A conical paper cup is 20 cm tall with a radius of 10 cm. The bottom of the cup is punctured so that the water leaks out at a rate of 2π/3 cm^3 / sec. At what rate is the water level changing when the water level is 8 cm?

Q: Suppose the radius of a sphere are expanding at a rate of 6 inches per minute. How fast is the…

A: Let us suppose the radius of sphere be R. Given that :   dRdt=6 incheminute.  Radius=Diameter2=122=6…

Q: A cylindrical tank with radius 6 m is being filled with water at a rate of 3 m³/min. How fast is the…

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Q: A 13-foot ladder rests against a vertical wall. If the bottom of the ladder slides away from the…

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Q: A water tank in the shape of an inverted cone is being filled up with water at a uniform rate of…

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Q: A bucket of water weighing 100 Newtons is pulled at constant velocity up to a platform 50 feet above…

A: Total weighing of bucket of water = 100 N Lifting height h = 50 ft

Q: All edges of a cube are expanding at a rate of 6 centimeters per minute. Draw an accurate  picture…

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Q: A board 5 feet long slides down a wall. At the instant the bottom end is 4 feet from the wall, the…

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Q: A Ferris wheel with a radius of 10 m is rotating at a rate of one revolution every 2 minutes. How…

A: the height is given byh = 10 sin (pi * t) + 10dh/dt = 10 cos (pi * t) * pi

Q: 3. Water is flowing out of a cylindrical storage tank at a rate of 2 m3/min. If the tank has a…

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Q: A stone dropped in a pond sends out a circular ripple whose radius increases at a constant rate of 3…

A: Given that:Rate of increase of radius, drdt=3 ft/s

Q: 2. All edges of a cube are expanding at a rate of 6 centimeters per second. How fast is the surface…

A: We have to find changing the surface area

Q: The side of an equilateral triangle was measured to be 233 cm with at most possible error of 0.5 cm.…

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Q: Oil from an uncapped well is radiating outward in the form of a circular film on the surface of the…

A: Let r and A be the radius and area of the circle respectively at time t. The radius of the circle is…

Q: All edges of a cube are expanding at a rate of 6 centimeters per minute. Draw an accurate  picture…

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Q: A water trough is 8 feet long, and its cross section is an equilateral triangle with sides 4 feet…

A: (a) Height of an equilateral triangle of side length s, is given by, h=3s2 ft

Q: A stone dropped into a still pond on a calm day sends out a circular ripple. If the radius increases…

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Q: All edges of a cube are expanding at a rate of 8 mm per hour. At what rate is the volume of the cube…

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Q: An object is thrown vertically upward from a point 32 feet above the ground with an initial velocity…

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Q: A 13 foot ladder is leaning against a wall. If the top of the ladder slips down the wall ata rate of…

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Q: A cylindrical tank with radius 6 m is being filled with water at a rate of 2 m/min. How fast is the…

A:

Q: A coat of paint of thickness 0.04 cm is to be applied uniformly to the faces of a cube of edge 30…

A: Given that a coat of paint of thickness 0.04 cm is to be applied uniformly to the faces of a cube of…

Q: A spherical balloon is to be deflated so that its radius decreases at a constànt rate of 18 cm/min.…

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Q: A 15 foot ladder is leaning against a wall when its bottom starts to slide away. By the time the…

A: Please refer to the diagram on the white board. l= Length of the ladder = 15 ftx = lcosϴAt the…

Q: A conical reservoir is losing water at the rate of 12 cubic feet per minute. If the radius is % the…

A: Let the height of the conical reservoir be h. Then the radius will be = h/4 Therefore we get the…

Q: Each side of a square is increasing at the rate of 8 cm/sec. At what rate is the area of the square…

A: Solution :let, side of square=xArea of square=Adxdt= 8 cm/secA= 36 sq. cmA=x2    Area of square=side…

Q: Air is pumped into a spherical balloon at the constant rate of 200 cubic centimeters per second. How…

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Q: A Ferris wheel with a radius of 13m is rotating at a rate of one revolution every 2 minutes. How…

A: Given thatRadius of the Ferris wheel is 13 mThe time period of the Ferries wheel is 2 min To find…

Q: Water is leaking out of an inverted conical tank at a rateof 10,000 cm3/min at the same time that…

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Q: A conical paper cup is 30 cm tall with a radius of 10 cm. The bottom of the cup is punctured so that…

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Q: An artist paints a portrait on a circular canvas and encloses it in a circular metal frame. At a…

A: Let the radius of the circular canvas be r.   The area of the canvas will be given by: A=πr2   Also,…

Q: A 26 foot ladder is sliding down a vertical wall.  The base of the ladder is sliding away from the…

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Q: stone dropped into a pond sends out a circular ripple whose radius increases at a constant rate of…

A:

Q: A stone dropped into a still pond sends out a circular ripple whose radius increases at a constant…

A: Given: A stone dropped into a still pond sends out a circular ripple whose radius increases at a…

Q: A water balloon is launched from a platform 96 feet above the ground, with an initial velocity of…

A: The location of the water balloon when hit the ground is (120, 36, 0).

Q: A cone with an altitude of 50 cm has its base radius changing at the rate of one millimeter per…

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Q: A cylindrical tank with radius 5 m is being filled with water at a rate of 2 m3/min. How fast is the…

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Q: A comet loses material when it gets close to the Sun at a rate of 100 cubic meters per minute.…

A: Given Comet is a sphere Its radius is 200 meters Let V be the volume of the comet then r be the…

Q: A liquid is flowing into a vertical cylindrical tabk of radius 6 ft at the rate of 8 ft³/min. How…

A: r=6 ft  &  dVdt=8 ft3min,  where r is the radius, V is the volume at any time t. Let h be the…

Q: A cylindrical tank with radius 6 m is being filled with water at a rate of 4 m3/min. How fast is the…

A: From the given information it is given that:Radius of cylindrical tank(r) = 6mRate at which the…

Q: A water balloon is launched from a platform 96 feet above the ground, with an initial velocity of…

A:

Q: A right circular cylinder has a radius increasing at the rate of 4 cm per second but its total…

A: A right circular cylinder has a radius increasing at the rate of 4 cm per second but its total…

Q: A circular disc of radius 3 cm is being heated. Due to expansion, its radius increases at a rate of…

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Q: All edges of a cube are expanding at a raete of 6 centimeters per second. How fast is the surface…

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Q: Water is spilling out at a rate of 10,000TT cm³/minute from an inverted tank shaped like a cone,…

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Q: A gas line-driven lawnmower has a blade that extends out 1 foot from its center. The tip of the…

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Q: A comment loses material when it gets close to the sun at a rate of 100 m³ per minute. Assuming that…

A: Given a comet loses material when it gets close to the sun at a rate of 100 m³ per minute.

Q: A light is placed on the ground 30 ft from a building. A man 6 ft tall walks from the light toward…

A: This question is based on application of derivative.

Q: A 5 meter ladder is sliding down a vertical wall so the distance between the bottom of the ladder…

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Q: Air is being pumped into a spherical balloon at rate of 5ft3/m. At what rate is the radius changing…

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Q: A cylindrical tank with a radius of 5 ft and a height of 20 ft is filled with a certain liquid…

A: topic - application of derivatives