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sierraurb Group Title

PLEASE HELP!! A rain gutter is to be constructed of aluminum sheets 12 inches wide. After marking off a length of 4 inches from each edge, this length is bent up at an angle Θ. The area A of the opening may be expressed as the function: A(Θ) = 16 sin Θ • (cos Θ + 1). If Θ = 90°, what is the area of the opening? When i plug 90 in i keep getting 15, but my choices are: 21.8 in2 16.0 in2 7.9 in2 1.0 in2

  • one month ago
  • one month ago

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  1. sierraurb Group Title
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    @dangerousjesse any luck?

    • one month ago
  2. sierraurb Group Title
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    @phi @vineeth10

    • one month ago
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    @ganeshie8 @MATHMALE

    • one month ago
  4. phi Group Title
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    first, you can do this without a calculator. But if you do use a calculator, be sure it is in degree mode. you should(!) know sin(90º)= 1 and cos(90º)= 0

    • one month ago
  5. sierraurb Group Title
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    @phi i just figured it out actually!! C right? and could you please help me with one more!! im stuck on it :/

    • one month ago
  6. sierraurb Group Title
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    Simplify \[\sqrt{\left( 1-\sin \Theta \right)\left( 1+\sin \Theta \right)}\]

    • one month ago
  7. sierraurb Group Title
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    @phi i have no idea what to do

    • one month ago
  8. phi Group Title
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    First, How did you get C 7.9? It seems if sin(90) is 1 and cos(90) is 0 you would do 16 sin Θ • (cos Θ + 1) 16 • 1 •(0+1) and now we add 0+1 (not *too* hard) and multiply that by 16*1 you don't get 7.9

    • one month ago
  9. sierraurb Group Title
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    For some reason i divided 16 in 2 idk why haha thank you!!

    • one month ago
  10. phi Group Title
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    any idea what the answer is for your first question?

    • one month ago
  11. sierraurb Group Title
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    b right?

    • one month ago
  12. sierraurb Group Title
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    any idea on how to solve the second one? i really have no idea what to do @phi

    • one month ago
  13. phi Group Title
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    do you know how to multiply the two binomials inside the square root (some people use FOIL)

    • one month ago
  14. phi Group Title
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    if you don't see http://www.khanacademy.org/math/algebra/multiplying-factoring-expression/multiplying-binomials/v/multiplying-binomials

    • one month ago
  15. sierraurb Group Title
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    yeah when i foil i get sqrt(1-sin O)

    • one month ago
  16. sierraurb Group Title
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    is that right? @phi

    • one month ago
  17. phi Group Title
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    can you show your work?

    • one month ago
  18. sierraurb Group Title
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    F: 1*1=1 O: 1*sinO=sinO I: -sinO*1=-sinO L: -sinO*sinO=-sin2 so its sqrt(1-sin^2) oops!

    • one month ago
  19. sierraurb Group Title
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    these are my options btw @phi ±sin Θ |cos Θ| ±tan Θ square root sine theta

    • one month ago
  20. phi Group Title
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    ok looks better there is a *very useful* identity you should remember for trig problems \[ \sin^2 x + \cos^2 x = 1 \] which you can rewrite as \[ \sin^2 x = 1 - \cos^2 x \] or \[ \cos^2 x= 1 - \sin^2 x \]

    • one month ago
  21. sierraurb Group Title
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    would it be B?

    • one month ago
  22. phi Group Title
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    yes. replace 1 -sin^2 with cos^2 inside the square root sqrt(cos^2) = cos is the only choice that looks close (they must only want the positive root) | cos Θ |

    • one month ago
  23. sierraurb Group Title
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    @phi thank you so so much!! i really truly appreciate it :)

    • one month ago
  24. phi Group Title
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    yw

    • one month ago
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