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joachimngeny

  • one year ago

can someone help with this. find the smallest solution, the largest solution and the number of solutions for x in the interval 0 ≤ x ≤ 2π

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  1. joachimngeny
    • one year ago
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    im stuck with the second solution

  2. madhu.mukherjee.946
    • one year ago
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    am i wrong

  3. joachimngeny
    • one year ago
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    @madhu.mukherjee.946 i just realised i didnt attach the equation sin(7 x) = 0.64

  4. madhu.mukherjee.946
    • one year ago
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    ok now its f9

  5. joachimngeny
    • one year ago
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    @Michele_Laino i just realise that i have to give answer in radian

  6. Michele_Laino
    • one year ago
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    hint: |dw:1440747531526:dw|

  7. madhu.mukherjee.946
    • one year ago
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    did you get the value of x

  8. Michele_Laino
    • one year ago
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    the smallest solution (in radians) is: \[\Large {x_1} = \frac{1}{7}\arcsin \left( {0.64} \right) = 0.0992\]

  9. joachimngeny
    • one year ago
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    i got x1 = 0.10 and X2= 3.04

  10. Michele_Laino
    • one year ago
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    whereas the second one, is: \[\Large {x_2} = \pi - 0.0992 = ...?\]

  11. Michele_Laino
    • one year ago
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    I have used windows calculator and the "radians" option

  12. Michele_Laino
    • one year ago
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    your answer is correct!

  13. Michele_Laino
    • one year ago
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    since you have used approximated values

  14. joachimngeny
    • one year ago
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    @Michele_Laino apparently my answer is partially wrong.

  15. joachimngeny
    • one year ago
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    I must have rounded it off wrong or something

  16. Michele_Laino
    • one year ago
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    yes! you have rounded off the smallest solution, nevertheless it is not a wrong answer

  17. joachimngeny
    • one year ago
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    @Michele_Laino could you show me how to get it right, using radian? Becuase i found the angles in degree then i changed it to radians that probably why im losing marks

  18. Michele_Laino
    • one year ago
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    here is the right setting on windows calculator

  19. joachimngeny
    • one year ago
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    @Michele_Laino is that what you got for the smallest value?

  20. joachimngeny
    • one year ago
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    im on mac computer atm

  21. Michele_Laino
    • one year ago
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    no, it is the smallest value multiplied by 7, namely: 7*x1=0.6944

  22. Michele_Laino
    • one year ago
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    as you can see from my image, there is the formula: "asinr(0.64)" at the upper right corner

  23. Michele_Laino
    • one year ago
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    now, in order to get the value of x1, you have to divide 0.694498... by 7, so you get this: 0.0992...

  24. joachimngeny
    • one year ago
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    yes i understand. this is what i answered

  25. joachimngeny
    • one year ago
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    @Michele_Laino

  26. Michele_Laino
    • one year ago
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    I'm reading...

  27. joachimngeny
    • one year ago
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    what i did seem right, yeah?

  28. Michele_Laino
    • one year ago
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    please wait a moment, I have to answer to my phone...

  29. Michele_Laino
    • one year ago
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    ok! I'm here

  30. joachimngeny
    • one year ago
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    @Michele_Laino did you see my previous reply

  31. Michele_Laino
    • one year ago
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    yes! I see, I'm sorry the second solution is: \[\Large 7{x_2} = \pi - 7{x_1} = \pi - \left( {7 \cdot 0.0992} \right) = ...?\] because, from my drawing above I get these values: \[\Large 7{x_1},7{x_2}\]

  32. Michele_Laino
    • one year ago
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    therefore: \[\Large \begin{gathered} {x_1} = \frac{1}{7}\arcsin \left( {0.64} \right) = 0.0992, \hfill \\ \hfill \\ {x_2} = \frac{{\pi - \left( {7 \cdot 0.0992} \right)}}{7} \hfill \\ \end{gathered} \]

  33. Michele_Laino
    • one year ago
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    number of solution is correct, namely, we have 14 solutions

  34. Michele_Laino
    • one year ago
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    and the highest solution is: \[\Large {x_2} + 6 \cdot \frac{{2\pi }}{7}\]

  35. joachimngeny
    • one year ago
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    I don't know why it says partially wrong.

  36. joachimngeny
    • one year ago
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    @Michele_Laino but isnt that outside the range? 0 -> 2pi?

  37. Michele_Laino
    • one year ago
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    I think that tne first value, namely 0.1 is right, the third value, namely 14 is also right, you have to correct the second value, namely: \[\Large {x_2} + 6 \cdot \frac{{2\pi }}{7} = \frac{{\pi - \left( {7 \cdot 0.0992} \right)}}{7} + 6 \cdot \frac{{2\pi }}{7} = 5.735\]

  38. Michele_Laino
    • one year ago
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    namely 3.04 is wrong, please replace it with 5.735

  39. Michele_Laino
    • one year ago
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    better is 5.74

  40. joachimngeny
    • one year ago
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    @Michele_Laino ok thank you. I appriciate your help

  41. Michele_Laino
    • one year ago
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    :)

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