Sodium Chlorate crystals are easy to grow in the shape of cubes by allowing a solution of sodium chlorate and water to evaporate slowly. Suppose that the Volume of such a cube is decreasing at a rate of 300 mm³/hr. If the cube has side length x, at what rate is the side length decreasing at the instant x = 10 mm? 10 mm/hr 1 mm/hr 900 mm/hr 3 mm/hr
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Given that the cube has a side length x, the volume V of the cube is given by V = x^3. Show more…
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Sodium Chlorate crystals are easy to grow in the shape of cubes by allowing a solution of sodium chlorate and water to evaporate slowly. Suppose that the volume of such a cube is decreasing at a rate of 300 mm³/hr. The cube has a side length x. At what rate is the side length decreasing at the instant x = 10 mm? Note: The formula for the volume of a cube is V = s³, where s is the length of any side.
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Sodium chlorate crystals are easy to grow in the shape of cubes by allowing a solution of water and sodium chlorate to evaporate slowly. If V is the volume of such a cube with side length x, calculate the derivative when x = 5 mm. V'(5) = mm^3/mm What does V'(5) mean in this situation? V'(5) represents the rate at which the side length is increasing with respect to the volume as x reaches 5 mm. V'(5) represents the rate at which the volume is increasing as x reaches 15 mm. V'(5) represents the rate at which the volume is increasing with respect to the side length as x reaches 5 mm. V'(5) represents the volume as the side length reaches 5 mm. V'(5) represents the rate at which the volume is increasing with respect to the side length as V reaches 15 mm^3.
The side of a cube decreases at a rate of 10 m/sec. Find the rate at which the volume changes when the side is 3 m. 360 m^3/sec 180 m^3/sec -90 m^3/sec -270 m^3/sec 270 m^3/sec ∫3dt = 30 18 36 24 6
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