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**demha****Member**- Registered: 2012-11-25
- Posts: 184

I got a math review today. I just wanted help to to check if I got these right and/or help understand any questions that I need to know better. Any questions/answers with this symbol ( *** ) means that I need help on it or do not understand. Thank you!

I have a pizza. The radius is 10 inches long. The pizza was cut into 16 equal slices. When 1 slice was left, my sister and I both wanted it, so we agreed to cut it in half, but I like the crust more than she does, so we decided to cut it the "other way." In other words, the two pieces would not be symmetrical. The inside piece would contain all topping, and the outer piece would contain some topping and some crust.

1. Find the area of the whole pizza.

Answer: (pi)(10^2) = 314.159

2. What is the area of one piece of pizza?

Answer: 314.159 divided by 16 = 19.634

3. What is the area of a half-piece?

Answer: 19.634 divided by 2 = 9.817

4. What would the area of the whole pizza be if it were made of half pieces?***

Answer: I am guessing they mean the 9.817 pieces. So 16 whole pieces make a pizza. They want to know how many halfs so 16 x 2 = 32. Now I do 32 x 9.817 = 314.144. Is this method correct? If not, what is the correct way?

5. What is the radius of a half-piece? (ie, where do I need to cut to make two equal halves out of a piece?)***

Answer: The area of half a piece is 9.817. So I do 9.817 divided by pie which comes up to 3.124, then i square it to get 1.767. Is this correct?

---

NOTE: this is the first half. i am currently doing the second half and will post later for help on this topic.

*Last edited by demha (2013-09-11 01:33:46)*

"The thing about quotes on the Internet is you cannot confirm their validity"

~Abraham Lincoln

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,347

Hi;

1) Is correct.

2) should be rounded to 19.635 instead of truncated to 19.634

3) Is correct if you use your value from 2).

4) 32 half pieces is the same as 16 whole pieces which is the same as 1 whole pie. No calculation is necessary, you could just say 314.149 from 1)

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**demha****Member**- Registered: 2012-11-25
- Posts: 184

If there is a goat tied to a rectangular barn on a 50 foot lead and the barn is 20 feet by 20 feet (floor), what is the maximum grazing area? If there are regions you can't find the area of, provide as good an estimate as you can. Assume the goat is tied to a corner outside the barn, cannot get in, and that the barn is not grazing area. (Remember, this will be based on parts of circles, no other shapes...the goat's rope will only get shorter when he tries to go around the barn...)

6. How much of the 50 foot circle can the goat reach without getting interrupted by the barn? What is that area?

Answer: I would say it can go 3/4 of the area. So 3/4 x 50^2 x pi = 1875 PI

7. When the rope goes around the barn, what is the new radius? How much of a circle can it make without hitting the barn or overlapping area you've already found? What is that area?

Answer: The area for this would be 1/4 and 30 would be the new radius here. So 1/4 x 30^2 x PI = 225 PI

8. When the rope goes around the barn the other way, what is the new radius? How much of a circle can it make without hitting the barn or overlapping area

you've already found? What is that area?

Answer: This would be the same as #7, answer being 225 PI.

9. The areas you found in 7 and 8 overlap each other. How much do they overlap? What *approximate* shape do they make? What is that area?***

10. What is the total grazing area the goat can reach?***

"The thing about quotes on the Internet is you cannot confirm their validity"

~Abraham Lincoln

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**demha****Member**- Registered: 2012-11-25
- Posts: 184

And thank you Bobbym for your help on Post #1!

"The thing about quotes on the Internet is you cannot confirm their validity"

~Abraham Lincoln

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,347

Hi;

Did you draw a diagram first?

10) Is a little bit tough and has a long answer.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**demha****Member**- Registered: 2012-11-25
- Posts: 184

Somewhat, I kind of drew one on paper and based it on that. #9 and #10 i am finding a little difficult to find the answer.

"The thing about quotes on the Internet is you cannot confirm their validity"

~Abraham Lincoln

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,347

10, will be very difficult for you. Is this an assignment?

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**demha****Member**- Registered: 2012-11-25
- Posts: 184

Yes they all are.

"The thing about quotes on the Internet is you cannot confirm their validity"

~Abraham Lincoln

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,347

Hi;

6) is correct!

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**demha****Member**- Registered: 2012-11-25
- Posts: 184

That's great to hear! What about 7 & 8?

"The thing about quotes on the Internet is you cannot confirm their validity"

~Abraham Lincoln

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,347

Hi;

7) Is incorrect.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**demha****Member**- Registered: 2012-11-25
- Posts: 184

#7

How would i do this one?

"The thing about quotes on the Internet is you cannot confirm their validity"

~Abraham Lincoln

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,347

There are 2 answers. At the first turn the line is 30 ft long. At the second turn it is only 10 ft long.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**demha****Member**- Registered: 2012-11-25
- Posts: 184

So I add them together to get 40 THEN do the equation?

"The thing about quotes on the Internet is you cannot confirm their validity"

~Abraham Lincoln

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,347

Do they want the first turn or the second one?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**demha****Member**- Registered: 2012-11-25
- Posts: 184

#7:

When the rope goes around the barn, what is the new radius? How much of a circle can it make without hitting the barn or overlapping area you've already found? What is that area?

I believe they are asking for the first turn because in #8 they say " When the rope goes around the barn the other way",

"The thing about quotes on the Internet is you cannot confirm their validity"

~Abraham Lincoln

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,347

First turn would be 30 ft left because you have used 20 ft up.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**demha****Member**- Registered: 2012-11-25
- Posts: 184

Yes, and then there will be 10 feet left just enough to get around another corner.

"The thing about quotes on the Internet is you cannot confirm their validity"

~Abraham Lincoln

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,347

Hi;

I believe they are asking for the first turn because in #8 they say " When the rope goes around the barn the other way",

Are you sure because it will be easier to come up with the shape they overlap you go 2 corners.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**demha****Member**- Registered: 2012-11-25
- Posts: 184

I'm really confused here right now >_<

"The thing about quotes on the Internet is you cannot confirm their validity"

~Abraham Lincoln

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**demha****Member**- Registered: 2012-11-25
- Posts: 184

Can we use the image for #6 to #10?

"The thing about quotes on the Internet is you cannot confirm their validity"

~Abraham Lincoln

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,347

I recommend going with the the second turn which leaves 10 ft of line and the green area overlap which is 75 π. See the drawing.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**demha****Member**- Registered: 2012-11-25
- Posts: 184

So I would do the equation with 10? As in:

1/4 x 10^2 x PI

"The thing about quotes on the Internet is you cannot confirm their validity"

~Abraham Lincoln

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,347

Wouldn't it be 3 / 4?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**demha****Member**- Registered: 2012-11-25
- Posts: 184

Yes I keep getting mixed up so sorry! The rope goes around the barn 3/4. But I have been thinking that #7 and #8 will be the same equation:

3/4 x 30^2 x PI

I know there is 10 left but that is what we can use for #9? It asks "The areas you found in 7 and 8 overlap each other. How much do they overlap? What *approximate* shape do they make? What is that area?" So I came to believe that the equation for THIS number will be:

1/4 x 10^2 x PI

Am I right on this?

"The thing about quotes on the Internet is you cannot confirm their validity"

~Abraham Lincoln

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