This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Welcome back Prime — missed you this week. To determine the temperature where Fahrenheit and Kelvin scales have the same reading, we need to use the conversion formulas between these scales. Let X be the temperature reading that is the same on both scales, so T_F = X and T_K = X. The conversion formulas are: 1. From Fahrenheit to Celsius: T_C = (5)/(9)(T_F - 32) 2. From Kelvin to Celsius: T_C = T_K - 273.15 Step 1: Express Celsius temperature in terms of X for both scales. Substitute T_F = X into the Fahrenheit to Celsius formula: T_C = (5)/(9)(X - 32) Substitute T_K = X into the Kelvin to Celsius formula: T_C = X - 273.15 Step 2: Equate the two expressions for T_C. Since both expressions represent the same temperature in Celsius, we can set them equal to each other: (5)/(9)(X - 32) = X - 273.15 Step 3: Solve the equation for X. Multiply both sides by 9 to eliminate the fraction: 5(X - 32) = 9(X - 273.15) Distribute the numbers on both sides: 5X - 160 = 9X - 2458.35 Rearrange the terms to isolate X: 2458.35 - 160 = 9X - 5X 2298.35 = 4X Divide by 4 to find X: X = (2298.35)/(4) X = 574.5875 The temperature at which the Fahrenheit and Kelvin scales have the same reading is 574.5875. The temperature is 574.5875 degrees Fahrenheit and Kelvin. Send me the next one 📸