Respuesta :
ANSWER:
7.5
STEP-BY-STEP EXPLANATION:
The mass factor of a human which exceeds that of a cat would be found by using the following expression:
[tex]\begin{gathered} m^{\frac{3}{4}} \\ m\text{ is the mass of total body} \end{gathered}[/tex]Mass of human will be calculated in metabolic process by using the following equation:
[tex]\begin{gathered} R_H\propto(m^{}_H)^{\frac{3}{4}} \\ R_H\text{ is the metabolic rate of human and }m_H\text{ is the mass of the human} \end{gathered}[/tex]Mass of cat will be calculated in metabolic process by using the following equation:
[tex]\begin{gathered} R_C\propto(m^{}_C)^{\frac{3}{4}} \\ R_C\text{ is the metabolic rate of cat and }m_C\text{ is the mass of the cat} \end{gathered}[/tex]The mass factor of a human that exceeds that of a cat would be found as below.
[tex]\begin{gathered} \frac{R_H}{R_C}=\frac{(m^{}_H)^{\frac{3}{4}}}{(m^{}_C)^{\frac{3}{4}}}_{} \\ \frac{R_H}{R_C}=(\frac{m_H}{m^{}_C})^{\frac{3}{4}} \end{gathered}[/tex]Replacing:
[tex]\begin{gathered} \frac{R_H}{R_C}=(\frac{70}{4.77^{}_{}})^{\frac{3}{4}} \\ \frac{R_H}{R_C}=7.497\cong7.5 \end{gathered}[/tex]Therefore, the metabolic rate of a 70 kg human by a factor 7.5 that of a 4.77 kg cat
