Air is pumped into a spherical balloon at the constant rate of 200 cubic centimeters per second. How fast is the surface area of the balloon changing when the radius is 5 centimeters?

Q: A balloon is being inflated by pumped air at the rate of 2 cubic inches per second. How fast is the…

A: Given: Rate at which air is pumped in the balloon=2 cubic inches per second……1   To find: Rate of…

Q: A spherical balloon is to be deflated so that its radius decreases at a constant rate of 5 cm/min.…

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Q: The length of the rectangle is increasing at a rate of 5 centimeters per second, and its width is…

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Q: Gas is being pumped into a spherical balloon at the rate of 10 cubic inches per second. When the…

A: we have given that Gas is being pumped into a spherical balloon at the rate of 10 cubicinches per…

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: All edges of a cube are expanding at a rate of 3 centimeters per second. (a) How fast is the surface…

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

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Q: Water is being poured at a rate of 10 cubic meters per second into a cylindrical tank of radius 4…

A: Given that , Rate of water pumped in tank=10m3/sec=dV/dt Radius of tank = r=4m Height /Altitude of…

Q: The radius of a spherical balloon is increasing at the rate of 0.8 cm / minute. How fast is the…

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Q: The volume of oil in a cylindrical container is increasing at a rate of 150 cubic inches per second.…

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Q: consider a rectangular bathtub whose base is 18 ft2. How fast is the water level rising if water is…

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Q: The depth of water in a 4m diameter cylindrical tank is increasing at the rate 0.7m/min. Find the…

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Q: 2. please help, they canceled class due to virus can't contact teacher.

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Q: A spherical balloon is inflated with gas at a rate of 10 cubic metres per minute. How fast is the…

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Q: The radius of a spherical ball is increasing at a rate of 2 cm/min. At exactly what rate (in…

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Q: Air is being pumped into a sperical balloon so that its volume increases at a 12. rate of 16 cubic…

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Q: A sphere is filled with air. If the volume of the sphere is decreasing at a rate of 534 cubic cm per…

A: Given

Q: Water is flowing into a vertical cylindrical tank at the rate of 5 cu ft/min. If the radius of the…

A: Given, water is flowing into a vertical cylindrical tank at the rate of 5 cu ft/min (ie) Volume is…

Q: The radius of a sphere is increasing at a rate of 5 mm/s. How fast is the volume increasing when the…

A: Let be the volume and r be the radius of the sphere respectively.

Q: The radius of a sphere is increasing at a rate of 4 mm/s. How fast is the volume increasing when the…

A: Volume of sphere= =43πR3 where R is the Radius of the sphere.

Q: Water is flowing at the rate of 6 ft/min into a tank that is in the shape of a right circular…

A: Given data:   The rate at which water is flowing in the cylindrical tank is dV/dt =6 ft3/min. The…

Q: An oil tanker aground on a reef is forming a circular oil slick about 0.1 foot thick. If the oil was…

A: Given that  An oil tanker aground on a reef is forming a circular oil slick about 0.1 foot thick. If…

Q: The area of an equilateral triangle is decreasing at a rate of 4 sq. cm. per minute. Find the rate…

A: Given that  The area of an equilateral triangle is decreasing at a rate of 4 sq. cm. per minute.…

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 flying kite is 100 m above the ground, moving in a horizontal direction at a rate of 10 m/s. How…

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Q: A 12-foot ladder is leaning against a vertical wall when Jack begins pulling the foot of the ladder…

A: A 12-foot ladder is leaning against a vertical wall when Jack begins pulling the foot of the ladder…

Q: The volume of a cube is increasing at a rate of 9 cubic centimeters per second .How fast is the…

A: Solution:-

Q: gas is escaping a spherical ballon at the rate of 4cm per minute . how fast is the surface area…

A: Given that, Gas is escaping a spherical balloon at the rate of 4 cm per minute. The objective is to…

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

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Q: A spherical balloon is to be deflated so that its radius decreases at a constant rate of 15 cm/min.…

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Q: If the radius of a sphere is increasing at the constant rate of 3 inches per second, how fast is the…

A: Given dr/dt = 3

Q: The radius of a sphere is increasing at a rate of 4 mm/s. How fast is the volume increasing when the…

A:

Q: Air is pumped into a spherical balloon so that its volume increases at a rate of 100 cm /s. How fast…

A: d[r^n]/dr = n r^(n-1)

Q: All edges of a cube are expanding at a rate of 7 cm per second. How fast is the surface area…

A: Given that all edges of a cube are expanding at a rate of 7 cm per second. Let the edge of a sphere…

Q: a spherical balloon is filled with gas at a rate of 300 mm3/sec. Find the rate at which the surface…

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Q: A girl is using a straw to drink coke from a right cylindrical glass at a rate of 6 cubic…

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Q: All edges of a cube are expanding at a rate of 8 centimeters per second. How fast is the surface…

A: Since, we have been given that all edges of a cube are expandingat a rate of 8 centimeters per…

Q: A 5-foot ladder is leaning against a vertical wall. If the bottom of the ladder is being pulled away…

A: Given: Length of the ladder, l=5 ft. Distance between wall and the bottom of the ladder, x=4 ft…

Q: How fast is the volume of a cube changing when the edge is 15 cm if the edge is changing at the rate…

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Q: ) A snowball is melting at a rate of 1 cm3 per second. If it remains spherical, how fast is the…

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Q: A spherical balloon is being deflated at the rate of 10 cm/s. What is the rate of change for the…

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Q: A spherical snowball is melting so that its diameter is decreasing at rate of 0.2 cm/min. At what is…

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Q: The sides of a square increases in length at a rate of 3 m/sec. At what rate is the area of the…

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Q: A cone shaped icicle has an initial radius of 10 inches and a height of 15 inches. Once the height…

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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: A conical glass whose radius is 5m and altitude 12m is being filled at the rate of 10 cu. m/sec. How…

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Q: A 3-meter long steel pipe has its upper end leaning against a vertical wall and lower end on a level…

A: Given that, Length of pipe is 8m, lower end moving away at the rate of 2 cm/sec. we have to find how…

Q: A piston is seated at the top of a cylindrical chamber with radius 5 cm when it starts moving into…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.