review assignment 3

course Mth 158

Ia the area of a pool with a raduis of 10 = 100? Ithought it would be 314. I also missed the problem with the sphere. I used the correct formula and a calculator. What did do wrong?

P???B??????V????assignment #003003. `query 3

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College Algebra

06-12-2008

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assignment #003

003. `query 3

College Algebra

06-12-2008

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10:21:06

R.3.12 (was R.3.6) What is the hypotenuse of a right triangle with legs 14 and 48 and how did you get your result?

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RESPONSE -->

c^2 = a^2 + b^2

c =50

confidence assessment: 3

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10:21:25

** The Pythagorean Theorem tells us that

c^2 = a^2 + b^2, where a and b are the legs and c the hypotenuse. Substituting 14 and 48 for a and b we get

c^2 = 14^2 + 48^2, so that

c^2 = 196 + 2304 or

c^2 = 2500.

This tells us that c = + sqrt(2500) or -sqrt(2500). Since the length of a side can't be negative we conclude that c = +sqrt(2500) = 50. **

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RESPONSE -->

ok

self critique assessment: 3

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10:23:57

R.3.18 (was R.3.12). Is a triangle with legs of 10, 24 and 26 a right triangle, and how did you arrive at your answer?

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RESPONSE -->

10^2 + 24^2 = 26^2

676 = 673

This is a right triangle.

confidence assessment: 3

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10:24:20

** Using the Pythagorean Theorem we have

c^2 = a^2 + b^2, if and only if the triangle is a right triangle. Substituting we get

26^2 = 10^2 + 24^2, or

676 = 100 + 576 so that

676 = 676

This confirms that the Pythagorean Theorem applies and we have a right triangle. **

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RESPONSE -->

ok

self critique assessment: 3

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10:29:29

R.3.30 (was R.3.24). What are the volume and surface area of a sphere with radius 3 meters, and how did you obtain your result?

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RESPONSE -->

V =[4/3[ * pi * 3^3

V = 113.1 m^3

SA = 4 * pi *362

SA = 113.1 m^2

confidence assessment: 3

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10:30:53

** To find the volume and surface are a sphere we use the given formulas:

Volume = 4/3 * pi * r^3

V = 4/3 * pi * 3^3

V = 4/3 * pi * 27

V = 36pi m^3

Surface Area = 4 * pi * r^2

S = 4 * pi * 3^2

S = 4 * pi * 9

S = 36pi m^2. **

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RESPONSE -->

My mistake- I did not multiply the values by 4/3.

self critique assessment: 2

36 pi probably is equal to 113.1 m^2.

36 pi is the exact answer to this question; 113.1 m^2 is an approximation to an exact value. Note that 36 pi is much easier to connect to the given information than 113.1, and that 36 pi does not require the use of a calculator (unless you want the decimal approximation, which in some situations you certainly would).

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10:38:33

R.3.42 (was R.3.36). A pool of radius 10 ft is enclosed by a deck of width 3 feet. What is the area of the deck and how did you obtain this result?

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RESPONSE -->

13^2 * 3.14=

530.66

10^2 * 3.14 = 314

530.66-3.14=216.66

The answer is 216. 66 ft^2 if the deck is circular.

confidence assessment: 2

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10:43:29

** The deck plus the pool gives you a circle of radius 10 ft + 3 ft = 13 ft.

The area of the deck plus the pool is therefore pi * (13 ft)^2 = 169 pi ft^2.

So the area of the deck must be

deck area = area of deck and pool - area of pool = 169 pi ft^2 - 100 pi ft^2 = 69 pi ft^2. **

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RESPONSE -->

If the area of a circle is is calculated as pi* r^2, how can it the radius of the pool be 100? It should be 100 * 3.14.

self critique assessment: 1

pi is not 3.14. 3.14 is a 3-significant-figure approximation to pi.

The area of the pool is 100 pi ft^2. The area of deck and pool is 169 pi ft^2.

100 pi is of course approximately equal to 314, and the 3-significant-figure approximation would almost certainly be sufficient for this application.

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10:44:22

005. `query 5

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RESPONSE -->

self critique assessment: 1

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Your work looks good. See my notes. Let me know if you have any questions. &#