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Answer:
a. y = 0.56x -17.78 . . . . y = Celsius temperature; x = Fahrenheit temperature
b. 37.436 °C
c. interpolation
d. 83.2 °F
Step-by-step explanation:
a. In most cases, finding the linear regression equation that fits a table of data involves somewhat tedious calculations best performed by a calculator or computer. The general approach is to enter the data into the necessary list(s) or table, and invoke the necessary function.
In Microsoft Excel (and many other spreadsheet programs), you can chart the data in the usual way, then choose the option to add the regression equation to the chart.
In the Desmos calculator used here, the data can be entered into a table, and a generic equation written relating the table entries. Any unknown constants in the equation are computed by Desmos so as to maximize the correlation between the equation and the data. Using a linear equation results in a linear regression computation.
This calculator tells us what we should already know (from previous knowledge of Fahrenheit–Celsius conversion).
y ≈ 0.56x -17.78
(We already know the actual conversion is y = (5/9)(x -32) = (5/9)x -(17 7/9). The above is what you get when the numbers are rounded to hundredths, as required by this problem.)
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b. Using the above equation for x=98.6, we get
y = 0.56·98.6 -17.78 = 55.216 -17.78 = 37.436 . . . °C
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c. Since we're finding a value <em>between</em> values already in the table, the process is called interpolation. (Extrapolation is used to find values beyond those that are already in the table. The prefixes <em>inter</em>- (between) and <em>extra</em>- (beyond) can help you remember what these terms mean.)
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d. In this part, we're asked to find x that corresponds to y=28.8. We fill in the value and solve.
28.8 = 0.56x -17.78
46.58 = 0.56x . . . . . . add 17.78
46.58/0.56 = x ≈ 83.179 ≈ 83.2 . . . . . divide by the coefficient of x; round appropriately. Units are °F.
The variable t represents the number of seconds that have passed after the release of the rocket.
<h3>Function</h3>The function can be defined as an expression that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
The height of a rocket a given number of seconds after it is released is modeled by,
As given in the above function, h (height) is the dependent variable which depends on the number of seconds t after the rocket is released (independent variable).
Hence we can conclude that the variable t represents the number of seconds after the rocket has been released.
To know more about the function, follow the link given below.