SOLUTION: The speed of sound in air changes with the temperature. When the temperature T is 32 degrees Fahrenheit, the speed S of sound is 1087.5 feet per second. For each degree increase in

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: The speed of sound in air changes with the temperature. When the temperature T is 32 degrees Fahrenheit, the speed S of sound is 1087.5 feet per second. For each degree increase in      Log On


   

Question 998962: The speed of sound in air changes with the temperature. When the temperature T is 32 degrees Fahrenheit, the speed S of sound is 1087.5 feet per second. For each degree increase in temperature, the speed of sound increases by 1.1 feet per second. (Round your answers to two decimal places.)
(a) Explain why speed S is a linear function of temperature T.
Because S always increases by 1.1 when T increases by ...., S has a constant rate of change and is a linear function of T.
Identify the slope of the function.
.....
(b) Use a formula to express S as a linear function of T.
S = .....
(c) Solve for T in the equation from part (b) to obtain a formula for temperature T as a linear function of speed S.
T = .....
(d) Explain in practical terms the meaning of the slope of the function you found in part (c).
The slope of T as a linear function of S is ..... , and this means that an increase in the speed of sound by 1 foot per second corresponds to an increase of ..... degree in temperature.
Found 2 solutions by ankor@dixie-net.com, josgarithmetic:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The speed of sound in air changes with the temperature.
When the temperature T is 32 degrees Fahrenheit, the speed S of sound is 1087.5 feet per second.
For each degree increase in temperature, the speed of sound increases by 1.1 feet per second. (Round your answers to two decimal places.)
:
(a) Explain why speed S is a linear function of temperature T.
Because S always increases by 1.1 ft/sec when T increases by .one degree,
S has a constant rate of change and is a linear function of T.
Identify the slope of the function.
slope = rise/run, therefore 1.1/1, or just +1.1
.....
(b) Use a formula to express S as a linear function of T.
S = 1.1(t-32) + 1087.5
S = 1.1t - 35.2 + 1087.5
S = 1.1t + 1052.3
:
(c) Solve for T in the equation from part (b) to obtain a formula for temperature T as a linear function of speed S.
1.1t + 1052.3 = S
1.1t = S - 1052.3
t = %28%28S-1052.3%29%29%2F1.1
t = S%2F1.1 - 1052.3%2F1.1
:
(d) Explain in practical terms the meaning of the slope of the function you
found in part (c). Approx 1 ft/sec change indicates 1 degree of temperature change
The slope of T as a linear function of S is .91 , and this means that an increase in the speed of sound by 1 foot per second corresponds to an increase of ..one... degree in temperature.

Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
You are really interested in making the equation to relate T and S. Think of the format of the model to be like S=mT%2Bb for general points (T,S). That equation for S is in slope-intercept form.

One point described is (32, 1087.5).
The slope, m, is described as positive, relating 1.1 feet per second with 1 degree Fahrenheit, so m=1.1.

Your choice to form the more specific equation. You can either use point-slope form, or you can use slope-intercept form.

Here, the work will stay in slope-intercept form (but not need to do so).
S=mT%2Bb
S-mT=b
b=S-mT
substitute the known point and slope:
b=1087.5-1.1%2A32
b=1052.3

Final formula is highlight%28S=1.1%2AT%2B1052.3%29.


The formula can easily be solved for T as a function of S.