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anonymous

  • one year ago

The cost to produce a product is modeled by the function f(x) = 5x2 − 70x + 258 where x is the number of products produced. Complete the square to determine the minimum cost of producing this product. 5(x − 7)2 + 13; The minimum cost to produce the product is $13. 5(x − 7)2 + 13; The minimum cost to produce the product is $7. 5(x − 7)2 + 258; The minimum cost to produce the product is $7. 5(x − 7)2 + 258; The minimum cost to produce the product is $258.

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  1. anonymous
    • one year ago
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    @Nnesha

  2. Nnesha
    • one year ago
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    Hey, do you know how to `complete the square` ?

  3. anonymous
    • one year ago
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    Barley

  4. Nnesha
    • one year ago
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    oh alright \[\huge\rm f(x)= 5x^2 − 70x + 258 \] this is our equation where a b ,c values are \[\rm Ax^2+Bx+C=0\] a=leading coefficient b=middle term c=constant term we need to complete the square of (5x^2+70x) \[(5x^2+70x)+258\]

  5. Nnesha
    • one year ago
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    first of all take out the common factor from (5x^2+70x) what is common factor(just common number not varaible ) ?

  6. anonymous
    • one year ago
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    2?

  7. Nnesha
    • one year ago
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    nope

  8. Nnesha
    • one year ago
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    \[\huge\rm \color{Red}{5}x^2+\color{reD}{70}x\] 5 isn't divisible by 2

  9. anonymous
    • one year ago
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    Oh, sorry, I mixed that up with something else. So, then what 5?

  10. Nnesha
    • one year ago
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    yes right take out the 5 from both terms 5x^2 and 70x\[5(??+??)\]

  11. anonymous
    • one year ago
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    would you divide 70 by 5?

  12. Nnesha
    • one year ago
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    when you take out 5 from 5 what would you get ?

  13. anonymous
    • one year ago
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    0

  14. Nnesha
    • one year ago
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    in other words divide both terms by common factor |dw:1441211901863:dw| what do you get when yo udivide 5 x^2 by 5 and 70x/5 = ? write ur answer in the parentheses

  15. anonymous
    • one year ago
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    5(x^2 +14)+258?

  16. Nnesha
    • one year ago
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    yes right!!

  17. Nnesha
    • one year ago
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    wait you forgot x

  18. Nnesha
    • one year ago
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    \(\color{blue}{\text{Originally Posted by}}\) @gigirained 5(x^2 +14)+258? \(\color{blue}{\text{End of Quote}}\) 5(x^2 +14x)+258 like this

  19. anonymous
    • one year ago
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    Oh alright

  20. Nnesha
    • one year ago
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    now to complete the square divide b/2 and then take square of (b/2)^2

  21. Nnesha
    • one year ago
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    i'll give you an example \[\huge\rm x^2+Bx+C=0\] \[\rm (x +\frac{ b }{ 2})^2 -(\frac{ b }{ 2})^2+C=0\] like this b = middle term

  22. Nnesha
    • one year ago
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    what's the middle term in that equation ?

  23. anonymous
    • one year ago
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    14?

  24. Nnesha
    • one year ago
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    yes right divide 14 by 2 then take square root of the result

  25. Nnesha
    • one year ago
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    \[\huge\rm 5(x-\frac{ 14 }{ 2 })^2-(\frac{ 14 }{ 2 })^2 +258\]

  26. anonymous
    • one year ago
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    5(x-7)^2 - 7^2 +258

  27. Nnesha
    • one year ago
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    i just noticed it supposed to be negative 14x cux in the original equation 70x is negative

  28. anonymous
    • one year ago
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    Okay

  29. Nnesha
    • one year ago
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    yes right! 7^2 = ?

  30. anonymous
    • one year ago
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    49

  31. anonymous
    • one year ago
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    do we do anything with 258?

  32. Nnesha
    • one year ago
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    hmm wait

  33. Nnesha
    • one year ago
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    ohh yeah we have common factor we have to multiply (b/2)^2 with 5

  34. Nnesha
    • one year ago
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    \[\huge\rm \color{Red}{5}(x-7)^2-[(7)^2\times \color{ReD}{5}] +258\]we should multiply (b/2)^2 wth the common factor

  35. anonymous
    • one year ago
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    would we multiply 7 by 5 for 49 by 5

  36. Nnesha
    • one year ago
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    first take square of 7 then multiply by 5

  37. anonymous
    • one year ago
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    245

  38. Nnesha
    • one year ago
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    yes right now combine like terms \[5(x-7)^2\color{Red}{-245+258}\]

  39. anonymous
    • one year ago
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    5(x-7)^2 + 13

  40. Nnesha
    • one year ago
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    then you will get vertex form equation of parabola \[\huge\rm y=a(x-h)^2+k\] where (h,k) is the vertex if a is positive then you wll get minimum point (h,k) if a is negative you will get maximum point (h,k) (h,k) where h represents x-coordinate and k represents y -coordinate cost usually represents by y -coordinate

  41. Nnesha
    • one year ago
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    yes right

  42. Nnesha
    • one year ago
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    done!

  43. anonymous
    • one year ago
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    So, i dont know which one, A or B @Nnesha

  44. Nnesha
    • one year ago
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    reread my my comment again which coordinate represent cost ?

  45. Nnesha
    • one year ago
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    what's the vertex point ?

  46. anonymous
    • one year ago
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    7

  47. anonymous
    • one year ago
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    well, the answer i got was b

  48. Nnesha
    • one year ago
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    that's one h what is k ?

  49. anonymous
    • one year ago
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    13

  50. anonymous
    • one year ago
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    ?

  51. Nnesha
    • one year ago
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    yes right (h,k) = (7,13) where y -coordinate represent cost

  52. anonymous
    • one year ago
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    how do i find the y-coordinate

  53. Nnesha
    • one year ago
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    (x,y) is same as (h,k) first number is x-coordinate 2nd one is y-coordinate

  54. anonymous
    • one year ago
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    oh lol never mind

  55. anonymous
    • one year ago
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    That went right over my head haha

  56. Nnesha
    • one year ago
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    in other words k represent cost in this question

  57. anonymous
    • one year ago
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    Thank you so much!

  58. Nnesha
    • one year ago
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    np :)

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