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anonymous

  • one year ago

HI

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  1. Hero
    • one year ago
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    Well, actually, it seems that you've made at least one mistake in your computation. But the overall approach appears to be correct.

  2. Hero
    • one year ago
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    Let's go over it step by step using an example.

  3. Hero
    • one year ago
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    Suppose you have \(-y^2\) And \(y = 6\) What value is \(-y^2\) equal to?

  4. Hero
    • one year ago
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    Yes. Correct. Now you must ask yourself if your approach here is consistent with what you did above.

  5. Hero
    • one year ago
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    There's one way to know for sure if it is correct.

  6. Hero
    • one year ago
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    Yes, but you want to know if what you've done is correct, right?

  7. Hero
    • one year ago
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    Graph to check: https://www.desmos.com/calculator/kuypcivoou

  8. Hero
    • one year ago
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    What do you think it means?

  9. Hero
    • one year ago
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    Mind sharing what you think it means?

  10. Hero
    • one year ago
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    Actually (x,y) = (25, 361) What the question wants us to do is describe the relationship between the x and y values for the vertex in terms of what is stated in the problem.

  11. Hero
    • one year ago
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    The first thing you should do is go back and ask yourself what x and f(x) represent.

  12. Hero
    • one year ago
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    Exactly, so now in a single sentence, interpret the values of x = 25 and f(x) = 361 in terms of what each represents.

  13. Hero
    • one year ago
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    You're on the right track, but do it in a way that shows the relationship. Say it this way: The yoga studio made $361 in profit for the 25 members it processed in its current month.

  14. Hero
    • one year ago
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    And yes, add "maximum profit" in that sentence as well. You were right with that.

  15. Hero
    • one year ago
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    To find the x-intercepts, simply replace f(x) with zero, then solve for x.

  16. Hero
    • one year ago
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    I'm sure you can figure this out on your own if you made it that far.

  17. Hero
    • one year ago
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    Looks right.

  18. Hero
    • one year ago
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    Now you have to ask yourself if both values for x make sense.

  19. Hero
    • one year ago
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    If one of them doesn't make sense, you're supposed to discard that value.

  20. Hero
    • one year ago
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    Does x = 6 make sense as well?

  21. Hero
    • one year ago
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    Explain

  22. Hero
    • one year ago
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    Remember, the x and y values always come in pairs. In this case we have (x,y) = (6,0)

  23. Hero
    • one year ago
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    How much profit was made from the six memberships?

  24. Hero
    • one year ago
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    Well, in this case, there is a plausible explanation for the six memberships.

  25. Hero
    • one year ago
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    If we assume that this is the first month of operation for the yoga studio since its grand opening, as part of its advertisement, the yoga studio could have stated something like, "The first six customers get a free membership".

  26. Hero
    • one year ago
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    It's a bit of a stretch, but it's a plausible explanation.

  27. Hero
    • one year ago
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    The other plausible explanation is that the first six members represent the original team who put the business together in the first place so of course they don't make any money off themselves.

  28. Hero
    • one year ago
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    The question says to explain each value in the context of the problem. We already know there's no such thing as negative members. That is impossible. However, for x = 6, for this particular problem we can't make sense of it either unless we come up with plausible explanations such as what I posted above. That's all you can do for this question.

  29. Hero
    • one year ago
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    Actually, the other point is (44,0) so you must have made a sign mistake somewhere.

  30. Hero
    • one year ago
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    https://www.desmos.com/calculator/mebdvn94g7

  31. anonymous
    • one year ago
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    really?

  32. anonymous
    • one year ago
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    ohh ok i see my mistake!

  33. Hero
    • one year ago
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    Yes, really. Which basically makes it a bit more difficult to explain why they have no profit after gaining 44 members.

  34. anonymous
    • one year ago
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    oh gosh

  35. anonymous
    • one year ago
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    They could have had a raffle and chose 44 people to get a free membership?

  36. Hero
    • one year ago
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    No, according to the graph, after 25 members, they start losing profits, so we have to explain in terms of that.

  37. anonymous
    • one year ago
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    ugh i have no clue >:(

  38. Hero
    • one year ago
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    The plausible explanation is that the studio can support up to 25 members at a time. If they have more than 25 members, then they have to rent more building space, purchase more equipment, etc.

  39. Hero
    • one year ago
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    Which causes them to lose the profits they gained. We should assume that the business is a small startup.

  40. anonymous
    • one year ago
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    oh ok

  41. anonymous
    • one year ago
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    Thank you so much for your time!

  42. Hero
    • one year ago
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    You're most welcome. Great job on this one.

  43. Hero
    • one year ago
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    I cannot help you with anymore questions.

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spraguer (Moderator)
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