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anonymous

  • one year ago

grr

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  1. Michele_Laino
    • one year ago
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    we know that your function has to be a polynomial of degree 2 from your drawing we see that x=6 and x=-6 are two zeroes of the requested polynomial

  2. anonymous
    • one year ago
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    Oh! So would it be -1(x+6)(x-6) ??

  3. Michele_Laino
    • one year ago
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    the simpler polynomial which satisfies those requisites is: \[y = \left( {x - 6} \right)\left( {x + 6} \right)\] even if, we have to check if my function contains the point (0,36) does my function pass at point (0,36)?

  4. Michele_Laino
    • one year ago
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    yes! that's right!

  5. anonymous
    • one year ago
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    Ok so then I got -x^2+36?

  6. Michele_Laino
    • one year ago
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    correct!

  7. anonymous
    • one year ago
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    There is a 2nd part to this question, I'm not getting

  8. anonymous
    • one year ago
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    I know, I'm lost too:)

  9. Michele_Laino
    • one year ago
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    you have to create a table for a straight line like this one: |dw:1438706644480:dw|

  10. Michele_Laino
    • one year ago
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    step#1 please chose two point on your rainbow

  11. Michele_Laino
    • one year ago
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    oops.. choose*

  12. anonymous
    • one year ago
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    um 3?

  13. Michele_Laino
    • one year ago
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    you have to choose 2 values for x-coordinate

  14. Michele_Laino
    • one year ago
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    between -6 and 6

  15. anonymous
    • one year ago
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    oh okay then 5

  16. Michele_Laino
    • one year ago
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    x1=5 and x2=?

  17. anonymous
    • one year ago
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    11?

  18. Michele_Laino
    • one year ago
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    no, your value has to be less than 6 and grater than -6

  19. Michele_Laino
    • one year ago
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    x=5 is right! the other value can be x=2

  20. Michele_Laino
    • one year ago
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    what do you think?

  21. anonymous
    • one year ago
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    yes, i agree

  22. Michele_Laino
    • one year ago
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    ok!

  23. Michele_Laino
    • one year ago
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    now we have to compute the corresponding y-value, so, if x=5 then: y=-5^2+36=-25+36=11

  24. Michele_Laino
    • one year ago
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    whereas if x=1, then: y=-1^2+25=...?

  25. anonymous
    • one year ago
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    I see, I see:)

  26. anonymous
    • one year ago
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    24

  27. Michele_Laino
    • one year ago
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    sorry if x=1, then: y=-1^2+36=35 we have these points: (1,35) and (5,11)

  28. anonymous
    • one year ago
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    I agree:)

  29. anonymous
    • one year ago
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    so then we would have to make a chart, and another function right?

  30. Michele_Laino
    • one year ago
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    now: step#2 we have to write the equation of the straight line which passes at points (1,35) and (5,11)

  31. Michele_Laino
    • one year ago
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    for example we can use this equation: \[\Large y - 35 = m\left( {x - 1} \right)\] where: \[\Large m = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}} = \frac{{11 - 35}}{{5 - 1}} = ...?\]

  32. anonymous
    • one year ago
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    -24/4

  33. anonymous
    • one year ago
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    -6

  34. Michele_Laino
    • one year ago
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    yes!

  35. Michele_Laino
    • one year ago
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    so, what is the equation of your straight line?

  36. anonymous
    • one year ago
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    um y=6x+1?

  37. anonymous
    • one year ago
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    i mean y=-6x

  38. Michele_Laino
    • one year ago
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    we have to substitute our value of m, into my equation above: \[\Large y - 35 = - 6 \cdot \left( {x - 1} \right)\]

  39. Michele_Laino
    • one year ago
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    please, simplify

  40. anonymous
    • one year ago
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    y-35=-6x+6

  41. Michele_Laino
    • one year ago
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    so: y=...?

  42. anonymous
    • one year ago
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    y=-6x-29

  43. Michele_Laino
    • one year ago
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    I got: Y=-6x+41 am I right?

  44. anonymous
    • one year ago
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    yes. whoops:)

  45. Michele_Laino
    • one year ago
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    ok! Now the exercise asks you at least four points

  46. Michele_Laino
    • one year ago
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    you have already two points: (1,35) and (5,11)

  47. Michele_Laino
    • one year ago
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    so you have to choose another 2 values for x, and compute the corresponding value for y. Please keep in mind that x has to be greater than -6 and less than 6

  48. anonymous
    • one year ago
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    what about 2?

  49. Michele_Laino
    • one year ago
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    whit those four points you have to create a table like this: |dw:1438708104245:dw|

  50. Michele_Laino
    • one year ago
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    ok! x=2 is good, so: y= -2^2+36=-4+36=...?

  51. anonymous
    • one year ago
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    32

  52. Michele_Laino
    • one year ago
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    so the third point is: (2,32)

  53. Michele_Laino
    • one year ago
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    now, we can choose x=-3

  54. Michele_Laino
    • one year ago
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    what is y?

  55. anonymous
    • one year ago
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    45

  56. Michele_Laino
    • one year ago
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    I got this: y=-(-3^2)+36=-9+36=27

  57. anonymous
    • one year ago
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    yes<3

  58. anonymous
    • one year ago
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    Yayyy! We did it! So just to make sure, the 2nd equation is y=-6x?

  59. Michele_Laino
    • one year ago
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    so, the requested table is: |dw:1438708531419:dw|

  60. Michele_Laino
    • one year ago
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    the second equation is: \[\Large y = - 6x + 41\]

  61. anonymous
    • one year ago
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    oh, so is it possible that we could have plug the points into that equation to get the points too?

  62. Michele_Laino
    • one year ago
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    please wait

  63. Michele_Laino
    • one year ago
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    I have made an error, at x=2 we have to compute the value of the y-coordinate of the line, namely: \[\Large y = - 6 \cdot 2 + 41 = ...\]

  64. Michele_Laino
    • one year ago
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    similarly at x=-3: \[\Large y = - 6 \cdot 3 + 41 = ...\]

  65. anonymous
    • one year ago
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    29

  66. anonymous
    • one year ago
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    so can we draw the chart again and see?

  67. Michele_Laino
    • one year ago
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    ok! so we got these points: (2,29) and (-3,23)

  68. anonymous
    • one year ago
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    |dw:1438708966376:dw|

  69. anonymous
    • one year ago
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    what would the domain/range be?

  70. Michele_Laino
    • one year ago
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    that's right!

  71. Michele_Laino
    • one year ago
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    the domain of the direction of the drone, it is all the real line

  72. anonymous
    • one year ago
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    so would the domain be -6 and 6 then?

  73. Michele_Laino
    • one year ago
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    it is the domain of the rainbow, I think

  74. anonymous
    • one year ago
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    ohhh

  75. anonymous
    • one year ago
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    Thanks for all your help!!!!! :D

  76. Michele_Laino
    • one year ago
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    please wait, I have made another error, the fourth point is: (-3,59)

  77. anonymous
    • one year ago
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    Good thing you caught that!

  78. Michele_Laino
    • one year ago
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    since we have: \[\Large y = \left( { - 6} \right) \cdot \left( { - 3} \right) + 41 = 18 + 41 = 59\]

  79. Michele_Laino
    • one year ago
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    the domain of the rainbow is the subsequent interval: (-6,6) whereas its range is (0,36)

  80. anonymous
    • one year ago
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    what would that represent?

  81. Michele_Laino
    • one year ago
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    the range is the set af possible values of the function -x^2+36 when x is inside the domain

  82. anonymous
    • one year ago
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    Is the linear function you created positive or negative? Explain.

  83. Michele_Laino
    • one year ago
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    I think that it represents the possible Rainbow heights with respect to the Earth's surface

  84. Michele_Laino
    • one year ago
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    the linear function which we have created has a negative slope, so I think it is negative

  85. anonymous
    • one year ago
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    What are the solutions or solution to the system of equations created? Explain what it or they represent.

  86. anonymous
    • one year ago
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    thanks so much:)

  87. Michele_Laino
    • one year ago
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    the requested solution is given by the coordinates of the intersection points, namely: (1,35) and (5,11)

  88. Michele_Laino
    • one year ago
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    :)

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