The total weight of a rock depends on its size and is proportional to its density. In this context, density is the weight per cubic inch. Le

Question

The total weight of a rock depends on its size and is proportional to its density. In this context, density is the weight per cubic inch. Let w denote the weight of the rock in pounds, s the size of the rock in cubic inches, and d the density of the rock in pounds per cubic inch. If a 48-cubic-inch rock weighs w pounds, write an equation that shows the proportional relation.

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Orla Orla 6 months 2021-08-04T12:17:46+00:00 1 Answers 14 views 0

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    2021-08-04T12:19:21+00:00

    Answer:

    d = \frac{w}{48}

    If  \frac{1}{48} \\ is constant, say k

    Then,

    d = kw

    ∴ d ∝ w

    Hence, weight is proportional to the density

    Step-by-step explanation:

    From the question,

    Let w denote the weight of the rock in pounds

    s denote the size of the rock in cubic inches and

    d denote the density of the rock in pounds per cubic inch.

    First, we will write the equation connecting w, s, and d.

    We get

    density (pounds/inch^{3} ) = \frac{weight(pounds)}{size (inch^{3}) }

    That is,

    d = \frac{w}{s}

    Now, given a 48-cubic-inch rock with weight w pounds, to show the proportional relation between the weight and the density, we will write

    d = \frac{w}{48}

    If  \frac{1}{48} \\ is constant, say k

    Then,

    d = kw

    ∴ d ∝ w

    Hence, density is proportional to the weight OR weight is proportional to the density

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