12. Car tires need to be inflated properly. Overinflation or underinflation can
ID: 3136119 • Letter: 1
Question
12. Car tires need to be inflated properly. Overinflation or underinflation can cause premature tread wear. The data in the table below show tire life (in thousands of miles) for different inflation pressures for a certain type of tire. (a) Find the quadratic function that best fits the data. Round the values to two decimal (b) What tire life does the equation predict for inflation of 28 lb/in2? (c) Use the equation from part (a) to estimate the inflation pressure that gives the longest Pressure Tire life (lb/in2) (mi x 1000) places. tire life. 26 31 78 81 74 59 38 45Explanation / Answer
(a)
Equation is fitted through excel scatter plot functionality.
y = -0.28x2 + 20.18x - 283.08
R² = 0.92
It is a good fit because R-square is above 90%.
(b)
y (28) = -0.28*282 + 20.18*28 - 283.08 = 62.23 thousand mi
(c)
y = -0.28x2 + 20.18x - 283.08
for longest tire life, the presurre is calculated by setting first derivate equation = 0.
y' = -0.56x + 20.18 = 0
x = 20.18/0.56 = 36 mi
please upvote the answer.
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