Terry Sleuth and thế Units. Units! Units! Why esn't everyone use the same simple SI system of units?" exclaimed Tim. Terry looked up and saw a little cloud over Tim's desk. "What seems to be the problem?" asked Terry. Tim looked up at Terry, gave a sigh of relief to see that help was at hand, and pushed over the sheets that he was working on. "I need to program the relative permittivity of water as a function of temperature. Unfortunately, the only correlation I could find expresses this in terms of degrees Celsius. Here it is: ɛ, = 78.5|1– 4.58 x10³(r – 25)+12 × 10“(T – 25)*] -6 where: &, is dimensionless and T[=] °C. For this stupid calculation, I need to be able to substitute in the temperature in degrees Fahrenheit. What I wanted to do was put a simple conversion into the program that would convert the data as they are fed in to change the temperatures from Fahrenheit to Celsius as they are processed. Then, the right values go into the equation. However, my boss Charlotte wants me to rework and reprogram the equation so that I can substitute the temperature in Fahrenheit directly into the equation. This means that I have to change the 'minus 25' and change the numbers outside the brackets as well. Every time I try it, I get different numbers. I tried converting the Centigrade to Fahrenheit as "1.8 x °C = °F". I even tried the "1.8 x °C = °F – 32". I substituted both in, but still had trouble with the minus 25. How do I take that into account?" Terry said, "Calm down!! Focus first on which conversion is needed and then systematically substitute into the equation so that as the equation stands now, a substitution of the temperature in Fahrenheit will yield the same value inside the brackets as you get when you plugged °C into the equation above." Tim breathed deeply and then worked it through. He obtained: (T(F)-77 T(F)-77 E, = 78.5 1-4.58 ×10 +12 x10-6 1.8 1.8 Did Tim derive the right equation? Justify your answer by deriving your own equation for ɛr.