Answer:
![d = \frac{w}{48}](https://tex.z-dn.net/?f=d%20%3D%20%5Cfrac%7Bw%7D%7B48%7D)
If
is constant, say k
Then,
![d = kw](https://tex.z-dn.net/?f=d%20%3D%20kw)
∴ 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}) }](https://tex.z-dn.net/?f=density%20%28pounds%2Finch%5E%7B3%7D%20%29%20%3D%20%5Cfrac%7Bweight%28pounds%29%7D%7Bsize%20%28inch%5E%7B3%7D%29%20%7D)
That is,
![d = \frac{w}{s}](https://tex.z-dn.net/?f=d%20%3D%20%5Cfrac%7Bw%7D%7Bs%7D)
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}](https://tex.z-dn.net/?f=d%20%3D%20%5Cfrac%7Bw%7D%7B48%7D)
If
is constant, say k
Then,
![d = kw](https://tex.z-dn.net/?f=d%20%3D%20kw)
∴ d ∝ w
Hence, density is proportional to the weight OR weight is proportional to the density