Chapter 7.7, Problem 66PPS

To determine

To Find:

How much does a person weigh who can lift at most 470 kilograms.

Answer to Problem 66PPS

About 163.54 kg

Explanation of Solution

Given Information:

The formula $M=512-146230B^{-\frac{8}{5}}$ can be used to estimate the maximum total mass M that a weightlifter of mass B kilograms can lift using the snatch and the clean and jerk.

Calculation:

  $\begin{array}{l}Given\\ M=470\\ \text{Substitute the value of M=470 in the equation and solve for B:}\\ M=512-146230B^{-\frac{8}{5}}\\ \Rightarrow 470=512-146230B^{-\frac{8}{5}}\\ \Rightarrow 146230B^{-\frac{8}{5}}=512-\mathrm{470.........}[\text{add }146230B^{-\frac{8}{5}}and\text{ subtract 470 from each side]}\\ \Rightarrow 146230B^{-\frac{8}{5}}=42\\ \Rightarrow \frac{146230}{B^{\frac{8}{5}}}=42\\ \Rightarrow \frac{146230}{B^{\frac{8}{5}}}\cdot B^{\frac{8}{5}}=42\cdot B^{\frac{8}{5}}\mathrm{.....}[\text{multiply }{B}^{\frac{8}{5}}\text{ each side]}\\ \Rightarrow B^{\frac{8}{5}}=\frac{146230}{42}\mathrm{..........................................}[\text{divide each side by 42]}\\ \Rightarrow {\left(B^{\frac{8}{5}}\right)}^{\frac{5}{8}}={\left(\frac{146230}{42}\right)}^{\frac{5}{8}}\mathrm{.............................}[e\lim inate\text{ the radical]}\\ \Rightarrow \text{B}\approx \text{163}\text{.54}\\ \text{The person whose weigh is about 163 kg can lift at most 470 kilograms}\text{.}\end{array}$