Car tires need to be inflated properly. Overinflation or underinflation can cause premature treadwear. The data below show tire life for different inflation values for a certain type of tire. Pressure Tire Life (Ib/in²) (mi) 26 50,000 28 66,000 31 78,000 35 81,000 38 75,000 42 70,000 45 60,000 (a) Find the quadratic polynomial that best fits the data. (Let y be the tire life in miles and x the pressure in Ib/in². Round all numerical values to three decimal places.) (b) Draw a graph of the polynomial from part (a) together with a scatter plot of the data. y (mi) y (mi) 80 000 60 000 80 000 60 000 40 000 40 000 20 000 20 000 49/in 50 20 49b/ in 10 20 30 10 30 - 20 000| O-20000| y (mi) y (mi) 80 000 80000 60 00 60 000 40 000 40 000 20 000 20000 20 49b/in 20 49b/ in50 10 30 10 30 – 20 000| - 20000| (c) Use your result from part (b) to estimate the pressure that gives the longest tire life. (Round your answer to two decimal places.) Ib/in?
Car tires need to be inflated properly. Overinflation or underinflation can cause premature treadwear. The data below show tire life for different inflation values for a certain type of tire. Pressure Tire Life (Ib/in²) (mi) 26 50,000 28 66,000 31 78,000 35 81,000 38 75,000 42 70,000 45 60,000 (a) Find the quadratic polynomial that best fits the data. (Let y be the tire life in miles and x the pressure in Ib/in². Round all numerical values to three decimal places.) (b) Draw a graph of the polynomial from part (a) together with a scatter plot of the data. y (mi) y (mi) 80 000 60 000 80 000 60 000 40 000 40 000 20 000 20 000 49/in 50 20 49b/ in 10 20 30 10 30 - 20 000| O-20000| y (mi) y (mi) 80 000 80000 60 00 60 000 40 000 40 000 20 000 20000 20 49b/in 20 49b/ in50 10 30 10 30 – 20 000| - 20000| (c) Use your result from part (b) to estimate the pressure that gives the longest tire life. (Round your answer to two decimal places.) Ib/in?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1
Transcribed Image Text:Car tires need to be inflated properly. Overinflation or underinflation can cause premature treadwear. The data below show tire life
for different inflation values for a certain type of tire.
Pressure
Tire Life
(Ib/in²)
(mi)
26
50,000
28
66,000
31
78,000
35
81,000
38
75,000
42
70,000
45
60,000
(a) Find the quadratic polynomial that best fits the data. (Let y be the tire life in miles and x the pressure in Ib/in². Round
all numerical values to three decimal places.)
(b) Draw a graph of the polynomial from part (a) together with a scatter plot of the data.
y (mi)
y (mi)
80 000
60 000
80 000
60 000
40 000
40 000
20000
20 000
49/in 50
20
49b/in
10
20
30
10
30
- 20 000|
O-20000|
y (mi)
y (mi)
80 000
80000
60 000
60 000
40 000
40 000
20 000
20 000
20
49b/in50
20
49p/in
10
30
10
30
– 20000|
- 20000
(c) Use your result from part (b) to estimate the pressure that gives the longest tire life. (Round your answer to two
decimal places.)
Ib/in?
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