4) Assume that the maximum speed your car will go varies linearly with the steepness of th that the car can go a maximum of 55 mph up a 5° hill, and a maximum of 104 mph down a thought of as going up a hill of -2°. Be sure to include the negative!) a) Write the equation expressing maximum speed, s, in terms of the steepness angle, a. b) How fast could you go down a 7° hill? c) If your top speed is 83 mph, how steep is the hill? Is it up or down?

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**Text Transcription for Educational Website:**

4) Assume that the maximum speed your car will go varies linearly with the steepness of the hill it is traveling on. Suppose that the car can go a maximum of 55 mph up a 5° hill, and a maximum of 104 mph down a 2° hill. (Going downhill can be thought of as going up a hill of -2°. Be sure to include the negative!)

a) Write the equation expressing maximum speed, \( s \), in terms of the steepness angle, \( a \).

b) How fast could you go down a 7° hill?

c) If your top speed is 83 mph, how steep is the hill? Is it up or down?

d) What does the speed-intercept equal? Write a sentence explaining what this number tells you about the real world.

e) What does the steepness angle-intercept equal? Write a sentence explaining what this number tells you about the real world.

f) Sketch the graph of the equation.

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**Graph/Diagram Explanation:**

For section (f), you need to sketch a linear graph where the x-axis represents the steepness angle \( a \) and the y-axis represents the maximum speed \( s \). The line should intersect the points corresponding to the given conditions (55 mph at 5°, 104 mph at -2°). The slope and intercepts will provide insights into the relationship between hill steepness and maximum achievable speed.
Transcribed Image Text:**Text Transcription for Educational Website:** 4) Assume that the maximum speed your car will go varies linearly with the steepness of the hill it is traveling on. Suppose that the car can go a maximum of 55 mph up a 5° hill, and a maximum of 104 mph down a 2° hill. (Going downhill can be thought of as going up a hill of -2°. Be sure to include the negative!) a) Write the equation expressing maximum speed, \( s \), in terms of the steepness angle, \( a \). b) How fast could you go down a 7° hill? c) If your top speed is 83 mph, how steep is the hill? Is it up or down? d) What does the speed-intercept equal? Write a sentence explaining what this number tells you about the real world. e) What does the steepness angle-intercept equal? Write a sentence explaining what this number tells you about the real world. f) Sketch the graph of the equation. --- **Graph/Diagram Explanation:** For section (f), you need to sketch a linear graph where the x-axis represents the steepness angle \( a \) and the y-axis represents the maximum speed \( s \). The line should intersect the points corresponding to the given conditions (55 mph at 5°, 104 mph at -2°). The slope and intercepts will provide insights into the relationship between hill steepness and maximum achievable speed.
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