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MATHPHYS HELP

1. Felicia wants to know the gas milgage of her new car. She starts recording how much gasoline
she puts into the car, and how many miles she travels before the warning light comes on and
she need to add more gas. A table of her data is shown below.
Gas (gallons)
1 4 8 10
Miles
19 84 160 203 218
a. Consider miles M as a function of gallon and use data points to find a linear function
to model the data.
b. Consider gallons G as a function of miles M and use data points to find a linear function
to model the data.
C. How do the functions of (a) and (b) compare? Are they both useful models?
d. What could be some reasons why the points do not fit perfectly with your equation?

MATHPHYS HELP 1 Felicia wants to know the gas milgage of her new car She starts recording how much gasoline she puts into the car and how many miles she travels class=

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MathPhys

Step-by-step explanation:

(a) If M is a function of G (M is the y-axis and G is the x-axis), then the linear function is approximately:

M = 20G

(b) If G is a function of M (G is the y-axis and M is the x-axis), then the linear function is approximately:

G = M / 20

(c) The two functions are inverse of each other.  The first function tells us how many miles she can drive with a certain number of gallons.  The second function tells us how many gallons she needs to drive a certain number of miles.

(d) There are multiple things that affect fuel mileage.  These include:

Speed - idling at a red light or driving at high speeds will lower your mileage.

Weather - high winds will lower your mileage.

Weight - adding weight (even the weight of the gas itself) will lower your mileage.

Tires - low pressure in the tires will lower your mileage.

MrRoyal

The given table is an illustration of a linear scatter plot, where:

  • [tex]M = 19.9G -0.9[/tex].
  • [tex]G = \frac{10}{199}M + \frac{9}{199}[/tex].
  • M and G are both inverse functions

(a) M as a function of G

From the table, we have the following points:

[tex](G_1,M_1) = (1,19)[/tex]

[tex](G_2,M_2) = (11,218)[/tex]

Calculate the slope (m)

[tex]m = \frac{M_2 - M_1}{G_2 - G_1}[/tex]

[tex]m = \frac{218-19}{11-1}[/tex]

[tex]m = \frac{199}{10}[/tex]

[tex]m = 19.9[/tex]

The equation is then calculated using the following linear equation formula:

[tex]M = m(G - G_1) + M_1[/tex]

[tex]M = 19.9(G - 1) + 19[/tex]

[tex]M = 19.9G - 19.9 + 19[/tex]

[tex]M = 19.9G -0.9[/tex]

(b) G as a function of M

From the table, we have the following points:

[tex](M_1,G_1) = (19,1)[/tex]

[tex](M_2,G_2) = (218,11)[/tex]

Calculate the slope (m)

[tex]m = \frac{G_2 - G_1}{M_2 - M_1}[/tex]

[tex]m = \frac{11-1}{218-19}[/tex]

[tex]m = \frac{10}{199}[/tex]

The equation is then calculated as follows:

[tex]G = m(M - M_1) + G_1[/tex]

[tex]G = \frac{1}{19.9}(M - 19) + 1[/tex]

[tex]G = \frac{1}{19.9}M - \frac{19}{19.9} + 1[/tex]

[tex]G = \frac{1}{19.9}M - \frac{19-19.9}{19.9}[/tex]

[tex]G = \frac{1}{19.9}M - \frac{-0.9}{19.9}[/tex]

[tex]G = \frac{1}{19.9}M + \frac{0.9}{19.9}[/tex]

[tex]G = \frac{10}{199}M + \frac{9}{199}[/tex]

(c) How (a) and (b) compares

Functions (a) and (b) are both inverse functions of one another;

Because they both represent inverse functions, both are useful models

(d) Reasons points do not fit in the equation

Some reasons why the points do not fit are:

  • Short trips
  • Vehicle break down
  • Speed
  • Heavy breaks

When any of these happens, the mileage will be affected because she won't be able to capture the accurate data by the time she continues her trip.

Read more about linear scatter plots at:

https://brainly.com/question/2764328

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