A circle has a circumference of 6pi feet (ft). An arc, x, in this circle has a central angle of 50^(@). Rounded to the nearest tenth of a foot, what is the length of x ?

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A circle has a circumference of  6pi feet (ft). An arc,  x, in this circle has a central angle of  50^(@). Rounded to the nearest tenth of a foot, what is the length of  x ?

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Find Radius using Circumference: Find the radius of the circle using the circumference. The formula for the circumference of a circle is C = 2 * pi * r, where C is the circumference and r is the radius. Given C = 6pi, we can solve for r: 6pi = 2 * pi * r Divide both sides by 2pi to isolate r: r = (6pi) / (2pi) r = 3Calculate Length of Arc: Calculate the length of the arc x. The length of an arc (s) in a circle is given by the formula s = r * theta, where r is the radius and theta is the central angle in radians. First, convert the central angle from degrees to radians. The conversion factor is pi radians = 180 degrees. theta = (50 degrees) * (pi radians / 180 degrees) theta = (50/180) * pi theta = (5/18) * piUse Radius and Central Angle: Use the radius and the central angle in radians to find the length of the arc. s = r * theta s = 3 * ((5/18) * pi) s = (3 * 5 * pi) / 18 s = (15pi) / 18 Simplify the fraction by dividing both numerator and denominator by 3: s = (5pi) / 6Convert Length of Arc to Decimal: Convert the exact length of the arc to a decimal and round to the nearest tenth. s ≈ (5 * 3.14159) / 6 s ≈ 15.70795 / 6 s ≈ 2.61799 Rounded to the nearest tenth: s ≈ 2.6 feet

A circle has a circumference of $6 \pi$ feet $(\mathrm{ft})$ . An arc, $x$ , in this circle has a central angle of $50^{\circ}$ . Rounded to the nearest tenth of a foot, what is the length of $x$ ?

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A circle has a circumference of 6π 6 \pi 6π feet (ft) (\mathrm{ft}) (ft). An arc, x x x, in this circle has a central angle of 50∘ 50^{\circ} 50∘. Rounded to the nearest tenth of a foot, what is the length of x x x ?

A circle has a circumference of $6 \pi$ feet $(\mathrm{ft})$ . An arc, $x$ , in this circle has a central angle of $50^{\circ}$ . Rounded to the nearest tenth of a foot, what is the length of $x$ ?