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 — This question requires a scale drawing, which I cannot physically create. However, I can provide all the necessary calculations and detailed instructions for you to construct the drawing accurately. Step 1: Calculate the distance traveled by each plane after 3 hours. The formula for distance is Distance = Speed × Time. Time elapsed for all planes is 3 hours. For Plane A: Distance_A = 400 km/h × 3 h = 1200 km For Plane B: Distance_B = 300 km/h × 3 h = 900 km For Plane C: Distance_C = 500 km/h × 3 h = 1500 km Step 2: Convert these distances to lengths on the scale drawing. The given scale is 1 cm represents 200 km. To find the length on the drawing, divide the actual distance by the scale factor (200 km/cm). For Plane A: Length_A = 1200 km200 km/cm = 6 cm For Plane B: Length_B = 900 km200 km/cm = 4.5 cm For Plane C: Length_C = 1500 km200 km/cm = 7.5 cm Step 3: Instructions for creating the scale drawing. To show the relative positions of the three planes, follow these steps: 1. Mark a point P in the center of your paper to represent the airport. 2. Draw a vertical line upwards from point P. This line represents the North direction. 3. For Plane A: • Using a protractor, measure an angle of 070^ clockwise from the North line at point P. • Draw a line segment from P along this 070^ bearing, with a length of 6 cm. Label the end of this segment as A. 4. For Plane B: • Using a protractor, measure an angle of 162^ clockwise from the North line at point P. • Draw a line segment from P along this 162^ bearing, with a length of 4.5 cm. Label the end of this segment as B. 5. For Plane C: • Using a protractor, measure an angle of 290^ clockwise from the North line at point P. • Draw a line segment from P along this 290^ bearing, with a length of 7.5 cm. Label the end of this segment as C. 6. Clearly indicate the scale used on your drawing: 1 cm = 200 km. The lengths to be drawn for each plane are: Plane A: 6 cm Plane B: 4.5 cm Plane C: 7.5 cm What's next?