Your school’s marching band is performing at halftime during a football game. In the last formation, the band members form a circle 100 feet wide in the center of the field. You start at a point on the circle 100 feet from the goal line, march 3008 around the circle, and then walk toward the goal line to exit the field.

*300 degrees around the circle

is there a question in there somewhere?

To answer this question, we need to calculate the distance you would have walked along the circular path and the distance you would have walked toward the goal line.

To find the distance you would have walked along the circular path, we can use the formula for the circumference of a circle: C = 2πr, where C is the circumference and r is the radius of the circle. In this case, the width of the circle is given as 100 feet, so the radius would be half of that, which is 50 feet.

C = 2π(50)
C = 100π

So the distance you walked along the circular path is 100π feet.

Next, we need to determine the distance you walked toward the goal line. We are told that you marched 3008 around the circle. To find the distance you walked toward the goal line, we need to find the length of the arc that corresponds to 3008 degrees.

To find the length of an arc in a circle, you can use the formula: L = (θ/360) * C, where L is the length of the arc, θ is the central angle (in degrees), and C is the circumference of the circle.

In this case, the central angle is 3008 degrees and the circumference is 100π feet, which we calculated earlier.

L = (3008/360) * (100π)
L = 8.355 π feet

So the distance you walked toward the goal line is approximately 8.355π feet.

Now, to calculate the total distance you walked, you need to add the distance along the circular path and the distance toward the goal line:

Total distance = Distance along circular path + Distance toward goal line
Total distance = 100π + 8.355π
Total distance = 108.355π feet

Therefore, you would have walked approximately 108.355π feet during this formation.

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