Answered

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A study finds that the metabolic rate of mammals is proportional to m^3/4 , where m is the total body mass. By what factor does the metabolic rate of a 70.0-kg human exceed that of a 4.91-kg cat?

Sagot :

Answer:

The mass of human is 2898 times of the mass of cat.

Explanation:

A study finds that the metabolic rate of mammals is proportional to m^3/4 i.e.

[tex]M=\dfrac{km^3}{4}[/tex]

Where

k is constant

If m = 70 kg, the mass of human

[tex]M=\dfrac{70^3}{4}\\\\=85750[/tex]

If m = 4.91 kg, the mass of cat

[tex]M'=\dfrac{4.91^3}{4}\\\\=29.59[/tex]

So,

[tex]\dfrac{M}{M'}=\dfrac{85750}{29.59}\\\\=2897.93\approx 2898[/tex]

So, the mass of human is 2898 times of the mass of cat.

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