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Ugo [173]
3 years ago
8

The cube root of r varies inversely with the square of s. Which two equations model this relationship?

Mathematics
1 answer:
77julia77 [94]3 years ago
3 0

Answer:

The following two equations model this relationship.

  • \:\sqrt[3]{r}=\:\frac{k}{s^2}
  • \:\:s^2\:r^{\frac{1}{3}}=\:\frac{k}{s^2}  

Step-by-step explanation:

We know that when 'y' varies inversely with 'x', we get the equation

y ∝ 1/x

y = k / x

k = yx

where 'k' is called the 'constant of proportionality'.

In our case, it is given that the cube root of 'r' varies inversely with the square of 's', then

\sqrt[3]{r} ∝ \frac{1}{s^2}

\:\sqrt[3]{r}=\:\frac{k}{s^2}

or

\:\:s^2\:r^{\frac{1}{3}}=\:\frac{k}{s^2}          ∵ \sqrt[3]{r}=r^{\frac{1}{3}}

Therefore, the following two equations model this relationship.

  • \:\sqrt[3]{r}=\:\frac{k}{s^2}
  • \:\:s^2\:r^{\frac{1}{3}}=\:\frac{k}{s^2}  
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