Final answer:
To find the arc length of a curve over an interval, one needs to multiply the radius (r) by the change in angle (Δθ) and round to four decimal places. For a full revolution, the arc length is the circumference of the circle (2πr).
Step-by-step explanation:
Calculating the Arc Length of a Curve
The student is asking to find the length of the arc of a curve over a given interval. To calculate the arc length, we utilize the formula As = r × Δθ, where As is the arc length, r is the radius of curvature, and Δθ is the change in angle measured in radians. For a complete revolution of a circle, the arc length is equal to the circumference, which is 2πr.
To find the arc length for a specific interval, we would typically be given or calculate the radius r and the angle Δθ. Once we have these values, we simply multiply them to get the arc length.
For example, if the radius of curvature of a circular path is 5 meters and the angle of rotation is 2 radians, the arc length As is calculated as As = 5 meters × 2 radians = 10 meters. Remember to round the answer to four decimal places as required.
If the problem requires calculating the linear equation based on data, the student needs to analyze the data and use regression techniques to find the best-fit line, which can then be expressed in the form y = mx + b.