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anonymous

  • one year ago

The following function represents the profit P(n), in dollars, that a concert promoter makes by selling tickets for n dollars each: P(n) = -250n^2 + 2,500n - 5,250 Part A: What are the zeroes of the above function, and what do they represent? Show your work.

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  1. anonymous
    • one year ago
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    @SolomonZelman

  2. SolomonZelman
    • one year ago
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    What does n represent?

  3. anonymous
    • one year ago
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    dollars

  4. SolomonZelman
    • one year ago
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    precisely, n, is a price per ticket.

  5. SolomonZelman
    • one year ago
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    What does P(n) represent?

  6. anonymous
    • one year ago
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    profit

  7. SolomonZelman
    • one year ago
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    Yes, when P(n) is 0, that means that the profit is zero (i.e. made nothing), right?

  8. anonymous
    • one year ago
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    yes

  9. SolomonZelman
    • one year ago
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    The x-intercepts of this function are the values of n (or the value of the price per ticket) with which the P(n) (or the profit) is 0. (There are going to be 2 x-intercepts)

  10. anonymous
    • one year ago
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    okay

  11. SolomonZelman
    • one year ago
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    So, if you find the x-intercepts, you are going to find the 2 possible values of a price per ticket with which the promoter will NOT profit (but will not lose).

  12. SolomonZelman
    • one year ago
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    So, do you see what these x-intercepts would mean?

  13. anonymous
    • one year ago
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    yes

  14. SolomonZelman
    • one year ago
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    Ok, now you have to solve for these x-intercepts.

  15. anonymous
    • one year ago
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    the x intercepts are 3 and 7?

  16. SolomonZelman
    • one year ago
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    yes, very good!

  17. SolomonZelman
    • one year ago
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    Perfect!

  18. SolomonZelman
    • one year ago
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    So, when the ticket costs 3$ or 7$ , then the promoter doesn't gain or lose.

  19. anonymous
    • one year ago
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    now what?

  20. SolomonZelman
    • one year ago
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    when the *average* ticket I should say

  21. SolomonZelman
    • one year ago
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    Well, all you had to do is to find these zero (these x-intercepts), and to then say what these x-intercepts represent in your situtation.

  22. SolomonZelman
    • one year ago
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    you found x=3, and x=7 ((( and that is correct ))) now you have to say what do these intercepts mean/do/represent?

  23. SolomonZelman
    • one year ago
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    just say what we have agreed on in the beginning.

  24. anonymous
    • one year ago
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    can you help me with part B?

  25. SolomonZelman
    • one year ago
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    what is part B?

  26. SolomonZelman
    • one year ago
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    I can try my best with it:)

  27. anonymous
    • one year ago
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    Part B: Find the maximum profit by completing the square of the function P(n). Show the steps of your work.

  28. SolomonZelman
    • one year ago
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    Oh, good

  29. SolomonZelman
    • one year ago
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    ``` SIDE - NOTE: Most people would say that this question requires calculus, but in a case of a parabola (a quadratic does not). (this what most people say is a mistake). ``` ALL YOU GOT TO DO: You have to write your P(n) in a vertex form, and the vertex is going to be the maximum.

  30. anonymous
    • one year ago
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    so (5,1000)?

  31. SolomonZelman
    • one year ago
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    Let me see.... i wil be typing, and if it is right I will post the work, and if it is not, then I will ask you to redo it and follow along with me.

  32. SolomonZelman
    • one year ago
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    hope that is fair.

  33. anonymous
    • one year ago
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    yes

  34. SolomonZelman
    • one year ago
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    \(\large\color{black}{ \displaystyle P(n) = -250{\rm n}^2 + 2,500{\rm n} - 5,250 }\) \(\large\color{black}{ \displaystyle P(n) = -250({\rm n}^2 -10{\rm n}) - 5,250 }\) \(\large\color{black}{ \displaystyle P(n) = -250({\rm n}^2 -10{\rm n}+25-25) - 5,250 }\) \(\large\color{black}{ \displaystyle P(n) = -250({\rm n}^2 -10{\rm n}+25)+(-250)(-25) - 5,250 }\) \(\large\color{black}{ \displaystyle P(n) = -250({\rm n}^2 -10{\rm n}+25)+1000 }\) \(\large\color{black}{ \displaystyle P(n) = -250({\rm n}-5)^2+1000 }\)

  35. SolomonZelman
    • one year ago
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    yes, that is correct

  36. SolomonZelman
    • one year ago
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    And quite quick

  37. anonymous
    • one year ago
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    1 graphed it

  38. SolomonZelman
    • one year ago
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    oh, you graphed it... good, but it is very good (I would insist that even required) to know that without graphing.... in any case though, lets do a little review of what you have actually found just now,

  39. anonymous
    • one year ago
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    the axis of symmetry would be 5 right? (Thats part C)

  40. anonymous
    • one year ago
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    okay

  41. SolomonZelman
    • one year ago
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    yes part C is correct

  42. SolomonZelman
    • one year ago
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    now the review of what does the vertex of (5,1000) actually mean in this case.

  43. anonymous
    • one year ago
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    thats the maximum about of profit the promoter can make?

  44. SolomonZelman
    • one year ago
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    that is you are refering to the point to a 5 or a 1000 ?

  45. anonymous
    • one year ago
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    1000 makes more sense 1 think

  46. SolomonZelman
    • one year ago
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    yes

  47. SolomonZelman
    • one year ago
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    and what does 5 mean, can you tell me?

  48. anonymous
    • one year ago
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    the amount the tickets cost?

  49. SolomonZelman
    • one year ago
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    yes

  50. SolomonZelman
    • one year ago
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    So when the average ticket costs 5$, you get a maximum profit of 1000

  51. anonymous
    • one year ago
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    makes sense

  52. SolomonZelman
    • one year ago
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    A quite small, if not miserable profit in a real life situation... but won't be talking about a real life situation because such situations are never modeled with quadratics in real life....

  53. SolomonZelman
    • one year ago
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    yeah, so you got any questions regarding any of the PARTS ?

  54. anonymous
    • one year ago
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    nope thats it

  55. anonymous
    • one year ago
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    as usual you're the most helpful person on the whole site. Thanks!

  56. SolomonZelman
    • one year ago
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    \(\large{\bbox[5pt, cyan ,border:2px solid black ]{ \rm Thanks! }}\)

  57. SolomonZelman
    • one year ago
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    I wouldn't say I am most helpful, but won't deny some use.; you are always welcome!

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