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
Hey Retha❤️, good to see you again. 4.1.1 Step 1: Understand the scale. A scale of 1:200 means that 1 cm on the map represents 200 cm in real life. Step 2: Calculate the real-life measurement. Real-life measurement = Map measurement × Scale factor Real-life measurement = 8.2 cm × 200 Real-life measurement = 1640 cm The real-life measurement is 1640 cm. 4.1.2 Step 1: Calculate the real-life measurement in cm. Real-life measurement in cm = Map measurement × Scale factor Real-life measurement in cm = 15 cm × 200 Real-life measurement in cm = 3000 cm Step 2: Convert the real-life measurement from cm to m. (1 m = 100 cm) Real-life measurement in m = 3000 cm100 cm/m Real-life measurement in m = 30 m The real-life measurement is 30 m. 4.1.3 Step 1: Calculate the measurement on the map. Map measurement = Real-life measurementScale factor Map measurement = 1400 cm200 Map measurement = 7 cm The measurement on the map is 7 cm. 4.2.1 A scale of "1:50 \ 000" means that one unit of distance on the map represents 50 \ 000 of the same units of distance in real life. For example, 1 cm on the map represents 50 \ 000 cm in real life. 4.2.2 Step 1: Convert km to m. (1 km = 1000 m) 4 km = 4 × 1000 m = 4000 m Step 2: Convert m to cm. (1 m = 100 cm) 4000 m = 4000 × 100 cm = 400 \ 000 cm 4 km is equal to 400 000 cm. 4.2.3 Step 1: Use the real-life distance from question 4.2.2, which is 400 \ 000 cm. Step 2: Calculate the distance on the topographical map using the scale 1:50 \ 000. Map distance = Real-life distanceScale factor Map distance = 400 \ 000 cm50 \ 000 Map distance = 8 cm The distance on the topographical map will be 8 cm. 4.2.4 Step 1: Calculate the real-life measurement in cm using the scale 1:50 \ 000. Real-life measurement in cm = Map measurement × Scale factor Real-life measurement in cm = 17 cm × 50 \ 000 Real-life measurement in cm = 850 \ 000 cm Step 2: Convert the real-life measurement from cm to km. (1 km = 100 \ 000 cm) Real-life measurement in km = 850 \ 000 cm100 \ 000 cm/km Real-life measurement in km = 8.5 km A measurement of 17 cm on the map will be equal to 8.5 km in real life. Send me the next one 📸