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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.

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  1. Curry
    • one year ago
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    So 16 = a(4)^2 - b4 -c and 48 = a(10)^2 -b(10) - c

  2. Curry
    • one year ago
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    Correction, 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.

  3. Curry
    • one year ago
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    you 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.

  4. anonymous
    • one year ago
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    yeah Im so lost I don't even know what this means :(

  5. anonymous
    • one year ago
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    @Curry

  6. anonymous
    • one year ago
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    do you still need help?

  7. anonymous
    • one year ago
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    yes!

  8. anonymous
    • one year ago
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    ok so can you tell me what the general form of a quadratic function is?

  9. anonymous
    • one year ago
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    if not thats ok, i need to see what you know and what you dont

  10. anonymous
    • one year ago
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    I don't

  11. anonymous
    • one year ago
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    ok, 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

  12. anonymous
    • one year ago
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    |dw:1433582094129:dw|

  13. anonymous
    • one year ago
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    those two are equivalent, the one on the left is a way of writing it that we can easily type with a keyboard

  14. anonymous
    • one year ago
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    so like a= 1/2 b= -2 c= 18 this is what I got so far

  15. anonymous
    • one year ago
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    ok so if a = 1/2 b = -2 and c = 18 then what would the general form look like?

  16. anonymous
    • one year ago
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    1/2x^2+(-2x)+18?

  17. anonymous
    • one year ago
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    perfect

  18. anonymous
    • one year ago
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    and simplying you get 1/2x^2 - 2x + 18

  19. anonymous
    • one year ago
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    ok good i think you are ready to set up the problem

  20. anonymous
    • one year ago
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    ok 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

  21. anonymous
    • one year ago
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    does this make sense?

  22. anonymous
    • one year ago
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    so you will input the number of widgets, x, into the function and the output will be the cost, c(x)

  23. anonymous
    • one year ago
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    does all of this make sense so far?

  24. anonymous
    • one year ago
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    can you set it up for me this is a little confusing

  25. anonymous
    • one year ago
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    you should set it up, so that when you are taking a test, you can do it yourself

  26. anonymous
    • one year ago
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    cost = c(x) = output number of widgets = x = input

  27. anonymous
    • one year ago
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    cost is the same thing as c(x) number of widgets is the same thing as x

  28. anonymous
    • one year ago
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    ok so lets start with the first example

  29. anonymous
    • one year ago
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    they said the cost was 16, so can you plug the 16 into this equation? c(x) = ax^2 + bx + c

  30. anonymous
    • one year ago
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    so c(x) = 16x^2 -2x +18

  31. anonymous
    • one year ago
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    no remember cost is the same thing as c(x)

  32. anonymous
    • one year ago
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    if cost is 16 and cost is c(x) what is c(x)?

  33. anonymous
    • one year ago
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    16

  34. anonymous
    • one year ago
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    perfect, so c(x) = 16 lets plug it in

  35. anonymous
    • one year ago
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    c(x) = ax^2 + bx + c now im plugging in c(x) = 16 16 = ax^2 + bx + c

  36. anonymous
    • one year ago
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    ok yes that makes sense

  37. anonymous
    • one year ago
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    good

  38. anonymous
    • one year ago
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    so now remember widgets is the same thing as x, and it says it costs 16 to produce 4 widgets

  39. anonymous
    • one year ago
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    so we have 16 = ax^2 + bx + c can you plug 4 in here in the correct place?

  40. anonymous
    • one year ago
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    x is the number of widgets the number of widgets is 4 so x must be?

  41. anonymous
    • one year ago
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    and what about a b and c?

  42. anonymous
    • one year ago
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    dont worry about those yet

  43. anonymous
    • one year ago
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    step by step

  44. anonymous
    • one year ago
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    so whats our equation look like now?

  45. anonymous
    • one year ago
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    16=a(4)^2 -2(4) +18?

  46. anonymous
    • one year ago
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    perfect

  47. anonymous
    • one year ago
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    ok now set up another equatoin in the exact same way, with the other information cost is 48 to produce 10 widgets

  48. anonymous
    • one year ago
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    oh actually that last one should be 16 = a(4)^2 + b(4) + c sorry

  49. anonymous
    • one year ago
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    yes I thought so too

  50. anonymous
    • one year ago
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    can you set up the other equatoin now?

  51. anonymous
    • one year ago
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    cost is 48 to produce 10 widgets, plug the given values into the equation c(x) = ax^2 + bx + c

  52. anonymous
    • one year ago
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    48= a(10^2) -b(10) +c

  53. anonymous
    • one year ago
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    very close, except its +b(10) not -b(10)

  54. anonymous
    • one year ago
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    sorry I got mixed up because b is -2

  55. anonymous
    • one year ago
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    ok perfect so we have these two equations: 16 = a(4)^2 + b(4) + c 48 = a(10)^2 + b(10) + c

  56. anonymous
    • one year ago
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    all good

  57. anonymous
    • one year ago
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    can you simplify those two equatoins?

  58. anonymous
    • one year ago
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    I don't know how

  59. anonymous
    • one year ago
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    ok i will do one you do the other

  60. anonymous
    • one year ago
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    16 = 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

  61. anonymous
    • one year ago
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    alright that was too easy all you did was square the 4

  62. anonymous
    • one year ago
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    exactly

  63. anonymous
    • one year ago
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    ok so we have these two equations: 16a + 4b + c = 16 100a + 10b + c = 48

  64. Curry
    • one year ago
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    well actually, hold on.

  65. anonymous
    • one year ago
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    48= a(10^2) +b10 +c 48= a100 +b10 +c

  66. anonymous
    • one year ago
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    perfect :)

  67. anonymous
    • one year ago
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    so now we have the two equations that @Curry posted in the first post

  68. anonymous
    • one year ago
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    so 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?

  69. anonymous
    • one year ago
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    nope

  70. Curry
    • one year ago
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    wait, are we missing the initial condition value?

  71. Curry
    • one year ago
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    that's only 2 equations. we have three unknowns.

  72. Curry
    • one year ago
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    hey @billj5, i calculated it ignoring the c too. And i got 36.2 as i posted earlier.

  73. Curry
    • one year ago
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    But 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

  74. anonymous
    • one year ago
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    ok are you still here sarah?

  75. anonymous
    • one year ago
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    brb i need to grab something to eat

  76. anonymous
    • one year ago
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    let me know if you are still here sarah and we can finish the problem

  77. anonymous
    • one year ago
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    yes

  78. anonymous
    • one year ago
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    ok great, are you familiar with solving systems of equations?

  79. anonymous
    • one year ago
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    yes!

  80. anonymous
    • one year ago
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    since 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?

  81. anonymous
    • one year ago
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    so we have these two equations: 16a + 4b = 16 100a + 10b = 48 so can you solve that system for a and b?

  82. anonymous
    • one year ago
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    @Curry you brought up a good point, sorry, I think we can assume c = 0

  83. anonymous
    • one year ago
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    let me know the values you get for a and b

  84. anonymous
    • one year ago
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    ok so what do I solve for a?

  85. anonymous
    • one year ago
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    you solve the system of those 2 equations for a and b

  86. Curry
    • one year ago
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    ye, 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.

  87. anonymous
    • one year ago
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    yes, i agree @Curry

  88. anonymous
    • one year ago
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    sarah please let me know what you get for the values of a and b

  89. anonymous
    • one year ago
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    a=-b/4+1 b=-4a+4 now the seconf one

  90. anonymous
    • one year ago
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    yes what you wrote is correct, however you need to find the number value for both a and b

  91. anonymous
    • one year ago
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    are you familiar with solving systems of equations by substitution or elimination or both?

  92. anonymous
    • one year ago
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    hey 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

  93. anonymous
    • one year ago
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    well i think @Curry posted the answer above

  94. anonymous
    • one year ago
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    i didnt check if it was correct though

  95. anonymous
    • one year ago
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    can you check and tell me because this test is gonna end and I need to pass. then we can continue learning

  96. anonymous
    • one year ago
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    what did he say was the answer?

  97. anonymous
    • one year ago
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    it was wrong... I failed.. and its 3 am im tired im just gonna cut and go to sleep ;c

  98. anonymous
    • one year ago
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    fill in

  99. Curry
    • one year ago
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    problem with rounding probably...

  100. Curry
    • one year ago
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    unless they assumed a value for c or something.

  101. math&ing001
    • one year ago
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    @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

  102. anonymous
    • one year ago
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    @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

  103. math&ing001
    • one year ago
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    Here 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.

  104. anonymous
    • one year ago
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    @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

  105. math&ing001
    • one year ago
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    I'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.

  106. anonymous
    • one year ago
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    @math&ing001, no you are giving wrong information, but thank you

  107. math&ing001
    • one year ago
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    Just 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 !

  108. anonymous
    • one year ago
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    @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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