Assignment 3

course MTH 158

ËÕçϨâwƒh›ê´±¹á»¹¬°dú‹õÁéFªæªassignment #003

003. `query 3

College Algebra

06-01-2009

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20:33:19

query R.3.16 \ 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^2=14^2 + 48^2

C^2= 196+2304

C^2= 2500

C=sqrt 2500

C= 50

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20:33:52

** 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 -->

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20:38:37

query R.3.22 \ 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 -->

Yes it is a right triangle.

26 would be the longest side which is the hypotenuse.

so we square the sides to see if they equal 26^2

10^2=100

24^2=576

26^2=676

100+576=676

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20:38:48

** 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 -->

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20:53:56

query R.3.34 \ 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 -->

Volume of a sphere 4/3pi r^3

Surface area of a sphere 4pi r^2

V=4/3 pi 3m^3

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

V=12m^3/3 pi

V=4 pi meters^3

S=4 pi 3m^2

S= 12 pi meters^2

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20:56:46

** 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 -->

I see the mistakes I made in this problem. I didnt do my exponents first. I totally confused myself.

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21:09:50

query R.3.50 \ 42 (was R.3.36). A pool of diameter 20 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 -->

Area of deck = 69 pi ft^2

First I found the diameter of the entire pool and deck.

20+3+3=26' diameter

I then found the area of the whole circle

A=pi*13^2

A=169 pi ft^2

Then I found the area of the swimming pool

A=pi * 10^2

A= 100 pi ft^2

Then I subtracted the area of the swimming pool from the entire circle to give me the area of the deck

169 pi ft^2-100 pi ft^2= 100 pi ft^2

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21:10:54

** 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 -->

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21:12:10

Query Add comments on any surprises or insights you experienced as a result of this assignment.

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RESPONSE -->

Just that I need to be careful with order of operations, take my time and do them in order.

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21:12:26

005. `query 4

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RESPONSE -->

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assignment #003

003. `query 3

College Algebra

06-01-2009

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21:15:21

query R.3.16 \ 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 -->

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21:15:24

** 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 -->

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21:15:27

query R.3.22 \ 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 -->

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21:15:30

** 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 -->

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21:15:34

query R.3.34 \ 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 -->

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21:15:38

** 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 -->

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21:15:41

query R.3.50 \ 42 (was R.3.36). A pool of diameter 20 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 -->

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21:15:44

** 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 -->

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21:15:46

Query Add comments on any surprises or insights you experienced as a result of this assignment.

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RESPONSE -->

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You did well on the questions you answered. Let me know if you have questions.