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You're soo right, Melody!
There are two minus signs. 

The triangle with the perimeter.

Thanks Heureka,

Do these need to be regular solids?

I am assuming that it will work for irregular ones as well but does it work for shapes such as stars where some of the intenal angles are acute ??

I've seen this formula a number of times before but I have never had cause to use it. ://

What is e=nf/2?

The Platonic Solids:

Euler's formula:

V - E + F = 2.

the number of vertices(V), minus the number of edges(E), plus the number of faces(F), is equal to two.

see e=nf/2 in : Proof of five Platonic solids in link:

The inverse of 

\(f(x) \qquad is  \qquad   f^{-1}(x)\)

Don't get this confused with a power of -1 it is not the same at all.

The inverse function is the reflection of the function in the line y=x

You have to be a bit careful though becasue it must still be a function which means domain restrictions often have to be imposed.

ex

Consider the function 

\(f(x)=x^2-4\)

this will only have an inverse if you resrtrict the domain to either  x>0  or x<0

I've chosen to restrict it to x>0

so

if     

\(f(x)=x^2-4 \qquad where \qquad x>0\\ then\\\)

to find the inverserse function we do this

change f(x)to  y and then make x the subject, then swap the x and y over.

\(y=x^2-4 \qquad x\ge0\\ y+4=x^2\\ x=\sqrt{y+4}\\swap\\ y=\sqrt{x+4}\\ \text{putting the function notation back again}\\ f^{-1}(x)=\sqrt{x+4}\)

This is the working of the graph if you want to look at it properly

maybe you have old eyes like I do asinus :)

there are 2 minus signs  - -   

Hi

I have never seen a degrees sign after the ratio value like you are talking about Gibsonj338.

I accept that it is what you have been taught but it may not be a universally used notation.

To me an answer in degrees or in radians is equally acceptable. 

2x = (360/40)  simplify

2x  = 9     divide both sides by 2

x  = 9/2

500 − 250  = 250 pieces left after donation

Yolanda got  180 pieces....then Enrique  got 70 pieces

So he got   70 /250  = 7/25  =  28%  of the remaining candy

39/52  * 38/51 * 37/50 * 36/49   = 6327/20825  ≈  30.38%

cos B= 0.2345

We are asking........at  what  rad measure  [or degree measure ] does the cosine = 0.2345 ???

So....arccos (0.2345)    =  1.334092 rads  = 76.44°

Clarification

IF B is in degrees   then B = arcos (.2345) = 76.437 DEGREES

If B is in RADIANS    then arccos(.2345) = 1.334092132482  RADIANS

The question does not say if B is in degrees or radians!!!

Cos starts at 1   for 0 degrees and goes to    a value of zero  at 90 degrees.

Also, to find out what B is, you cannot take an inverse cosine number in degrees and get an answer in degrees.  You can only take a inverse cosine number in radians and get a number in degrees.  The answer has to be in degrees.

You are incorrect Gibson, sorry      cos (76.437 DEGREES) = .2345     NOT .2345 degrees !!!

What about sin B = 0.7071 This is equal to 45degrees so why does cosB= 0.2345 have a much lower answer?

Read my post to you.  You can disagree with me all you want, but you are wrong.  No degree symbol next to the number mean radians,  Degree symbol next to the number means degrees.

Your answer should be in radians ...not degrees

Sorry....I disagree Gibson    the .2345 is the cosine of B  which is only a numerical value between 1 and -1    B MIGHT BE in DEGREES OR RADIANS.....the question does not state which...I used the more common degrees.

Multiply top and bottom by sqrt3

EDIT: 0.2345 not 9.2345.

Your answer of 76.437848672801 degrees is incorrect because 9.2345 is not in degrees but in radians.  In order for 0.2345 to be in degrees instead of radians, it need to have the degree symbol: 0.2345°.

\(cos(B)=0.2345\)

\({cos}^{-1}(cos(B))={cos}^{-1}(0.2345)\)

\(B= 1.334092132482°\)

Midpoint of AB   =   ( (5 − 2) / 2  , ( +2) /2  )  =     ( 3/2  , 5/2)  = ( 1.5, 2.5)

Slope of AB  =   [ 3 − 2] / [ 5 − − 2]   =   [1 / 7]  .... − reciprocal slope.....  = −7

Equation of perp. bisec.   =    y   = − 7 (x  − 1.5) + 2.5    →  y = − 7x + 10.5 + 2.5 →

  y = − 7x + 13     (1)

Midpoint of BC   =   ( (2 − 2) / 2  , (−6 +2) /2  )  =     ( 0/2  , −4/2)  = ( 0, −2)

Slope of BC  =   [ 2 − − 6] / [  −2 − 2]   =   [8 / −4]  = −2  .... − reciprocal slope..... =  1/2

Equation of perp. bisec.   =    y   = (1/2) (x  − 0) − 2    →  y = (1/2)x  − 2   (2)

Midpoint of AC   =   ( (5 + 2) / 2  , (−6 +3) /2  )  =     ( 7/2  , −3/2)  = ( 3.5, −1.5)

Slope of AC  =   [ 3 − − 6] / [  5 − 2]   =   [9 / 3]  = 3  .... − reciprocal slope..... =  −1/3

Equation of perp. bisec.   =    y   = (−1/3) (x  − 3.5) − 1.5    →  y = (−1/3)x + 7/6  − 1.5 →

y = (−1/3)x   −  1/3  (3)

Intersection  of (1) and (2) 

− 7x + 13   =  (1/2)x  − 2    add 2, 7x to both sides.....

15  = (1/2)x + 7x

15  = 7.5x     divide both sides by  7.5

2  = x    and  y = − 7(2) + 13   =  −1         =    ( 2, −1)

And y = (−1/3)x   −  1/3   also passes  through the point   ( 2, −1)   → y = (−1/3)(2)   −  1/3  =

  −2/3  − 1/3  =  −1

Distance from ( 2, −1)  to  A  = √[ ( 2−5)^2  + ( −1 − 3)^2  ]  = 5

Distance from ( 2, −1)  to  B  = √[ ( 2− − 2)^2  + ( −1 − 2)^2  ]   = 5

Distance from ( 2, −1)  to  C  = √[ ( 2− 2)^2  + ( −1 − − 6)^2  ]   = 5

I'll leave it to you, Tony,  to check the distance computations above

arc cos b = b = arc cos .2345 = acos(.2345) = 76.437848672801 degrees