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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 1 Correct: Your answer is correct. , S has a constant rate of change and is a linear function of T. Identify the slope of the function. 1.1 Correct: Your answer is correct. (b) Use a formula to express S as a linear function of T. S = Incorrect: Your answer is incorrect. (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.

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Answer and Explanation:

A. We have temperature t = 32

Speed of sound, s = 1087.5

As t increases by 1⁰f speed increases by 1.2

So that

S = 1088.6

T= 33⁰f

We have 2 equations

1087.5 = k(32) + c

1088.6 = k(33) + c

Subtracting both equations

(33-32)k = 1088.6-1087.5

K = 1.1

b.). S = kT + c

1087.5 = 32(1.1) + c

Such that

C = 1052.3

Therefore

S = 1.1(t) + 1052.3

C.). S = 1.1t + 1052.3

We make t subject of the formula

T = s/1.1 - 1052.3/1.1

T = 0.90(s) - 956.3

D. This means that We have temperature to rise by 0.90 whenever speed is increased