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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