suppose we have a rectangular aquarium with dimenstions of length 8m.width 4m .Suppose we are filling the tank with watter at the rate of 0.4m3/sec.How fast is the height of water charging when the water level is 2.5m?

Q: 2. Sand is being dropped at the rate of 10ft.3/min into a conical pile. If the height of the pile is…

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Q: The legs of an isosceles right triangle increase in length at a rate of 2 m/s. a. At what rate is…

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Q: A 13ft ladder rests against a vertical wall. If the bottom of the ladder is sliding away from the…

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Q: A balloon is being inflated. If its volume increases at the rate of 5cm^3/sec, how fast is the…

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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: Sugar is poured into a conical tank at the rate of 15cm3/sec whose bottom radius is always quarter…

A: The volume of a cone is given by the formula V=13πr2h. Where, V-volume, r-radius and h is the height…

Q: A spherical balloon is inflating at a rate of 277T in³/sec. How fast is the radius of the balloon…

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Q: A spherical balloon is being filled with air at a constant rate of 3 cm3/s. How fast is the radius…

A: Let,Volume of sphere = VRadius of sphere = rRate at which the volume of sphere is increasing = dVdt…

Q: At what rate is water pouring into a rectangular bathtub with base 65 fť if the water level rises at…

A: According to the given information it is required to calculate the rate at which water is pouring…

Q: A cylindrical tank with radius 5 m is being filled with water at a rate of 3 m°, Imin: How fast 1.…

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Q: Water is poured into a conical tank 6 m across the top and 8 m deep at the rate of 10 m3min. How…

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Q: A substance evaporates at a rate proportional to the exposed surface. If a sphericalmothball of…

A: The rate of evaporation is proportional to the exposed surface, and the exposed surface is that of a…

Q: A l10-ft ladder is leaning against a vertical wall. If the bottom of the ladder is pulled away from…

A: If you like the solution then please give it a thumbs up.. The Answer is:        dy/dt = -3/2  or…

Q: Rain is falling into a cylindrical barrel at the rate of 20 cm3/min. If the radius of the base is 18…

A: Given,            Rain is falling into a cylindrical barrel at the rate of 20 cm3/min.…

Q: m Oil is running into an inverted conical tank at the rate of 37 -. If the min tank has a radius 2.5…

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Q: The radius of a sphere is increasing at a rate of 2 mm/s. How fast is the volume increasing (in…

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Q: Consider a pool shaped like the bottom half of a sphere, that is being filled. The radius of the…

A: The volume of hemisphere filled with liquid to height h = πrh2-π3h3

Q: A cylindrical tank has a radius of 7.0 m and a depth of 17.0 m. It is being filled at a rate of 2.9…

A: Consider the given: Radius = 7 mDepth = 17 mRate at which the tank is filled = 2.9 m3/minVolume of…

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: A ladder 20 ft. long leans against a vertical wall. If the top slides downward at the rate of 2…

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Q: A spherical balloon is expanding. If the radius is increasing at the rate of 2 inches per minute, t…

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Q: A water trough is 10m long and a cross-section has the shape of an isosceles trapezoid that is 30cm…

A:

Q: The top of a ladder slides down a vertical wall at a rate of 0.375 m/s. At the moment when the…

A: Let the length of the ladder is L.

Q: The top of a ladder slides down a vertical wall at a rate of 0.125 m/s. At the moment when the…

A: To find: -

Q: A cube is expanding at the rate of change 64 m³/s. What is the rate of change of its surface area…

A: This question is based on application of derivative.

Q: An isosceles triangular water trough is 5 meters long, 3 meters across the top, and 2 meters deep is…

A: Where we see the application of derivatives to solve the given problem

Q: Rain is falling into a cylindrical barrel at the rate of 20 cm3 /min. If the radius of the base is…

A:

Q: The volume of a cube is increasing at the rate of 8 cm /sec.How fast is the surface area in creasing…

A: We can find the answer as below

Q: A spherical balloon is inflated at a rate of 10 cm3>min. At what rate is the diameter of the…

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

A:

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

A:

Q: An edge of a variable cube is increasing at the rate of 10cm/sec.How fast the volume of the cube is…

A:

Q: A 25-ft ladder is leaning against a wall. If we push the ladder toward the wall at a rate of 1…

A:

Q: A spherical balloon is inflated so that its volume is increasing at the rate of 2.8 ft^3/min. How…

A: Given  dVdt=2.8  ft3/ min and D=1.6 ft

Q: A kite, at a height of 60 ft. is moving horizontally at a rate of 5ft/sec. away from the boy who…

A: From the given information, draw a picture.

Q: The side of a cube is increasing at a rate of 2 mm/s. How fast is the volume Q4. - increasıng when…

A: To find  How fast is the volume of a cube increasing.

Q: The top of a ladder slides down a vertical wall at a rate of 0.25 m/s. At the moment when the bottom…

A: Given:

Q: At what rate is the height of the water rising at the instant the tank is half full?

A: To find the rate at water rising

Q: A trough 21m long has ends shaped like isosceles triangles, with base 5m and height 14m. Water is…

A:

Q: A kite, at a height of 60ft.is moving horizontally at rate of 5ft./sec away from the boy who flies…

A: In right angle triangle ,According to the Pythagoras theorem , H2 = P2 + B2 Where H is horizontal ,…

Q: An inverted conical tank 10 m high and 3 m radius at the top fills with water at a constant rate. At…

A: Given: An inverted conical tank 10 m high and 3 m radius at the top fills with water at a constant…

Q: A 20-foot ladder is leaning against a vertical wall. Suppose the base of the ladder slides away from…

A:

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

A:

Q: A spherical balloon is inflating with helium at a rate of 300r min How fast is the balloon's radius…

A:

Q: A spherical balloon is being filled with air at the constant rate of 2 cm³ How fast is the radius…

A: Given that The spherical balloon is being filled with air at constant rate of 2cm3/sec. Since the…

Q: A spherical balloon is inflating with helium at a rate of 48π ft^3/min. How fast is the​ balloon's…

A: Let V be the volume of a spherical balloon with radius r at any time t.

Q: coffee is draining out of a conical filter at a rate of 2.25 inches cubed per minute. If the cone is…

A: given: coffee is draining out of a conical filter at a rate of 2.25 inches cubed per minute. If the…

Q: The top of a ladder slides down a vertical wall at a rate of 0.675 m/s. At the moment when the…

A: Given: The top of a ladder slides down a vertical wall at a rate of 0.675 m/s. At the moment when…

Q: Rain is falling into a cylindrical barrel at the rate of 20 cm3/min. If the radius of the base is 18…

A:

Q: How do you solve question 2?

A: Let x= horizontal distance y= vertical distance Given that dx/dt=1 ft/sec We have to find dy/dt at…