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math456

  • 3 years ago

a) If P is the point (15,250) on the graph of V, find the slopes of the secant lines PQ when Q is the point on the graph with t=5,10,20,25 & 30; a) Estimate the slope of the tangent line at P by averaging the slopes of two secant lines.

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  1. math456
    • 3 years ago
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    |dw:1347078037836:dw|

  2. Hero
    • 3 years ago
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    Have you graphed the function yet?

  3. math456
    • 3 years ago
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    yea as the time increases the volume decreases!

  4. Hero
    • 3 years ago
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    Okay, so where are you stuck with this? You have two points P = (15,250) and Q = (20, 111). Use the slope formula and find the slope of PQ

  5. math456
    • 3 years ago
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    y did u picked the time 20?

  6. Hero
    • 3 years ago
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    Because it is the next point P = (15,250) Q = (20,111) R = (25,28) Get it?

  7. math456
    • 3 years ago
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    okay so i thought we hv to pick the closest point to 15

  8. math456
    • 3 years ago
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    so is the slope -27.8?

  9. Hero
    • 3 years ago
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    I will assume you have calculated it correctly

  10. math456
    • 3 years ago
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    okay so how do i find the other part of this question?

  11. Hero
    • 3 years ago
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    Find the slope of Point PR

  12. math456
    • 3 years ago
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    -22.2

  13. Hero
    • 3 years ago
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    Okay, now find the average of both both slopes

  14. math456
    • 3 years ago
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    how? by subtracting them?

  15. Hero
    • 3 years ago
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    then dividing by 2

  16. math456
    • 3 years ago
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    -2.8?

  17. Hero
    • 3 years ago
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    That's not what I got

  18. math456
    • 3 years ago
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    like: -27.8-(-22.2)/2

  19. Hero
    • 3 years ago
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    No, not like that

  20. math456
    • 3 years ago
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    is it -25?

  21. Hero
    • 3 years ago
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    Yes

  22. math456
    • 3 years ago
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    great so this the slope of the tangent line at P!

  23. Hero
    • 3 years ago
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    It's an "estimate"

  24. math456
    • 3 years ago
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    lastly how do i use a graph of the function to estimate the slope of the tangent line at P?

  25. math456
    • 3 years ago
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    (This slope represents the rate at which the water is flowing form the tank after 15 mins)

  26. Hero
    • 3 years ago
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    I would use rise over run to find the slope.

  27. math456
    • 3 years ago
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    u mean delta y/delta x?

  28. Hero
    • 3 years ago
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    I don't know what kind of answer they expect from you however. Yes, delta y/delta x if you want to say it that way.

  29. math456
    • 3 years ago
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    hmm in this case how can I find my delta y/x values?

  30. Hero
    • 3 years ago
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    By using points on the tangent line. You have to find them for yourself.

  31. Hero
    • 3 years ago
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    Actually, use the tangent line approxmation formula

  32. math456
    • 3 years ago
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    which is?

  33. Hero
    • 3 years ago
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    Well, that depends on how far along you are.

  34. math456
    • 3 years ago
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    like i can pick (15,250) ; (14.09, 249.99)

  35. Hero
    • 3 years ago
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    On second thought, you don't need tangent line approximation formula. You just need graph paper, really.

  36. math456
    • 3 years ago
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    |dw:1347079571561:dw|

  37. Hero
    • 3 years ago
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    Graph the points on graph paper, draw a smooth curve through them, then take a ruler and draw a tangent line through point P and through the x-axis

  38. Hero
    • 3 years ago
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    Then you will have two points on the tangent line. Use those two points to find the slope

  39. math456
    • 3 years ago
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    |dw:1347079627933:dw| something like this

  40. Hero
    • 3 years ago
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    Yeah, something like that. But use graph paper.

  41. math456
    • 3 years ago
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    okay

  42. Hero
    • 3 years ago
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    Use the good kind with the smaller squares.

  43. math456
    • 3 years ago
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    okay and after doing it lets say my values are 14.009 and 249.001

  44. math456
    • 3 years ago
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    i just divide them out?

  45. Hero
    • 3 years ago
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    I just told you what to do. Now you have just came up with random values that don't mean anything.

  46. math456
    • 3 years ago
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    alright well thanks for your help. I appreciate it..

  47. Hero
    • 3 years ago
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    Should I repeat the steps again?

  48. math456
    • 3 years ago
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    no its fine thank you once i come up with the accurate values i will ask u again.!

  49. Hero
    • 3 years ago
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    1. Get some graph paper 2. Plot the points you were given on an xy plane 3. Draw a smooth curve through them 4. Draw a tangent line through point P and the x-axis 5. Take those two points and find the slope of the tangent line.

  50. math456
    • 3 years ago
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    thanks ^^

  51. Hero
    • 3 years ago
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    When I say draw tangent line, I mean a straight line using a ruler

  52. Hero
    • 3 years ago
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    If your line goes through the y-axis, you can use that too. Try to set up your xy axes in a way where your points are convenient to calculate.

  53. math456
    • 3 years ago
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    okay, gotch ya..

  54. math456
    • 3 years ago
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    |dw:1347081039622:dw| so this is how it looks like on my graph paper

  55. Hero
    • 3 years ago
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    Well, you can't really draw the line without a curve. That's why you need the other points AND the curve drawn through them first.

  56. math456
    • 3 years ago
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    |dw:1347081239380:dw| a lil more like this!

  57. Hero
    • 3 years ago
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    Well, I'm sure you're getting the hang of it. All you have to do is find a point on the line that goes through one of the intersections on the graph paper and use that point as your second point for a more accurate measure of slope. It's a pretty intuitive thing if you know what you're doing.

  58. math456
    • 3 years ago
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    yea i am finding the values now. and i hope i found the precise one!

  59. Hero
    • 3 years ago
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    You already know what it should be close to.

  60. math456
    • 3 years ago
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    yea

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