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31 October, 09:18

Once Kate's kite reaches a height of 52 ft (above her hands), it rises no higher but drifts due east in a wind blowing 6 ft divided by s. How fast is the string running through Kate's hands at the moment that she has released 105 ft of string?

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  1. 31 October, 12:42
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    5.213ft

    Explanation:

    Z² = x² + y²

    x = √ (z² - y²)

    y = 52ft, dx = 6ft, z = 105ft, dz = ?

    d (z² = x² + y²)

    2zdz = 2xdx

    dz = xdx/z

    But x = √ (z² - y²)

    dz = √ (z² - y²) / z * dx

    dz = [√ (105² - 52²) / 105] * 6

    dz = √ (8521) / 17.5

    dz = 5.213ft
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