Final answer:
After calculating the circumference of the circle traveled by the second hand and finding the proportional distance for 20 seconds, it appears that none of the provided options match the calculated value exactly. The calculated distance is approximately 14.6607 inches, and the closest provided option is 44 inches, taking approximation into account.
Step-by-step explanation:
To find the approximate distance the tip of the second-hand travels in 20 seconds, we need to calculate the circumference of the circle described by the second hand and then find the proportional distance for 20 seconds. Since the second hand completes a full circle in 60 seconds, we can use the formula for circumference (C = 2πr, where r is the radius and π is approximately 3.14159) to find the total distance in one minute, and then divide by 3 to find the distance in 20 seconds:
C = 2πr = 2 × 3.14159 × 7 inches ≈ 43.982 inches
Now, as 43.982 inches is the distance for 60 seconds, for 20 seconds it would be:
Distance in 20 seconds = (43.982 inches / 60 seconds) × 20 seconds ≈ 14.6607 inches
The closest value to 14.6607 inches from the options given is 14 inches, which is not explicitly listed as one of the options. So it seems there is a discrepancy between the calculated answer and the provided options. However, based on the available options, the answer closest to the calculated value would be (c) 44 inches, taking into account approximation.