of the denominator 12, add up to equal

We will use the first quadrant angles, and only the "important" ones:

When expressed in terms of the denominator of 12, these angles have the equivalent angles, in order from above:

We need to find the 2 whose numerators add up to a 5.  That would be:

Remember that

and  so

angle x is  and angle y is , making our tangent sum:

Filling that into our formula for the sum of tan(x + y):

It just so happens that

 and

so our formula then becomes

which simplifies to

and then bring up the lower fraction and flip it to multiply giving you:

I have the feeling that you need to rationalize that denominator, and if you do that, the final answer will be:

I know I kind of left you hanging at the very end with rationalizing, but there was so much already that went into this problem in such depth, that I didn't want to risk possibly confusing you even more than I may have already done so.  Try and follow the best that you can.

the answer is simply just 6n add the two together as they have an n

step-by-step explanation:

ok one would be money, and the other would be refreshments or something similar. if each bag of popcorn is 5.00 and each drink is half of that that means drinks are 2.50 the proper way to do that would to look and see how much of each you can buy without exceeding a limit of 30.00