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I need help with the following questions.

  1. Mar 8, 2005 #1
    1. Given csc(-) = 1.4, what is one possible value of (-) in radians?

    2. Solve for (-) in each equation. Give the exact value if possible. The domain is the set of all real numbers.

    a) 2sin(3theta)=1 b) 2sin(-) cos(-) =sin(-)

    (-) = theta btw

    3. A rectange has a length of x and width of y. If 3x + 2y = 96, find the largest area the rectange can have and the dimensions of the largest rectange.
     
  2. jcsd
  3. Mar 8, 2005 #2

    dextercioby

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    3.It's rectangle (sic).Do you know how to use Lagrange multipliers...?

    2 & 1.Post your work.

    Daniel.
     
  4. Mar 8, 2005 #3
    For 3 write the area in terms of x.
    How do you maximize a function of one variable?
     
  5. Mar 9, 2005 #4
    For number 3 I ended up getting x as 16 and y as 24, using guess and check. Is this correct?
     
  6. Mar 9, 2005 #5

    dextercioby

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    U can't use guess and check.U need to use CALCULUS...


    Daniel.
     
  7. Mar 9, 2005 #6

    matt grime

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    It may be the correct answer but it'd be better to learn a method, or a reason.

    The above hints were one way. here's another.


    you want to maximize xy subject to 3x+2y=96

    that's the same as maximizing 2r*3s, letting 2r=x and 3y=s, subject to

    r+s=16, which by symmetry always happens when r=s=8 so x=16 and y=24 indeed.
     
  8. Mar 9, 2005 #7

    HallsofIvy

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    1. How is csc defined? After you have answered that, use a calculator.

    2. a) Divide both sides of the equation by 2: sin(3θ)= 1/2 You should be able to write 3θ immediately - if not use a calculator.
    b) An obvious possibility is sin(θ)= 0. If sin(θ) is not 0, you can divide the equation by sin(θ) to get 2cos(θ)= 1 so cos(θ)= 1/2 .
    Now see part (a)!

    3. The area of a rectangle with sides x and y is A= xy. You are told 3x+ 2y= 96 so
    y= 48- (3/2)x. A= x(48- (3/2)x)= 48x- (3/2)x2. You can now complete the square to find the largest possible value of that.
     
  9. Mar 9, 2005 #8
    I'm in Grade 12 Pre Calculus and this assignment isn't based on new material, but material most likely learned in Grade 11 Pre Calculus, so I doubt I have to use Calculus. Unless the Calculus needed is very basic.
     
  10. Mar 13, 2005 #9
    For number 2a) I got 9.6 and 170.4 degrees. and for 2b) I got 60 and 300 degrees. Is this correct?
     
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