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The record height of a man to date is 8 feet 11 inches​ (107 inches). If all men had identical body​ types, their weights would vary directly as the cube of their heights. Assume that all men do have identical body types. If a man who is 5 feet 10 inches tall​ (70 inches) weighs 175175 ​pounds, approximately how much would a man with a height of 9 feet 2 inches9 feet 2 inches (110 inches )(110 inches) ​weigh? A man with a record height of 9 feet 2 inches9 feet 2 inches would weigh approximately nothing lbs.

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Answer:

679.08 lbs

Explanation:

Here it is given that

[tex]m\propto h^3[/tex]

[tex]m_1[/tex] = Mass of first person = 175 pounds

[tex]h_1[/tex] = Height of first person = 70 inches

[tex]m_2[/tex] = Mass of second person

[tex]h_2[/tex] = Height of second person = 110 inches

[tex]\frac{m_1}{m_2}=\frac{h_1^3}{h_2^3}\\\Rightarrow m_2=\frac{m_1h_2^3}{h_1^3}\\\Rightarrow m_2=\frac{175\times 110^3}{70^3}\\\Rightarrow m_2=679.08\ lb[/tex]

The weight of the second person would be 679.08 lbs