Final answer:
To find the perimeter of the arc AM, use the formula L = 2πrθ/360, where r is the radius and θ is the central angle in degrees. Substitute the given values to find the length of the arc.
Step-by-step explanation:
To find the perimeter of the circle M, we can use the formula P = 2πr, where r is the radius. In this case, the radius is given as 4 cm, so we have P = 2π(4) = 8π cm. However, the question asks for the perimeter of the arc AM, so we need to find the length of that arc. The formula for the length of an arc is L = 2πrθ/360, where θ is the central angle in degrees. In this case, we need to find the central angle of the arc AM. To do this, we can use the fact that the angle at the center of the circle is twice the angle at the circumference, so θ = 2(AM/r) = 2(17/4) = 34/4 = 17/2. Now we can substitute this value of θ into the formula for the arc length:
L = (2π(4)(17/2))/360 = (8π(17/2))/360 = (136π)/360 = 34π/90 cm.
Therefore, the perimeter of the arc AM is approximately 34π/90 cm.