CPhill

Natasha....this is just like this one:

a)  We can use the the "tangent-secant' theorem, here.....specifically....

m<BAC = 1/2 (minor arc BC - "x")

14 = 1/2 (112 - x)

28 = 112 - x

x = 112 - 28  = 84°

b) For this one we need to find the measure of minor arc CD ......"y" will be 1/2 of this.....

So we have...(360 - 112 - 84 ) =  164°

And 1/2 of this = 82°

a)

Since OM is perpendicular to CD, it also bisects it. Then CM = 22. And we can find radius CO thusly..

CM^2 +  OM^2 = CO^2

22^2 + 20^2 = CO^2

884 = CO^2      take the square root of both sides

√884 = CO = 2√221

b)

OF^2 - ON^2 = FN^2     .....but OF = CO (since both are radii)

CO^2 - ON^2 = FN^2

884 - 19^2 = FN^2

884 - 361 = FN^2

523 = FN^2          take square root of both sides

√523 = FN

c) Since ON is perpendicular to EF it bisects it.....and FN = √523....so EF = 2√523 = 45.7

IF AB is a tangent......then

AB^2 + BO^2 = AO^2  (because OB would have to meet AB at right angles)  .......therefore......

(7.75)^2 + (4)^2  =  (8.75)^2   ????

60.0625 + 16 = 76.5625   ???

76.0625 = 76.5625  ???      Nope......  AB is not a tangent!!!

a)

<PAO = <PBO since tangents meet radii at right angles

AO = BO   both are radii

PO = PO

Then by HL, PA = PB

Then, by SSS  .......ΔAPO ≅ ΔBPO

b) <AOD = <BOD = 180 - <AOP =  180 - 64 = 116°   [<AOP + <AOD = 180. And <AOD = <BOD by symmetry. Thus (180 - <AOP) = (180 - <BOP) = <BOD = 116°]

Undefined...to see why.....consider

6/2 = 3     because 3 x 2 = 6

But what is 3/0  ??

3/0  =  ???    .....   In other words.....what multiplied by 0 returns 3  ???

Answer.......nothing !!!    Whatever "it" is.......we can't define it!!!

Also. we have an "indeterminate" form which is 0/0......What is 0/0  ??

I claim it could be anything........  it could be 11 or it could be "pi".....(can you see why???)

Area of bottom  = (17)*(8)

Area of "top"  = (17)*(10)

Area of "back" = (17)*(6)

Area of sides = 2*(1/2)*(8)*(6) = 48

So we have 

17(8 + 10 + 6) + 48 =

17(24) + 48 =

456 sq m

We have a outer circle with a radius of 7.5m and an inner circle with a radius of  (7.5 -1.25) = (6.25)m

So the arc length of the outer circle = pi*(7.5)m   and the arc length of the inner circle is pi*(6.25)m

And the length of the 11 segments = 11*(1.25)m

So putting all these together, we have:

[pi(7.5 + 6.25) + 11*1.25] m =  about 56.95m = 57m  (rounded)

Nice answer and graph, Melody......jboy314 had an answer yesterday, if I remember correctly....ghosts, indeed!!!

1.74 = 

1 + 74/100  =   

174/100 =

87/50 ......in simplest form