Marvin Mccormick

2021-03-11

An automobile tire manufacturer collected the data in the table relating tire pressure x (in pounds per square inch) and mileage (in thousands of miles). A mathematical model for the data is given by

$f\left(x\right)=-0.554{x}^{2}+35.5x-514.$

$\begin{array}{|cc|}\hline x& Mileage\\ 28& 45\\ 30& 51\\ 32& 56\\ 34& 50\\ 36& 46\\ \hline\end{array}$

(A) Complete the table below.

$\begin{array}{|ccc|}\hline x& Mileage& f(x)\\ 28& 45\\ 30& 51\\ 32& 56\\ 34& 50\\ 36& 46\\ \hline\end{array}$

(Round to one decimal place as needed.)

$A.20602060xf(x)$

A coordinate system has a horizontal x-axis labeled from 20 to 60 in increments of 2 and a vertical y-axis labeled from 20 to 60 in increments of 2. Data points are plotted at (28,45), (30,51), (32,56), (34,50), and (36,46). A parabola opens downward and passes through the points (28,45.7), (30,52.4), (32,54.7), (34,52.6), and (36,46.0). All points are approximate.

$B.20602060xf(x)$

Acoordinate system has a horizontal x-axis labeled from 20 to 60 in increments of 2 and a vertical y-axis labeled from 20 to 60 in increments of 2.

Data points are plotted at (43,30), (45,36), (47,41), (49,35), and (51,31). A parabola opens downward and passes through the points (43,30.7), (45,37.4), (47,39.7), (49,37.6), and (51,31). All points are approximate.

$C.20602060xf(x)$

A coordinate system has a horizontal x-axis labeled from 20 to 60 in increments of 2 and a vertical y-axis labeled from 20 to 60 in increments of 2. Data points are plotted at (43,45), (45,51), (47,56), (49,50), and (51,46). A parabola opens downward and passes through the points (43,45.7), (45,52.4), (47,54.7), (49,52.6), and (51,46.0). All points are approximate.

$D.20602060xf(x)$

A coordinate system has a horizontal x-axis labeled from 20 to 60 in increments of 2 and a vertical y-axis labeled from 20 to 60 in increments of 2. Data points are plotted at (28,30), (30,36), (32,41), (34,35), and (36,31). A parabola opens downward and passes through the points (28,30.7), (30,37.4), (32,39.7), (34,37.6), and (36,31). All points are approximate.

(C) Use the modeling function f(x) to estimate the mileage for a tire pressure of 29

$\frac{lbs}{sq}\in .$ and for 35

$\frac{lbs}{sq}\in .$

The mileage for the tire pressure$29\frac{lbs}{sq}\in .$ is

The mileage for the tire pressure$35\frac{lbs}{sq}$ in. is

(Round to two decimal places as needed.)

(D) Write a brief description of the relationship between tire pressure and mileage.

A. As tire pressure increases, mileage decreases to a minimum at a certain tire pressure, then begins to increase.

B. As tire pressure increases, mileage decreases.

C. As tire pressure increases, mileage increases to a maximum at a certain tire pressure, then begins to decrease.

D. As tire pressure increases, mileage increases.

(A) Complete the table below.

(Round to one decimal place as needed.)

A coordinate system has a horizontal x-axis labeled from 20 to 60 in increments of 2 and a vertical y-axis labeled from 20 to 60 in increments of 2. Data points are plotted at (28,45), (30,51), (32,56), (34,50), and (36,46). A parabola opens downward and passes through the points (28,45.7), (30,52.4), (32,54.7), (34,52.6), and (36,46.0). All points are approximate.

Acoordinate system has a horizontal x-axis labeled from 20 to 60 in increments of 2 and a vertical y-axis labeled from 20 to 60 in increments of 2.

Data points are plotted at (43,30), (45,36), (47,41), (49,35), and (51,31). A parabola opens downward and passes through the points (43,30.7), (45,37.4), (47,39.7), (49,37.6), and (51,31). All points are approximate.

A coordinate system has a horizontal x-axis labeled from 20 to 60 in increments of 2 and a vertical y-axis labeled from 20 to 60 in increments of 2. Data points are plotted at (43,45), (45,51), (47,56), (49,50), and (51,46). A parabola opens downward and passes through the points (43,45.7), (45,52.4), (47,54.7), (49,52.6), and (51,46.0). All points are approximate.

A coordinate system has a horizontal x-axis labeled from 20 to 60 in increments of 2 and a vertical y-axis labeled from 20 to 60 in increments of 2. Data points are plotted at (28,30), (30,36), (32,41), (34,35), and (36,31). A parabola opens downward and passes through the points (28,30.7), (30,37.4), (32,39.7), (34,37.6), and (36,31). All points are approximate.

(C) Use the modeling function f(x) to estimate the mileage for a tire pressure of 29

The mileage for the tire pressure

The mileage for the tire pressure

(Round to two decimal places as needed.)

(D) Write a brief description of the relationship between tire pressure and mileage.

A. As tire pressure increases, mileage decreases to a minimum at a certain tire pressure, then begins to increase.

B. As tire pressure increases, mileage decreases.

C. As tire pressure increases, mileage increases to a maximum at a certain tire pressure, then begins to decrease.

D. As tire pressure increases, mileage increases.

Daphne Broadhurst

Skilled2021-03-12Added 109 answers

Given that

$f\left(x\right)=-0.554{x}^{2}+35.5x-514$

$f\left(28\right)=-0.554{\left(28\right)}^{2}+35.5\left(28\right)-514$

$=-434.336+994-514$

$f\left(28\right)=45.67$

$f\left(30\right)=-0.554{\left(30\right)}^{2}+35.5\left(30\right)-514$

$=-498.6+1065-514$

$f\left(30\right)=52.4$

$f\left(32\right)=-0.554{\left(32\right)}^{2}+35.5\left(32\right)-514$

$=-567.296+1136-514$

$f\left(32\right)=54.704$

$f\left(34\right)=-0.554\left(34\right)2+35.5\left(34\right)-514$

$=-640.424+1207-514$

$f\left(34\right)=52.58$

$f\left(36\right)=-0.554{\left(36\right)}^{2}+35.5\left(36\right)-514$

$=-717.984+1278-514$

$f\left(36\right)=46.02$

(A) The completed table is

$\begin{array}{|ccc|}\hline x& Mileage& f(x)\\ 28& 45& 45.67\\ 30& 51& 52.4\\ 32& 56& 54.7\\ 34& 50& 52.58\\ 36& 46& 46.02\\ \hline\end{array}$

(C) Use the modeling function f(x) to estimate the mileage for a tire pressure of$29\frac{lbs}{sq}$ in. and for $35\frac{lbs}{sq}$ in.:

The mileage for the tire pressure$29\frac{lbs}{sq}$ in. is

$f\left(29\right)=-0.554{\left(29\right)}^{2}+35.5\left(29\right)-514$

$=-465.914+1029.5-514$

$f\left(29\right)=52.59$

The mileage for the tire pressure$35\frac{lbs}{sq}$ in. is

$f\left(35\right)=-0.554{\left(35\right)}^{2}+35.5\left(35\right)-514$

$=-678.65+1242.5-514$

$f\left(35\right)=49.85$

(D) To write a brief description of the relationship between tire pressure and mileage:

From the table it is clear that, as tire pressure increases mileage increases for 28, 30 and attains its maximum value at 32, and began to decrease for 34,36.

Hence, as tire pressure increases, mileage increases to a maximum at a certain tire pressure, then begins to decrease.

(A) The completed table is

(C) Use the modeling function f(x) to estimate the mileage for a tire pressure of

The mileage for the tire pressure

The mileage for the tire pressure

(D) To write a brief description of the relationship between tire pressure and mileage:

From the table it is clear that, as tire pressure increases mileage increases for 28, 30 and attains its maximum value at 32, and began to decrease for 34,36.

Hence, as tire pressure increases, mileage increases to a maximum at a certain tire pressure, then begins to decrease.