A circle with a radius of 6 meters has an arc that measures 35. If this arc and its associated sector are completely removed from the circle, what is the length of the major arc that remains, to the nearest tenth of a meter?
Length of arc that remains =
Circumference Length of arc removed from the circle Length of arc that remains =
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To find the length of the major arc that remains after removing the given arc and its associated sector, we first need to find the angle of the sector.
The formula to find the angle of a sector is:
[ \text{Angle of Sector} = \frac{\text{Arc Length}}{\text{Radius}} \times \frac{180^\circ}{\pi} ]
Given that the arc measures (35) meters and the radius is (6) meters, we can substitute these values into the formula:
[ \text{Angle of Sector} = \frac{35}{6} \times \frac{180}{\pi} ]
[ \text{Angle of Sector} ≈ 105.35^\circ ]
Since the sector is removed, the remaining angle of the circle is (360^\circ - 105.35^\circ = 254.65^\circ).
The length of the major arc that remains is (254.65^\circ) of the circumference of the circle:
[ \text{Length of Major Arc} = \frac{254.65}{360} \times 2\pi \times 6 ]
[ \text{Length of Major Arc} ≈ 31.8 \text{ meters} ]
So, to the nearest tenth of a meter, the length of the major arc that remains is approximately (31.8) meters.
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To find the length of the major arc that remains after removing the given arc and its associated sector from the circle:
- Find the circumference of the original circle using the formula: Circumference = 2 * π * radius.
- Subtract the length of the given arc from the circumference of the original circle to find the remaining length of the major arc.
Given that the radius of the circle is 6 meters and the given arc measures 35 degrees:
- Circumference = 2 * π * 6 meters ≈ 37.7 meters.
- Length of the given arc = (35/360) * Circumference ≈ (35/360) * 37.7 meters ≈ 3.66 meters.
- Remaining length of the major arc = Circumference - Length of the given arc ≈ 37.7 meters - 3.66 meters ≈ 34.04 meters.
So, the length of the major arc that remains, to the nearest tenth of a meter, is approximately 34.0 meters.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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