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The following situation involves a rate of change that is constant. Write a statement that describes how one variable changes with respect to the​ other, give the rate of change numerically​(with units), and use the rate of change rule to answer any questions.A​ 1-degree change​ (increase or​ decrease) on the Celsius temperature scale is equivalent to a nine fifths 9/5 degree change on the Fahrenheit temperature scale. How much does the Fahrenheit temperature increase if the Celsius temperature increases 2 degrees? How much does the Fahrenheit temperature decrease if the Celsius temperature decreases 24 degrees?1. Which statement describes this​ situation?A. The Celsius temperature varies with respect to the Fahrenheit temperature with a rate of change of ​9/5degrees F per degree C.B. The Celsius temperature varies with respect to the Fahrenheit temperature with a rate of change of ​9/5degrees C per degree F.C.The Fahrenheit temperature varies with respect to the Celsius temperature with a rate of change of ​9/5degrees F per degree C.D. The Fahrenheit temperature varies with respect to the Celsius temperature with a rate of change of ​9/5degrees C per degree F.2. What is the increase in Fahrenheit temperature if the Celsius temperature increases by 2 degrees​? _______ F (type an integer or a decimal.)3. What is the decrease in Fahrenheit temperature if the Celsius temperature decreases by 24 degrees? ______ F (type an integer of a decimal)

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Answer:

1) Option C is correct.

The Fahrenheit temperature varies with respect to the Celsius temperature with a rate of change of ​9/5degrees F per degree C

2) The increase in Fahrenheit temperature if the Celsius temperature increases by 2 degrees = (18/5) degrees = 3.6°F

3) The decrease in Fahrenheit temperature if the Celsius temperature decreases by 24 degrees = 43.2°F

Step-by-step explanation:

1-degree change​ (increase or​ decrease) on the Celsius temperature scale is equivalent to a nine fifths 9/5 degree change on the Fahrenheit temperature scale

Let temperature in Celsius be C

And temperature in Fahrenheit be F

ΔC ∝ ΔF

ΔC = k ΔF

k = constant of proportionality

When ΔC = 1°, ΔF = (9/5)°

1 = k (9/5)

k = (5/9)

ΔC = k ΔF

ΔC = (5/9) ΔF

(ΔC/ΔF) = (5/9)

1) Which statement describes this​ situation?

The derivative or rate of change of C with respect to F for small changes in both quantities is approximately given as

(dC/dF) = (ΔC/ΔF)

And (ΔC/ΔF) = (5/9)

Hence,

(dC/dF) = (ΔC/ΔF) = (5/9)

Taking an inverse,

(dF/dC) = (ΔF/ΔC) = (9/5) °F/°C

So, It is evident that the right option is that the Fahrenheit temperature varies with respect to the Celsius temperature with a rate of change of ​9/5degrees F per degree C

2) (dC/dF) = (ΔC/ΔF) = (5/9)

ΔC = 2°C

ΔF = ?

(ΔC/ΔF) = (5/9)

(2/ΔF) = (5/9)

ΔF = (2×9)/5 = (18/5) = 3.6°F

3) (dC/dF) = (ΔC/ΔF) = (5/9)

ΔC = -24°C

ΔF = ?

(ΔC/ΔF) = (5/9)

(-24/ΔF) = (5/9)

ΔF = (-24×9)/5 = (-216/5) = -43.2°F

Hope this Helps!!!

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