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You are designing a rain gutter made from a piece of sheet metal
that is 1 foot by 5 feet. The gutter is formed by turning up two sides. You
want the rain gutter to have the greatest volume possible. Below is the
polynomial function that represents the volume of the gutter. Use the
graph program by typing in the polynomial function just as it is
to look at the graph. Change your axes to the following:

x max = 4
x min = 4
y max = 1
y min = -4

From the volume formula (V=L*W*H)

V = (5)(x)(1-2x) Where x is representing the amount that should be turned up to create the gutter.

Looking at the graph, which x-value do you think would provide the maximum volume? Why?

a. x = 0
b. x = 2
c. x = ¼
d. x = ½

Looking at the graph, what do you think is the maximum volume? Why?

a. V = 0
b. V = 2
c. V = -1
d. V = ½

  • math - ,

    v = 0 at x = 0 and 1/2
    so, the vertex is at x=1/4
    v(1/4) = 5(1/4)(1/2) = 5/8

  • math - ,

    Thank you very much. That is what I thought it was, but I wasn't sure.

  • math - ,

    Beaufort Scale and Wind Effects

    0 Smoke rises vertically
    1 Smoke shows wind direction
    2 Wind felt on face
    3 Leaves move, flags extend
    4 Paper, small branches move
    5 Small trees sway, flags beat
    6 Large branches sway, flags beat
    7 Large branches sway, walking is difficult
    8 Twigs break, walking is hindered
    9 Slight roof damage
    10 Severe damage, trees uprooted
    11 Widespread damage
    12 Devastation

    The Beaufort scale was devised by Frances Beaufort in 1805 to measure wind speeds. The scale is numbered from 0 to 12, and represents wind speeds in the open, 33 feet above ground. The Beaufort scale, B, can be modeled by the function

    where x is the speed of the wind in miles per hour.
    Sketch the graph of this function.

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