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How can i calculate cosh with complex number?

How can i calculate cosh with complex number?

^(add on to my first post) I found that there are 7!/2! ways to label the heptagon considering that there are two O's in "OCTAGON". Since there are 4! = 24 ways where the O's are next to an N, so is the answer 7!/2! - 24?

Am I on the right track?

y=-3

x=-2

ABCD is a rectangle. Given PA = 1; PB=3 and PD=7​, find the area of rectangle ABCD.

Let angle BAP be 45º

Draw the altitudes from point P to point M on side AB, and to point N on side AD.

MP = NP = sqrt( 0.5) = 0.707106781

MB = sqrt ( 3² - 0.5 ) = 2.915475947

ND = sqrt ( 7² - 0.5 ) = 6.964194139

Area  = ( AN + ND )*( AM + MB )  

Thank you so much I appreciate it!

Add both equations up and the y's cancel out. So we have:

2x = 18

x = 9

Plug this into our first equation:

9 + y = 15

y = 6

So (9, 6)

thank you electricpavlov!!

I say this for every geometry problem I solve, but I really wish I had a diagram. In order for my solution to make sense, please draw out what I wrote below while reading it. :)

Extend line BA to the other side of the circle. Let's call the point where it touches the circle F. Inscribed angle CBF, as given by the problem, is x. So arc CF is 2x because a central angle/arc equals twice the inscribed angle.

Arc CE is 6x because ∠CDE=3x.

Since∠BAE=90, and line BAF is straight, then EAF is also ∠90.

arc CF + arc CE = arc EAF

2x + 6x = 90

8x = 90

x = 11.25

I'm not sure if my solution is correct because I didn't utilize ∠BCD=2x.

I got it, it was 49, thanks melody!

Put the point (4, -3) in.

1-k*4 = 9

4k = -8

k = -2

TRAPDOOR =8 letters =8! =40,320 permutations. But, we have 2 repeated pairs [O,O  and  R,R], so we have a total of 8!/2!.2! =10,080 permutations. Each permutation begins with a letter, A,D,O,O,P,R,R,T. Each permutation that begins with any letter continues with that letter for: 10,080 / 8 =1,260 permutations. And since you have 4 letters, out of total 8 letters, repeated, the two "Os" and the two "Rs" are going to be adjacent to each other:1,260 x 4 =5040 times  out of a total of 10,080 permutations, or 5040 /10,080 =1/2.This makes sense since 1/2 of the 8 letters are repeated.

y = 1/4x + b

7 = 1/4 (2) + b      b = 6 1/2

y = 1/4 x + 6 1/2

y - 1/4 x = 6 1/2

Starting with y = mx + b form

y = -3x + b     sub in the point to calc 'b'

5 = -3(0) + b     b = 5

y = -3x+5

y + 3x = 5    in standard form  

Midpoint1 = 1,1

Midpoint2 = 3,3      slope   =   (y1-y2)/(x1-x2) =   (1-3)/(1-3) = 1

wonder why I said "trust bro"

The first one factors to   

(x+y)(x^2+y) = 91

the second one factors to  (x^2+y)^2 = 169      sooooo    x^2 + y = 13   sub into the first equation above

(x+y)(13) = 91

x+y = 91/13 = 7

No worries! :)

Sorry, I just got it. My bad. Sorry.

28! means 28 factorial which is 28*27*26...*1. 

27! is 27*26*25...*1.

So we can take out 27!. 

I don't get were you get the 28+1

Y, beacuse if you simply look at it, even though it starts at a smaller number, it has 100 terms and the last term (100^2) is 10000 which is way bigger. So from here, I strongly belive that Y is larger.

The center will be      x, 0     because it is on the x axis

    the distance from the center to EACH of the points is the radius

  Then using the ditance formula:

(x - - 3)^2   +  (0-2)^2    =   (x- -2)^2 + (0-3)^2 

x^2 +6x+9 +4  = x^2 +4x+4 + 9

2x = 0

x= 0     and y = 0

(0- -3)^2 + (0-2)^2 = d^2

    9 + 4

       13 = d^2     d = sqrt 13 = r

maybe this should be off topic....

this solution make no sense at all!