Solve each problem. Wind chill. The wind chill temperature W...

Solve each problem. Wind chill. The wind chill temperature $W$ (how cold the air feels) is a function of the air temperature $t$ and the wind velocity $v .$ Through experimentation in Antarctica, Paul Siple developed a formula for $W$ : $W=91.4-\frac{(10.5+6.7 \sqrt{v}-0.45 v)(457-5 t)}{110}$ where $W$ and $t$ are in degrees Fahrenheit and $v$ is in miles per hour (mph). a) Find $W$ to the nearest whole degree when $t=25^{\circ} \mathrm{F}$ and $v=20 \mathrm{mph}$ b) Use the accompanying graph to estimate $W$ when $t=25^{\circ} \mathrm{F}$ and $v=30 \mathrm{mph}$.

Solve each problem.
Wind chill. The wind chill temperature $W$ (how cold the air feels) is a function of the air temperature $t$ and the wind velocity $v .$ Through experimentation in Antarctica, Paul Siple developed a formula for $W$ :
$W=91.4-\frac{(10.5+6.7 \sqrt{v}-0.45 v)(457-5 t)}{110}$ where $W$ and $t$ are in degrees Fahrenheit and $v$ is in miles per hour (mph).
a) Find $W$ to the nearest whole degree when $t=25^{\circ} \mathrm{F}$ and $v=20 \mathrm{mph}$
b) Use the accompanying graph to estimate $W$ when $t=25^{\circ} \mathrm{F}$ and $v=30 \mathrm{mph}$.

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Key Concepts

Function Evaluation

This concept involves calculating the output of a function by substituting specific input values into the function’s formula. In problems like this one, evaluating the wind chill formula requires replacing the variables with given numerical values and carrying out the necessary arithmetic operations to determine the desired outcome.

Substitution and Order of Operations

Substitution is the process of inserting given numerical values into an algebraic expression. It is critical to follow the order of operations (parentheses, exponents, multiplication and division, addition and subtraction) to correctly simplify and compute the expression, thereby obtaining an accurate result.

Graphical Analysis

Graphical analysis refers to interpreting and extracting numerical estimates from a graph. In cases where a function is represented by a graph instead of an explicit formula, it is important to accurately read the corresponding values from the graph to estimate outputs that match given inputs.

Rounding

Rounding is the process of adjusting a numerical value to a specified degree of precision, such as to the nearest whole number. This concept is essential when final answers must be reported in a specific format or when simplifying the result for practical interpretation.

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