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Homework Help: Functions & Graphs ( help ! )

  1. Jul 10, 2010 #1
    1. The problem statement, all variables and given/known data

    Draw the graph of y = 3x + 60/x - 35.
    Range : x= 1.5 less than or equal to 10
    y= 9.5 to 1
    Find Gradient
    **Find solutions to the equation 4x + 60/x = 40 by drawing a suitable line.



    2. Relevant equations
    none


    3. The attempt at a solution

    The graph is drawn, Gradient is found, which is 10.
    ** i have solved the question ' Find solutions to the equation 4x + 60/x = 40 by drawing a suitable line.' by other means but i just do not know where to draw a straight line at. how does this relate to y = 3x + 60/x - 35 ??
     
  2. jcsd
  3. Jul 10, 2010 #2

    rock.freak667

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    You found the gradient at what point?

    4x + 60/x = 40

    What do you get if you subtract 35 from each side and then subtract x from each side?
     
  4. Jul 10, 2010 #3
    sorry, my scale for the y axis is 1cm per unit, and for the x axis, 2cm 2units.

    i drew the tangent and gradient was drawn from ( 1.4, 7 ) all the way down to ( 1.4 , -3 )
    Rise / Run = 10/1 = 10.
     
  5. Jul 10, 2010 #4

    rock.freak667

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    Once you had two points to use.

    For the second part, did you do what I suggested?
     
  6. Jul 10, 2010 #5
    where wouldnt be any changes even if i have done so isnt it ? 4x + 60/x = 40
    4x + 60/x - 35 - x = 40-35-x
    i still ended up with 4x + 60/x = 40.
     
  7. Jul 10, 2010 #6

    rock.freak667

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    No from here 4x + 60/x - 35 - x = 40-35-x

    you end up with

    3x+ 60/x - 35 = 5-x


    Now say you had to solve x3 = x, you can solve it using algebra or you can do it graphically. There will be a solution where the graph of the left side intersects the graph of the right side i.e. where y=x3 and y=x intersect.

    So in your question, what graphs do you need to draw?
     
  8. Jul 10, 2010 #7
    im only required to draw the y = 3x + 60/x - 35 graph
    am i required to simplify 3x+ 60/x - 35 = 5-x further??
     
    Last edited: Jul 10, 2010
  9. Jul 10, 2010 #8

    rock.freak667

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    Did you understand what I typed?

    You started with 4x + 60/x = 40. You did not draw this graph.

    So from each side you subtracted (35+x) and got

    4x + 60/x -35 - x = 40 -35 - x

    which came out as

    3x + 60/x -35 = 5 - x

    So solutions for this equation will be the same as the solutions for 4x + 60/x = 40.

    The graph of the left side is y=3x + 60/x -35. If you draw the graph of the right side on the same page, you will get the solutions you want.
     
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