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A companys revenue increased by 20% in the first year and then decreased by 10% in the second year. If the initial revenue was $500,000, what is the revenue at the end of the second year?
#### 540,000Question: The radius of a cylinder is $ x $ units and its height is $ 3x $ units. The radius of a cone with the same volume is $ 2x $ units. What is the height of the cone in terms of $ x $?
Question: A triangle has vertices at $ A(0, 0) $, $ B(6, 0) $, and $ C(3, 6) $. What is the area of triangle $ ABC $?
Solution: Use the formula for the area of a triangle given coordinates of its vertices:
Substitute $ A(0, 0) $, $ B(6, 0) $, $ C(3, 6) $:
Question: A circle has a chord of length $ 10 $ cm that is $ 6 $ cm from the center. What is the radius of the circle?
Solution: Let the radius be $ r $. A perpendicular from the center to a chord bisects the chord. So, half the chord is $ 5 $ cm, and the perpendicular distance from the center is $ 6 $ cm. Using the Pythagorean Theorem in the right triangle formed by the radius, half the chord, and the perpendicular:
Solution: Let the side length of the cube be $ s $. The space diagonal $ d $ of a cube satisfies:
Solution: Let the weekly growth values be $ a_1, a_2, a_3, a_4, a_5 $, where each $
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