Anonymous
Anonymous asked in Science & MathematicsMathematics · 4 weeks ago

A belt is stretched tightly over two wheels having a radii of 1 and 5 inches, respectively. If the center of the wheels...?

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are 8 inches apart, what is the total length of the straight sections of the belt?

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  • Ian H
    Lv 7
    4 weeks ago
    Favorite Answer

    Look at the very helpful second diagram in the link given by RealPro

    https://tasks.illustrativemathematics.org/content-...

     but replace 5cm, 3cm 14 cm by 5 inches, 1 inch, 8 inches

    One straight section is given by L =√[8^2 – (5 – 1)^2] = 2√(7) inches

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  • 4 weeks ago

    Refer to the 'rough' sketch below.

    The belt touches the circumference of each wheel at points A and B. The lengths make up a trapezium. The parallel sides are the radii of 1 inch and 5 inches. The distance between them is AB and the slant side has length 8 inches.

    From this, a right triangle is evident

    so, using Pythagoras' theorem we have:

    8² = (AB)² + (5 - 1)²

    so, 64 = (AB)² + 16

    => (AB)² = 48

    Hence, AB = √48 => 6.93 inches

    so, straight sections total 2 x 6.93 = 13.9 inches

    :)>

    Attachment image
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  • 4 weeks ago

    Do you have a question?

    r1 = 5 in

    r2 = 1 in

    d = 8 in

    2sqrt( d^2 - (r1-r2)^2 ) + 2pi r1 + 2(r2-r1)arccos( (r1-r2)/d ) = 36.89 in

    Output of arccos needs to be in radians.

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