can anyone answer this?
the company discovered that it costs $45 to produce 2 calculators, $143 to produce 4 calculators and $869 to produce 10 calculators. find the cost of producing 7 calculators. use the quadratic function to solve

- anonymous

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- amistre64

we can formulate a "slope" with the ratios provided I believe

- amistre64

45/2
143/4
869/10
might help ....

- amistre64

k2x = 45
k4x = 143
k10x = 869 ...
or maybe plot the points on a graph and find a quadratic that matches the points?

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## More answers

- amistre64

does it come with a quadratic function for us to use?

- anonymous

i could find out but i would have to close the assignment to open another and it may not come up with the same question

- amistre64

sounds like mathLab...

- anonymous

it's through plato. i do all online courses for school.

- amistre64

if it doesnt provide a quadratic to begin with, you probably have to use this data to construct one.....

- amistre64

A(2^2) +B(2) +C = 45
A(4^2) +B(4) +C = 143
something like that

- amistre64

The ABC that are normally constants become the "variables" to find... in a system of equations

- anonymous

thanks but someone already helped me figure it out (:

- amistre64

yay!! ... howd they do it?

- anonymous

i really don't know. they just gave me the equation and what to plug in and that gave me the answer. now 4 more questions to go!!
After a second, the rock is 58 feet in the air; after two seconds , it is 112 feet in the air. find the height, in feet, of the rock after 10 seconds.

- amistre64

ahhh... instead of teaching youto fish, they simply gave you a fish....

- anonymous

basically.

- amistre64

the rock question usually comes with a formula for the effect of gravity on an object....

- amistre64

is this a physics quiz or a math quiz? the difference being of course that physics wants youto apply a formula, and math wants you to figure out the formula...

- anonymous

it's algebra 2

- amistre64

Newtons here, hes gravity based I think :)

- anonymous

I answered it, and for the record, 'amistre64' I tried for a considerable amount of time to give hints without the answer (and a full method is there anyway, if someone has time to read my entire posts...)

- amistre64

Newton, kudos then :) I recant my fishy commentary :)

- anonymous

I'll carry on the answer to the gravity one in here then, rather than clog up this place; for the record, are we taking g = 10 or 9.8 or what?

- anonymous

what do you mean

- anonymous

I believe it it impossible to find an answer if the solution is from a general quadratic Distance = ax^2 + bx + c (but if I am wrong someone say), so we need to simplify it. either we assume it started on the ground (c=0), or assume the value of g.

- anonymous

it says "rock launched from cannon"

- anonymous

OK, if we assumed it was from the ground, we can use the equation:
s = ut - (1/2)at^2, or in this case
height = (initial speed)*t - (g/2)t^2
Using this we can form two equations from the given information:
58 = u(1) - g/2(1^2) => 58 = u - g/2
112 = (u)2 - g/2(2^2) => 112 = 2u - 2g
We can find g and u from this, and use them in the eqation:
height = u(10) - (g/2)(10^2) for time = 10. Try it

- anonymous

This gives a wildy inaccurate value of g, though, so I am unsure if it was the intention. See if you can get an answer and check if it is what they wanted; if not, post back.

- anonymous

i got 544 but it was wrong

- anonymous

next queston;
the company discovered that it costs $45 to produce 3 camera cases, $257 to produce 7 camera cases, and $792 to produce 12 camera cases. find the total of one camera case. use the quadratic function to solve.

- anonymous

i think the answer would be 15 for this question

- anonymous

Try 400? If it is right, I will give a much more detailed explanation; if it was wrong I will think of a new plan (if you can still try the rock one)

- anonymous

it only gives me one chance & i have to move on to the next question

- anonymous

Oh OK then. So why do you think this one is 15? What is your method?

- anonymous

Well, I don't think it is 15 (so I wouldn't enter that!)
For this one, you know it is controlled by a general quadratic function, so let this be
cost = ax^2 + bx + c (x = number of cameras)
You can generate equations using the given information:
45 = (3^2)a+3b+c (*)
257 = (7^2)a+7b+c (**)
792=(12^2)a+12b+c (***)
You can solve these equations to give values for a, b and c, and then use cost = ax^2 + bx + c with x = 1 to find the cost of 1 camera.

- anonymous

how do i do that

- anonymous

To start off:
(**) - (*) gives
257 - 45 = (49 - 9)a + (7-3)b => 212 = 40a + 4b
(***) - (**) gives:
792 - 257 = (144-49)a + (12-7)b => 535 = 95a+5b
You now have:
212 = 40a + 4b
535 = 95a+5b
Can you solve these two for a and b? (Then plug these back into (*) for c)

- anonymous

i'm lost on how to got it to this point or how to solve for a and b.

- anonymous

OK - do you see how the question can be used to get the first 3 equations with a, b and c, though? Or not that, either?

- anonymous

yes

- anonymous

if i was to use a graphing calculator, how do i figure it out?

- anonymous

OK. I do not use graphics calculators, but I assume if you plot the points (x,y):
(3,45); (7, 257); (12, 792)
Then it can solve it for y = f(x) = ax^2 + bx + c, with values for a, b and c, which you can use to find f(1).
But really, what I did above is just solving simultaneous equations, which will give you the same answer:
Take one away from the other to eliminate c; do this again; get two equations in only a and b. Then use these to eliminate either a or b (probably b), etc.

- anonymous

i was just seeing which way would be easier and less confusing

- anonymous

i was just seeing which way would be easier and less confusing

- amistre64

less confusing? i didnt think that was possible in math :) but I like newtons way, it just validiates what I was thinking as a solution in me head

- anonymous

i mean when i see what he is doing, i think i understand but then when it comes to doing it on my own, i get lost /:

- amistre64

how good are you at "solving a system of equations"?

- amistre64

either by elimination, substitution, or matrix.... they all amount to the same thing in the end

- anonymous

Yes, as above. Although, personally, I like to avoid matrices unless absolutely necessary!

- amistre64

Matrices can get rather confused if you dont keep track of all your work...so on complicated stuff, id perfer the elimination/substitution as well.

- anonymous

i mean if it was down to where you plug in the annswer, i could do it. but figuring it out to there is completely confusing to me.

- amistre64

9a+3b+c = 45
49a+7b+c = 257
144a+12b+c = 792
What do you "feel" is the first step to solving this system of equations? lets step through it

- anonymous

9a+3b+c = 45 to solve this

- amistre64

ok ... but we can only solve it part way... because we have other variables to consider; but would you agree that:
c = 45 -9a -3b?

- amistre64

we can use this "value" of c to work the other 2 equations with... but first we have to agree that this is a good "value" for c

- anonymous

I think that is probably a better way to go about it if you are explaining how to do it along the way than mine, actually; regardless, they appear to have left us. Ah well.

- amistre64

mighta got booted :) theyll be back... they always come back :)

- amistre64

Just so I can finish the problem.... Ill step through it like this:
c = 45 -9a -3b
substitute the "value" of c into the other 2 equations like this:
---------------------
49a+7b+(45 -9a -3b) = 257
49a +7b +45 -9a -3b = 257
40a +4b +45 = 257
40a +4b = 257 -45
40a + 4b = 212
--------------------
144a+12b+(45 -9a -3b) = 792
144a +12b +45 -9a -3b = 792
135a +9b +45 = 792
135a +9b = 792-45
135a +9b = 747
---------------------
we now have 2 equations to compare:
40a + 4b = 212
135a +9b = 747
lets solve the first one for "b":
40a + 4b = 212 ; divide all by 4
10a+b = 53
b = 53-10a
------------------
Now lets use this "value" of b to solve the other equation by substituting it in:
135a +9(53-10a) = 747
135a + 477 - 90a = 747
135a -90a = 747 -477
45a = 270
a = 270/45 ; reduce this to a=6
a=6
------------------
we know have a "solid" value for "a". lets use that in our equation for "b".
b = 53-10a
b = 53-10(6)
b = 53-60
b = -7
-------------------
with a "solid" value for "a" AND "b"
we can use these in our equation for "c".
-------------------------------
c = 45 -9a -3b
c = 45 -9(6) -3(-7)
c = 45 -54 +21
c = 12
----------------
a=6, b=-7; c=12 .... if I did it all correctly.
So our quadratic equation becomes:
f(x) = ax^2 +bx +c
f(x) = 6x^2 -7x +12

- amistre64

check to see if that works with our "known" values....
6(3)^2 -7(3) +12 = 45
6(9) -21 +12 = 45
54 - 9 = 45
45 = 45 ..... that checks
---------------------
6(7)^2 -7(7) +12 = 257
6(49) - 49 +12 = 257
294 - 37 = 257
257 = 257 ....... checks out so far...
-------------------
6(12)^2 -7(12) +12 = 792
6(144) - 84 + 12 = 792
864 - 72 = 792
792 = 792 .... the equation is GOOD!!! lol

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