Question

15 Police can tell the speed a driver was going by the length of the skid mark a car leaves on the road after a sudden stop. The table on the next page gives the length of skid marks, in feet, and the speed of the car that made the skid mark, in miles per hour Math 101, Winter Week 8: Other Types of Equations 9.11 20 76.46 40 172.0360 305.84 80 477.88 100 (e) Enter this table in Desmos. Notice that this data does not fit either a linear nor an exponen- tial shape. In fact, the relationship between length of skid mark and speed of car involves a square root! Create a space in Desmos to type in a new formula. Then enter in the following You can make a square root symbol by typing in sqrt. Write the formula you get here, with the value of a found by Desmos included in the formula. Use this formula to answer the next two questions. (b) If a car leaves of skid mark that is 414 feet long, how fast was the driver going? (c) The driver claims that they were driving the speed limit, which was 65 mph. How long the skid mark be if that were true? would

Answer 1

400 (19.11.20)(76.4640),(172.03.60),(30× 囵 Label. 300 พี่ a = 4.6 200 -10 (477.88, 100) (305.81, 80) 100 (76.46, 40) (19.11,20 (172.03.60) 700 -100 100 200 300 400 500 600 100 by esmos

By changing the value of the slider, we found that value of a = 4.6 satisfies the plot.

So,

y = 4.6*sqrt(x)

b.

x = 414

y = 4.6*sqrt(x) = 4.6*sqrt(414) = 93.596

c.

y = 65

Therefore

y = 4.6*sqrt(x) = 65

sqrt(x) = 65/4.6 = 14.13

x = (14.13)² = 199.66