Question

The minute hand of a clock is 7 inches long. how far does the tip of the minute hand move in 5 minutes? if necessary, round the answer to two decimal places.

Answer 1

The tip of the minute hand on a clock with a 7-inch radius will travel approximately 3.67 inches in a 5-minute span.

Step-by-step explanation:

The tip of the minute hand of a clock that is 7 inches long will move along the circumference of a circle with a radius of 7 inches. To calculate the distance the tip moves in 5 minutes, we can find the length of the arc corresponding to 5 minutes on the clock.

Since there are 60 minutes in a full rotation (360 degrees), 5 minutes would correspond to an arc that is 5/60 or 1/12 of the full circle. The circumference of the full circle (C) is calculated using the formula C = 2πr, where r is the radius and π (pi) is approximately 3.14159.

First, let's calculate the full circumference:

• C = 2π(7 inches) = 2(3.14159)(7 inches) ≈ 43.9823 inches

Now, let's find the length of the arc for 5 minutes:

• Arc length = (1/12) × 43.9823 inches ≈ 3.6652 inches

Therefore, the tip of the minute hand moves approximately 3.67 inches in 5 minutes.

Answer 2

7/6π" (or 1.17π"). To find the circumference (therefore the distance the hand travels) you do 2rπ (radius is 7in), which is 14π, then divide it by 12 bc the hand is only moving five minutes (which is simplified to 7/6π). You can't simplify π.