In a model for Ms. Fowler’s science class, the distance from the sun to Earth is 7 inches and the distance from the sun to Neptune is 12 inches. If the actual distance from the sun to Earth is 91.549 million miles and the actual distance from the sun to Neptune is 2,780.5 million miles, are the model's distances proportional to the actual dimensions of the solar
To determine if the model's distances are proportional to the actual dimensions of the solar system, we can set up a ratio using the model's distances and the actual distances for both Earth and Neptune.
For Earth:
Model distance / Actual distance = 7 inches / 91.549 million miles
For Neptune:
Model distance / Actual distance = 12 inches / 2,780.5 million miles
To compare the ratios, we simplify by converting inches to miles.
Earth ratio: (7 inches / 63360 inches) / 91.549 million miles = 7 / (63360 * 91.549 * 10^6) miles
Neptune ratio: (12 inches / 63360 inches) / 2,780.5 million miles = 12 / (63360 * 2,780.5 * 10^6) miles
If the two ratios are equal, then the model's distances are proportional to the actual dimensions of the solar system.
Assuming all calculations are correct, we can compare the two ratios.