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Thank You So Much! Youre the Best!

This is already simplified.  However you may want it in another form.  When you have an exponent that is a fraction the numerator represents the power a base is raised to and the denominator represents a radical. 

as such, you can rewrite this as the cubed root of x^7

If you're looking for a decimal approximation then that is absolutely the right way.

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°

The probablility distribution table would look like a table.  I'll do my best to make one below though please note that the lines are missing.  it should be noted that these probabilities have been simplified.  For example the probability for t=11 was 2/50 which reduces to 1/25

t                    11           12             13           14           15            16           17

P(X=t)           1/25      1/10          4/25         1/5         21/50        1/25         1/25    

I usually just use division as my fraction and the answer comes out right, But someone else probably knows how to do it the right way.

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

C.  EF=2FN=2sqrt(523)=45.74

b. To find FNwe construct the radius from O to F and recall that its length is sqrt(884).  Then apply the pythagorean theorem to the new triangle

19^2+FN^2 =(sqrt(884))^2

361+FN^2=884

FN^2=523

FN=sqrt(523)

a. Construct a radius from C to O.  Since CD=44 and OM is a right angle to the chord it bisects the chord, ergo CM=22.  We can use the pythagorean theorem to find CO.

22^2+20^2=CO^2

CO=sqrt(884) which is about 29.7

You could certainly express it in coordinates.    For the x intercept we let y =0.  Therefore, since we found x=4 of -4 the coordinates are  (4,0) or (-4,0)

similarly for y  intercept (and i just realized I mistyped my first response, it should be -16) we have coordinates (0,-16)

Thank You! :)

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!!!

If it is a tangent then angle B is a right angle.  The easy way to test is with the pythagorean theorem.

7.75^2+4^2=8.75^2

76.0625=76.5625

This means that Angle b is not a right angle so Segment AB is not a tangent (though it is extraordinarily close to being one.)

3/7 is the answer. 36/12=3 and 84/12=7

b.  Since we proved the triangles congruent in part A it follows that angle POB has a measure of 64.  POB is supplementary to angle BOD (they sum to 180 degrees) there fore the measure of BOD is 180-62=114 degrees

Wouldn't it be coordinates?

A. The tricky part of this proof is that we must recognize that angles PAO and PBO are both right angles because they are formed by radii to tangents.  Therefore they are congruent.

Segment AO is congruent to segment BO as they are both radii.

Segment PO is congruent to itself by the reflexive property of congruence. This essentially means that it is a segment that is a side length of both triangles.  We should also note that is the hypotenuse. 

With these pieces of information hand we are able to say the triangles are congruent by the Hypotenuse Leg theorem of triangle congruence!

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°]

x intercepts are where the y value is zero.  Therefore to find the x intercept we let y=0

x^2-16=0

x^2=16

x=4 or -4

To find y intercept we need to recognize that it occurs where x=0 so we set x to 0

y=0^2 +16

y=16

Thanks for the help!

Well it sort of depends.  I once asked a professor this question and he responded with, "it blows up, like a bomb."

One way I like to think of it is in a real context.  First of all lets say I had no hamburgers and five friends, and I wanted to share my hamburgers with my friends.  since there are six of us this is 0/6.  The question, then, is how much food do each of my friends get?  None of course because there is no food!   Now we flip the script.  Lets say i have six burgers but i have not friends to share them with.  How many burgers do each of my friends get?  Mathematically this looks like 6/0 and at first many people think this is also zero.  Consider it more closely though, the question was how many burgers do each of my friends get?  Since I have no friends in this context it the question makes no sense and therefore we cannot answer the questions.  When we run into things like this in math we say they are undefined.

another answer to this is infinity.  Pick a number, any number and divide it by 1.  Then divide by .5, then by .2 then .1.  Divide it by .01 and .001 and .0001 and notice the pattern.  The numbers get massive!  This is undoubtedly what my professor meant when he said it blows up like a bomb!

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

let's start testing factors and see what we get.  The factors of 24 are 2, 3, 4, 6, 8, 12, and 24

As it turns out the only one of these that is a factor of 74 is 2