Question

last question!!! (:

the company discovered that it costs $30 to produce 2 widgets, $106 to produce 4 widgets, and $670 to produce 10 widgets. Using the quadratic function, find the cost of producing 5 widgets.

Answer 1

cost = ax^2+bx+c
30 = 4a+2b+c
106 = 16a +4b +c
670 = 100a +10b +c
solve the equations to get a,b,c

Answer 2

dhats got a good start for us...

Answer 3

-30 = - 4a -2b -c -30 = -4a -2b -c
106 = 16a +4b +c 670 = 100a +10b +c
----------------------------------------------
76 = 12a +2b 640 = 96a +8b

Answer 4

640 = 96a +8b
-608 = -96a -16b
------------------
32 = -8b

b = -4

Answer 5

i got a = 7

Answer 6

a = 76-2b//12

a = 84/12 = 7

good job....now lets hope its right :)

Answer 7

30 = 4(7)+2(-4)+c

Answer 8

One thing I don't get about these questions is why buying more in total increases the cost per thing? As far as I recall, all have been like this ... :(

Answer 9

30 = 28 -8 +c
30 = 20 + c
10 = c

7x^2 -4x +10 = y should work, lets check ourselves

Answer 10

economy of scale :)

Answer 11

Economy of scale... in reverse, though, more like :/

Answer 12

2,30 4,106 10,670

700 -40 +10 = 700 - 30 = 670..checks
7(16) -4(4) + 10 = 112-16+10 = 112 - 6 = 106 checks
28 -8 + 10 = 28+2 = 30 its good

Answer 13

7(5)^2 -4(5) +10 = y

7(25) -20 +10 = y

175 -10 = 165 should be our answer...

Answer 14

yeah....in reverse :)

Answer 15

THANK YOU SO MUCH!!!
do you have an email i could get ahold of you on? just in case i need help in other stuff.

Answer 16

lol....youre welcome, but I think ill just stick to openstudy stuff ;)

Answer 17

maybe widgets are one of those products that consumes more than its worth....like tribbles :)

Answer 18

¬_¬

Answer 19

A Mathematica approach:

let data = {{2, 30}, {4, 106}, {10, 670}}
Fit[ data, {1, x, x^2}, x] /. x -> 5 yeilds 10. - 4. x + 7. x^2 =165 at x=5

The Fit function is a curve fitter.

Answer 20

i never trust a machine to do a "man"s job. unless its a slide rule :)

Answer 21

Why the quotation marks around man?

Answer 22

trying to preserve my anonymity lol

Answer 23

:(

Answer 24

i try to remain androgenous online ;)

Answer 25

As a 76 year old person who could not integrate x^2 with pencil and paper I am very impressed with amistre64 solving this thing in real time.

Answer 26

Hmm, but which are you ¬_¬

Answer 27

You are 76?

Answer 28

yes.

Answer 29

But you can integrate x^2, right?

Answer 30

if i had done this with pencil and paper i would have been done long time ago.... but trying to remember which keys to press is a challange

Answer 31

I graduated in the lower 1/3 of my class at San Jose State College as a Math major.
I cannot remember all of the rules. Rather I'm using software developed by a group of World class mathematicians and computer programmers.

Using Mathematic 8. The installation "file" is about 3Gb in size.
By the way, Wolfram practically gives their system to students and acedemics.

Answer 32

Hmm, intriguing.

I personally find it easier to learn the rules than to learn what format to type things into Wolfram|Alpha (though maybe Mathematica is slightly easier to use). Can of course be useful at times, though.

Answer 33

i just make up my own rules half the time, and guess at the the rest :)

Answer 34

Got to go now. Thanks for the exchange.