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
You're on a roll — To draw a simple scale with R.F. 1:63360 to read miles and furlongs, follow these steps: Step 1: Calculate the Length of the Scale (LOS). We assume a convenient maximum length to be measured, for example, 6 miles. The formula for the Length of the Scale (LOS) is: LOS = R.F. × Maximum length Given R.F. = 1:63360 and Maximum length = 6 miles. We know that 1 mile = 63360 inches. LOS = (1)/(63360) × (6 × 63360 inches) LOS = 6 inches To convert this to centimeters for drawing on paper, use 1 inch = 2.54 cm: LOS = 6 × 2.54 cm LOS = 15.24 cm So, the total length of the scale to be drawn on paper will be 15.24 cm. Step 2: Determine primary and secondary divisions. The 15.24 cm line represents 6 miles. • Primary Divisions (for miles): Divide the 15.24 cm line into 6 equal parts. Each part will represent 1 mile. Length of each primary division = 15.24 cm6 = 2.54 cm. • Secondary Divisions (for furlongs): The leftmost primary division represents 1 mile. Since 1 mile = 8 furlongs, this 2.54 cm segment needs to be divided into 8 equal parts. Length of each secondary division = 2.54 cm8 ≈ 0.3175 cm. Each of these will represent 1 furlong. Step 3: Instructions for drawing the scale. 1. Draw a horizontal line segment 15.24 cm long. 2. Divide this line into 6 equal main parts, each 2.54 cm long. 3. Mark the main divisions starting from the second mark from the left as 0, 1, 2, 3, 4, 5 miles. The first main division (to the left of 0) is reserved for furlongs. 4. Divide the leftmost main division (the 2.54 cm segment to the left of 0) into 8 equal sub-parts, each approximately 0.3175 cm long. 5. Mark these sub-divisions as 0, 1, 2, ..., 8 furlongs. 6. Draw a rectangle around the scale and add text labels: "R.F. = 1:63360", "Miles" below the main divisions, and "Furlongs" below the sub-divisions. The final scale will be a 15.24 cm line representing 6 miles, with main divisions of 2.54 cm for miles and sub-divisions of approximately 0.3175 cm for furlongs. What's next?