The Function Graphed Is of the Form Y $$y = a \tan b x \text { or } y = a \cot b x , \text { where } b > 0 \text {. }$$

question 12

Multiple Choice

The function graphed is of the form y $$y = a \tan b x \text { or } y = a \cot b x , \text { where } b > 0 \text {. }$$ etermine the equation of the graph.
-The minimum length $L$ of a highway sag curve can be computed by
$$\mathrm { L } = \frac { \left( \theta _ { 2 } - \theta _ { 1 } \right) \mathrm { S } ^ { 2 } } { 200 ( \mathrm {~h} + \mathrm { S } \tan \alpha ) ^ { \prime } }$$
where $\theta _ { 1 }$ is the downhill grade in degrees $\left( \theta _ { 1 } < 0 ^ { \circ } \right) , \theta _ { 2 }$ is the uphill grade in degrees $\left( \theta _ { 2 } > 0 ^ { \circ } \right) , \mathrm { S }$ is the safe stopping distance for a given speed limit, $h$ is the height of the headlights, and $\alpha$ is the alignment of the headlights in degrees. Compute L for a 55-mph speed limit, where $\mathrm { h } = 2.4 \mathrm { ft }$ , $\alpha = 0.8 ^ { \circ } , \theta _ { 1 } = - 4 ^ { \circ } , \theta _ { 2 } = 3 ^ { \circ }$ , and $S = 336 \mathrm { ft }$ . Round your answer to the nearest foot.

• A) \(543 \mathrm { ft }\)
• B) \(557 \mathrm { ft }\)
• C) \(588 \mathrm { ft }\)
• D) \(572 \mathrm { ft }\)

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Definitions:

Indifference Curves

Graphical representations in economics to show different combinations of goods or services among which a consumer is indifferent.

Advanced Calculus

A branch of mathematics focusing on the study of rates of change (differential calculus) and the accumulation of quantities (integral calculus), often dealing with more complex concepts than those in introductory calculus.

Risk Tolerance

An investor's capacity to endure market volatility and the possibility of losing money on investments.

Financial Security

An investment instrument issued by corporations, governments, or other entities that signifies ownership or a creditor relationship and promises payment of a financial obligation.