Final answer:
To find a curve that passes through the point (0,0) and has an arc length on the interval [2,6], we can choose any radius that satisfies the given conditions. Let's choose a radius of 2 units. Therefore, the curve that passes through the point (0,0) and has an arc length of 2 units is part of a circle with radius 2 units and an angle of 1 radian.
Step-by-step explanation:
To find a curve that passes through the point (0,0) and has an arc length on the interval [2,6], we need to consider the equation for arc length. The arc length (s) on a circular path with radius (r) is given by the formula s = rθ, where θ is the angle subtended by the arc at the center of the circle. Since the arc length is given and the radius is not specified, we can choose any radius that satisfies the given conditions.
Let's choose a radius of 2 units. Using the formula, we can find the angle θ that corresponds to an arc length of 2 units. Since s = rθ, we have 2 = 2θ, which gives us θ = 1 radian. Therefore, the curve that passes through the point (0,0) and has an arc length of 2 units is part of a circle with radius 2 units and an angle of 1 radian.