assignment 3

Very good work. See my notes on the reasons why it's often a good idea to leave pi in your expressions, at least until the very last step.

drʬޙڬ assignment #003 ؾ{]Uӂ͛ξ College Algebra 09-14-2005

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23:42:31 query 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 --> hypotenuse is 50 c^2=a^2+b^2 c^2=14^2+48^2 c^2=196+2304 c^2=2500 c=sqrt 2500=50

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23:42:40 ** 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

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23:47:58 query 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 --> yes it is a right triangle the sum of the lowest two squares equals the third square which makes it right

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23:48:10 ** 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

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00:17:35 query 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 --> 113.04 volume=4/3pie r^3=113.10 for pie but if you use 3.14 you get 113.04 4/3*3.14*3^3=113.04

surface area=4pie(r^2)=113.10 but if you use 3.14 for pie you get= 113.04 surface area

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00:22:35 09-15-2005 00:22:35 ** 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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NOTES -------> this makes no sense if you do as the book on pg 32 with the formulas they are worked out not with just pi in the answer

Volume = 4/3 * pi * r^3 V = 4/3 * pi * 3^3 V = 4/3 * pi * 27 V = 36pi m^3

The author chooses to do that, but 36 pi is a much easier number to understand than 113.04. If you multiply 36 by pi you get 113.04, so the two are equivalent (except for roundoff) and either is acceptable and either might be used in any application.

However note that 36 pi is exact, while 113.04 is rounded off.

And note also that it's much easier to how 36 pi comes from the given information--you can get that in your head from the formula and the radius of 3. You can't get 113.04 in your head, so if this was an intermediate step in a problem you would have no quick way to verify it and identify a possible error.

In general with problems of this nature multiplication by pi is the very last thing you should do, and it's an optional step.

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00:22:37 ** 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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00:49:00 query 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 --> area of deck = 216.77

pool pir^2=pi*100=314.16

pool and deck pi*r^2=pi*169=530.93

deck and pool -pool= 216.77

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00:52:23 ** 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 --> this is very hard to understand do they want the answer or how to solve it? did i do it wrong because i solved to far?? why does it not go past filling in for pi?

69 pi is the same as 216.77, assuming you multiplied correctly.

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00:52:31 005. `query 4

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RESPONSE -->

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