This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: State the formula for the area of a rectangle and rearrange it to find the length. The area of a rectangle (A) is given by the formula A = length × width. Given A = 7462 m^2 and width w = 82 m. We need to find the length l. l = (A)/(w) = (7462)/(82) Step 2: Express the division using logarithms. To use logarithm tables, we convert the division into a subtraction of logarithms. l = ((7462)/(82)) = (7462) - (82) Step 3: Find (7462) using logarithm tables. The characteristic of (7462) is 3 (since 7462 = 7.462 × 10^3). From logarithm tables, the mantissa for 746 is 0.8727. The mean difference for 2 is 1. So, the mantissa for 7462 is 0.8727 + 0.0001 = 0.8728. (7462) = 3.8728 Step 4: Find (82) using logarithm tables. The characteristic of (82) is 1 (since 82 = 8.2 × 10^1). From logarithm tables, the mantissa for 820 is 0.9138. (82) = 1.9138 Step 5: Subtract the logarithms. l = 3.8728 - 1.9138 l = 1.9590 Step 6: Find the antilogarithm of 1.9590 to determine the length. The characteristic is 1, which means the number has two digits before the decimal point. From antilogarithm tables, the antilog of 0.9590 is approximately 9.099. Multiplying by 10^1 (due to the characteristic of 1): l = 9.099 × 10^1 = 90.99 The length of the farm is approximately 90.99 m. 90.99 m