Final answer:
The radius R of a circle, which is initially 18 inches and expands at a rate of 0.35 inches per second, will be 28.5 inches after 30 seconds.
Step-by-step explanation:
To calculate the new radius R of a circle after 30 seconds when the initial radius R is 18 inches and it expands at a rate of 0.35 inches per second, we follow a straightforward application of linear motion. The expansion rate can be seen as a "velocity" of the radius's increase over time. Given the constant expansion rate, we can use the basic distance formula, which in this context is: final radius = initial radius + (rate of change × time).
Plugging in the values we have:
- Initial radius, R = 18 inches
- Rate of change = 0.35 inches/second
- Time = 30 seconds
Let's calculate the final radius:
Final radius = 18 inches + (0.35 inches/second × 30 seconds)
Final radius = 18 inches + 10.5 inches
Final radius = 28.5 inches
After 30 seconds, the radius of the circle will have increased to 28.5 inches.