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anonymous
 one year ago
please help! I need to pass algebra to graduate!
widget wonders produces widgets. They have found that the cost, c(x), of making x widgets is a quadratic function in terms of x.
the company also discovered that it cost $16 to produce 4 widgets, ans $48 to produce 10 widgets.
find the total cost of producing 8 widgets.
anonymous
 one year ago
please help! I need to pass algebra to graduate! widget wonders produces widgets. They have found that the cost, c(x), of making x widgets is a quadratic function in terms of x. the company also discovered that it cost $16 to produce 4 widgets, ans $48 to produce 10 widgets. find the total cost of producing 8 widgets.

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Curry
 one year ago
Best ResponseYou've already chosen the best response.2So 16 = a(4)^2  b4 c and 48 = a(10)^2 b(10)  c

Curry
 one year ago
Best ResponseYou've already chosen the best response.2Correction, those minus signs should be positive. so solve for those two equations, and the Cs cancel immediately. so your'e left with 16 =16a+4b. and 48 = 100a+10b.

Curry
 one year ago
Best ResponseYou've already chosen the best response.2you can figure out a and b frmo there, and then you can find c once you have a and b. Lastly, when you have the three constants, (a,b,c), you can just plug in 8 for x into the quadratic eqauation. let me know if you need more help.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yeah Im so lost I don't even know what this means :(

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0do you still need help?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok so can you tell me what the general form of a quadratic function is?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0if not thats ok, i need to see what you know and what you dont

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok, the general form of a quadratic function is this ax^2 + bx + c a = some number that is not 0 b = some number c = some number for example 2x^2 + 5x + 4

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1433582094129:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0those two are equivalent, the one on the left is a way of writing it that we can easily type with a keyboard

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so like a= 1/2 b= 2 c= 18 this is what I got so far

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok so if a = 1/2 b = 2 and c = 18 then what would the general form look like?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and simplying you get 1/2x^2  2x + 18

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok good i think you are ready to set up the problem

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok so now it says the cost, c(x), of making x widgets is quadratic, so lets write it out c(x) = ax^2 + bx + c x is the input of the function, c(x) is the output of the function

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0does this make sense?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so you will input the number of widgets, x, into the function and the output will be the cost, c(x)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0does all of this make sense so far?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0can you set it up for me this is a little confusing

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0you should set it up, so that when you are taking a test, you can do it yourself

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0cost = c(x) = output number of widgets = x = input

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0cost is the same thing as c(x) number of widgets is the same thing as x

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok so lets start with the first example

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0they said the cost was 16, so can you plug the 16 into this equation? c(x) = ax^2 + bx + c

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so c(x) = 16x^2 2x +18

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0no remember cost is the same thing as c(x)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0if cost is 16 and cost is c(x) what is c(x)?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0perfect, so c(x) = 16 lets plug it in

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0c(x) = ax^2 + bx + c now im plugging in c(x) = 16 16 = ax^2 + bx + c

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok yes that makes sense

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so now remember widgets is the same thing as x, and it says it costs 16 to produce 4 widgets

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so we have 16 = ax^2 + bx + c can you plug 4 in here in the correct place?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0x is the number of widgets the number of widgets is 4 so x must be?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and what about a b and c?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dont worry about those yet

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so whats our equation look like now?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.016=a(4)^2 2(4) +18?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok now set up another equatoin in the exact same way, with the other information cost is 48 to produce 10 widgets

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh actually that last one should be 16 = a(4)^2 + b(4) + c sorry

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes I thought so too

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0can you set up the other equatoin now?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0cost is 48 to produce 10 widgets, plug the given values into the equation c(x) = ax^2 + bx + c

anonymous
 one year ago
Best ResponseYou've already chosen the best response.048= a(10^2) b(10) +c

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0very close, except its +b(10) not b(10)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0sorry I got mixed up because b is 2

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok perfect so we have these two equations: 16 = a(4)^2 + b(4) + c 48 = a(10)^2 + b(10) + c

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0can you simplify those two equatoins?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok i will do one you do the other

anonymous
 one year ago
Best ResponseYou've already chosen the best response.016 = a(4)^2 + b(4) + c simplifies to this: 16 = a(16) + b(4) + c written in a standard way looks like this: 16 = 16a + 4b + c

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0alright that was too easy all you did was square the 4

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok so we have these two equations: 16a + 4b + c = 16 100a + 10b + c = 48

anonymous
 one year ago
Best ResponseYou've already chosen the best response.048= a(10^2) +b10 +c 48= a100 +b10 +c

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so now we have the two equations that @Curry posted in the first post

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so now we have to find the values of a, b, and c that make those two equations true, do you know how to do that?

Curry
 one year ago
Best ResponseYou've already chosen the best response.2wait, are we missing the initial condition value?

Curry
 one year ago
Best ResponseYou've already chosen the best response.2that's only 2 equations. we have three unknowns.

Curry
 one year ago
Best ResponseYou've already chosen the best response.2hey @billj5, i calculated it ignoring the c too. And i got 36.2 as i posted earlier.

Curry
 one year ago
Best ResponseYou've already chosen the best response.2But strictly speaking, we can't jsut assume that c is 0. if you did, then yes, you can just ignore c. and the answer would be 36.2

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok are you still here sarah?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0brb i need to grab something to eat

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0let me know if you are still here sarah and we can finish the problem

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok great, are you familiar with solving systems of equations?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0since this is a cost function and they didnt give us any information about initial cost before you take into account the number of widgets, lets assume that c = 0 ok?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so we have these two equations: 16a + 4b = 16 100a + 10b = 48 so can you solve that system for a and b?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@Curry you brought up a good point, sorry, I think we can assume c = 0

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0let me know the values you get for a and b

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok so what do I solve for a?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0you solve the system of those 2 equations for a and b

Curry
 one year ago
Best ResponseYou've already chosen the best response.2ye, that's what i did too. Assumed c = 0. This is a bad problem, considering they didn't give us an initial condition. Hence, we're basically forced to omit C. which defeats half the purpose of a quadratic equation.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0sarah please let me know what you get for the values of a and b

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0a=b/4+1 b=4a+4 now the seconf one

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes what you wrote is correct, however you need to find the number value for both a and b

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0are you familiar with solving systems of equations by substitution or elimination or both?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0hey im running out of time can you tell me the answer and then we can continue working on it so I can learn? and no im not familiar with those

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0well i think @Curry posted the answer above

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i didnt check if it was correct though

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0can you check and tell me because this test is gonna end and I need to pass. then we can continue learning

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0what did he say was the answer?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0it was wrong... I failed.. and its 3 am im tired im just gonna cut and go to sleep ;c

Curry
 one year ago
Best ResponseYou've already chosen the best response.2problem with rounding probably...

Curry
 one year ago
Best ResponseYou've already chosen the best response.2unless they assumed a value for c or something.

math&ing001
 one year ago
Best ResponseYou've already chosen the best response.0@Curry @billj5 Here the c is the cost we're looking for. A quadratic equation looks like this ax^2+bx+c=0 hence c=ax^2+bx Since c is a function of x, we can write it like this c(x)=ax^2+bx. The rest is pretty much what you said: 16a + 4b = 16 100a + 10b = 48 When solved you get a=2/15 and b=54/15 Calculating the cost for 8 widgets: c(8) = 2/15 * 8^2 + 54/15 * 8 = $37.33

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@math&ing001, b is 52/15 and c is not the cost we are looking for, c(x) is the cost we are looking for, c is a constant in the quadratic function which is not what we are looking for, also, if you did what you said it would be c=ax^2+bx not c=ax^2+bx

math&ing001
 one year ago
Best ResponseYou've already chosen the best response.0Here the c is not a constant and is a function of x hence the notation c(x). You're right b=52/15 which makes it $36.27. As for the minus sign, because it's a variable, writing c or c is absolutely the same.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@math&ing001, no you are confusing c in the general form of a quadratic which is a constant term and c(x) which is the function itself, and c is not the same as c

math&ing001
 one year ago
Best ResponseYou've already chosen the best response.0I'm just trying to teach you something new, but if you're not open to learning then there's not much I can do about it.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@math&ing001, no you are giving wrong information, but thank you

math&ing001
 one year ago
Best ResponseYou've already chosen the best response.0Just because you don't understand it, doesn't make it wrong. Anyways, I'm not going to keep this conversation going, it's not taking us anywhere. Have a good day !

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@math&ing001, please have any of the mods come in here and verify what you are saying.. i promise that you are wrong, and im very open to learning by the way
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