# A chord with a length of #6 # runs from #pi/3 # to #pi/2 # radians on a circle. What is the area of the circle?

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To find the area of the circle, we need to determine its radius. Since the chord length is given as 6 units and the central angle subtended by the chord is ( \frac{\pi}{2} - \frac{\pi}{3} = \frac{\pi}{6} ) radians, we can use trigonometric properties to find the radius. The chord bisects the central angle, forming a right triangle where the radius is the hypotenuse. Using trigonometry, we can determine the length of the radius. Once we have the radius, we can use the formula for the area of a circle, ( A = \pi r^2 ), to find the area.

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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.

- A triangle has two corners with angles of # pi / 4 # and # (3 pi )/ 8 #. If one side of the triangle has a length of #15 #, what is the largest possible area of the triangle?
- Cups A and B are cone shaped and have heights of #32 cm# and #16 cm# and openings with radii of #15 cm# and #12 cm#, respectively. If cup B is full and its contents are poured into cup A, will cup A overflow? If not how high will cup A be filled?
- Cups A and B are cone shaped and have heights of #32 cm# and #37 cm# and openings with radii of #16 cm# and #17 cm#, respectively. If cup B is full and its contents are poured into cup A, will cup A overflow? If not how high will cup A be filled?
- Two corners of a triangle have angles of # (5 pi )/ 12 # and # ( pi ) / 12 #. If one side of the triangle has a length of # 5 #, what is the longest possible perimeter of the triangle?
- A parabola is drawn on the plane. Build its axis of symmetry with the help of a compass (drawing tool) and a ruler.?

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