query 2

I don't see anything wrong with your process but can't check all the arithmetic. I checked your solution for a in my head and I can't spot the error. It's easy to make a small error. If all your arithmetic was correct you would get 0 deviation for all three of your chosen points (i.e., for 16, 48 and 96 you would have gotten deviation zero). Let me know if you don't see why.
Here's how DERIVE would solve that system, using matrices:
row_reduce([256,16,1,111;2304,48,1,81.3;96^2,96,1,16.3]) means that we simplify the augmented matrix
256,16,1,111 2304,48,1,81.3 96^2,96,1,16.3
When we simplify that command we get
[1, 0, 0, -0.005325520833; 0, 1, 0, -0.5872916666; 0, 0, 1, 121.76]
which is the same as the matrix
1, 0, 0, -0.005325520833 0, 1, 0, -0.5872916666 0, 0, 1, 121.76
This means that a = -.00533, b = -.587, c = 121.76.
This doesn't differ a whole lot from your model, but enough that you get unreasonably large deviations, as you noted.
In any case you've got the process right; try to be careful of the arithmetic on the tests, think about using DERIVE or something else to solve the equations to check yourself, but don't lose any more sleep over it.

-----Original Message----- From: William Johnson [mailto:johnson_big12b@hotmail.com] Sent: Sunday, March 27, 2005 5:47 PM To: dasmith@naxs.com Subject: RE: mth 173

this is prob set 2. 1) (0 ,111) (16, 111) (32, 89.92782) (48, 81.29913) (64, 73.73517) (80, 67.10455) (96, 61.29212 ) (112, 56.19691)

i will use points (16, 111), (48, 81.29913) and (96, 61.29212 )

I (256)a+16b+c=111 II (2304)a+48b+c=81.29913 III (9216)a+96b+c=61.29212

subtract I from II is 2048a+32b=-29.70087 subtract I from III is 8960a+80b=-49.70788

multip. IV times 10 = 65536a+320b=-297.0087 multip. V times 4 = 35840a+320b=-198.83152

subtr. V from IV = 29696a=-98.17718 so a =-.00330607

plug a into V: 8960(-.00330607)+80b=-49.70788 so 29.62243+80b=-49.70788 then 80b=-79.33031 b=-.99163

plug b into I: I (256)(-.00331)+16(-.99163)+c=111 so c=127.71344

the equation is: y= -.00330607x^2 - .99163x + 127.71344

my Model Function's Prediction of Temp.(x,y---tru y --dev.) 0 , 127.7134-------111-------16 16 , 111.001-------111-------0 32 , 92.5959----89.92782---2.7 48 , 72.4980----81.29913---8.8 64 , 50.7075----73.73517---23 80 , 27.2242----67.10455---39.9 96 , 2.0482-----61.29212 ---59.3 112 , -24.820---56.19691---81 ok. that is the 1st problem in the set. is that graph dev. supposed to be off that much???

query 2

Looks good. You can use DERIVE anytime it seems appropriate, and I'll be using DERIVE syntax for derivatives and integrals (also giving you pointers about how to do derivatives and integrals in DERIVE, which once you understand what derivatives and integrals are is pretty easy).
Of course you have to be able to show things analytically (i.e., by working them out on paper), but DERIVE can be very handy for checking yourself and exploring patterns you don't have time to work out by hand. Then when you actually apply calculus in your engineering courses you'll likely be making extensive use of computer software like DERIVE.

T痈G＜糖鞔新倆箷柵櫸叩 assignment #002

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Calculus I 03-27-2005

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19:07:52 Were you able to complete the DERIVE exercise?

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RESPONSE --> yes.

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19:09:19 ** If you weren't able to complete the exercise you should download the 30-day trial version of DERIVE and do so.

Note that the instructor neither recommends nor discourages you from purchasing DERIVE. Except for the basic worksheet and other assignments that may occur in the first part of the coruse DERIVE is not required and references to DERIVE in the later part of the course will be optional.

This ends Query 2.**

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RESPONSE --> ok, so when do i use it?

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