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Chapter 10: Problem 34

At what temperature, the Fahrenheit and the Celsius scales will give numerically equal (but opposite in sign) values? (A) \(-40^{\circ} \mathrm{F}\) and \(40^{\circ} \mathrm{C}\) (B) \(11.43^{\circ} \mathrm{F}\) and \(-11.43^{\circ} \mathrm{C}\) (C) \(-11.43^{\circ} \mathrm{F}\) and \(+11.43^{\circ} \mathrm{C}\) (D) \(+40^{\circ} \mathrm{F}\) and \(-40^{\circ} \mathrm{C}\)

Short Answer

Expert verified
The Fahrenheit and Celsius scales will show numerically equal but opposite values at -40 degrees. Therefore, the correct answer choice is -40\( ^{\circ}\mathrm{F} \) and +40\( ^{\circ}\mathrm{C} \).

Step by step solution

01

Write Conversion Formula

Write down the conversion formula between Fahrenheit and Celsius which is, F = (9/5)*C + 32 or C = (5/9)*(F-32).
02

Substitute Variables

Since we are asked to find the temperature where the Fahrenheit and Celsius scales show numerically equal but opposite signs, we treat F as x and C as -x and substitute these in the conversion formula. So, we rewrite the equation as x = (9/5)*-x + 32.
03

Solve the Equation

Solving for x, we want to add (9/5)*x on both sides to isolate x on one side. The equation now becomes (9/5)*x + x = 32. Simplifying this further will result in x = -40. Solving for x in this manner ensures it is numerically equal in both scales but opposite in sign.

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