Steepness of a Hill Problem: On roads in hilly areas, you sometimes see signs like this

Chapter 5, Problem 5

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Steepness of a Hill Problem: On roads in hilly areas, you sometimes see signs like this. Steep hill 20% grade The grade of a hill is the slope (rise/run) written as a percentage, or, equivalently, as the number of feet the hill rises per hundred feet horizontally. Figure 5-2g shows the latter meaning of grade. Figure 5-2g a. Let x be the grade of a hill. Explain why the angle, degrees, that a hill makes with the horizontal is g b. Find an equation for d in terms of xand dx. Then find d in terms of dx forgrades of x = 0%, 10%, and 20%.c. You can estimate at x = 20% by simplymultiplying d at x = 0 by 20. How mucherror is there in the value of found byusing this method rather than by using theexact formula that involves the inversetangent function?d. A rule of thumb you can use to estimate thenumber of degrees a hill makes with thehorizontal is to divide the grade by 2. Wherein your work for part c did you divide byapproximately 2? When you use this methodto determine the number of degrees forgrades of 20% and 100%, how much error isthere in the number?