owentout

wait! I'm a doofus, add all the given numbers and divide by 4 ( 4 because you are taking into account the numbers excluding the one you are looking at)

THAT would get you 66

37 + 29

this is quite an interesting problem indeed, I apologize for not explaining, it's new to me as well!

https://web2.0calc.com/questions/someone-help-me-please_2 

check this out, it will help you greatly :)

try 5/6 for the first fraction question. Let me know what happens.

https://web2.0calc.com/questions/hyperbola-help_1

I think this has been answered before, let me know if I'm wrong :)

The perpendicular bisector of a line segment goes through the midpoint and has slope which is the negative reciprocal of the slope of the line segment.

So, a point on the perpendicular bisector is ((1+7)/2, (5-1)/2) = (4, 2)

Slope of MN = (-1-5) / (7-1) = -6/6 = -1

Slope of perpendicular bisector = -1(1/(-1)) = 1

Equation of perpendicular bisector: y - 2 = 1(x - 4)

y = x - 2

Let the numbers be a < b < c < d < e

Then the smallest two, a and b, must have sum 16,

a + b = 16

and the largest two, d and e, must have sum 37,

d + e = 37.

Then the middle number c is equal to 66 - (a+b) - (d+e) = 66 - 16 - 37 = 13.

 OK. So, the two smallest numbers a and b give the sum of 16, and the third number is 13.

It means that the next sum, 20 (see the condition) is a+c.

It can not be nothing else.

If a + c = 20 and c = 13, then a = 20 - 13 = 7.

It implies b = 16-7 = 9.

So, the first three numbers are a = 7, b = 9 and c = 13.

OK. Now we can make the similar analysis from the other end.

So, the two largest numbers d and e give the sum of 37, and the third number in the descending order is 13.

It means that the next from the largest sum, 34 is e+c.

It can not be nothing else.

If e + c = 34 and c = 13, then e = 34 - 13 = 21.

It implies d = 37-21 = 16.

Thus the numbers are 7, 9, 13, 16 and 21.

Their product is 275184.

hope this helps!

hope this helps, the answer will be 3 due to this theorem.

This was an unnecessarily difficult problem, but thank you very much for the continuous assistance :) 

why does the cot^2 x happen after finding the common denominator?

I would very much hope so! Thank you for your gracious attempt though!

I hate to be this person but this problem has to be solved whilst keeping -tan alone on the right side