Solve each problem. See Example 11. The threshold weight T...

Solve each problem. See Example 11. The threshold weight $T$ for a person is the weight above which the risk of death increases greatly. The threshold weight in pounds for men aged $40-49$ is related to height $h$ in inches by the formula $$ h=12.3 \sqrt[3]{T} $$ What height corresponds to a threshold weight of 216 Ib for a 43 -year-old man? Round your answer to the nearest inch and then to the nearest tenth of a foot.

Solve each problem. See Example 11.
The threshold weight $T$ for a person is the weight above which the risk of death increases greatly. The threshold weight in pounds for men aged $40-49$ is related to height $h$ in inches by the formula
$$
h=12.3 \sqrt[3]{T}
$$
What height corresponds to a threshold weight of 216 Ib for a 43 -year-old man? Round your answer to the nearest inch and then to the nearest tenth of a foot.

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Key Concepts

Cube Roots

Cube roots are the inverse operation of raising a number to the third power. They allow one to determine a value that, when multiplied by itself three times, yields the original number. This operation is particularly useful in various algebraic formulas and equations involving volume and scaling properties.

Algebraic Manipulation

Algebraic manipulation involves rearranging equations and applying arithmetic operations to isolate desired variables. It is a fundamental concept in algebra that enables the solving of equations, substitution, and simplification of expressions in various mathematical contexts.

Unit Conversion

Unit conversion is the process of transforming measurements from one set of units to another, while maintaining the same quantity. This concept is essential when interpreting or presenting results accurately, such as converting measurements from inches to feet.

Rounding

Rounding is the technique used to reduce the number of significant digits in a numerical value while maintaining its approximate value. It is important for achieving simplicity and clarity in numerical expressions, especially when a high degree of precision is not required.

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