1. Suppose that oil spills from a container and spreads in a circular pattern. If the radius of the oil spill increases at a rate of 1m/s, how fast is the area spill increasing when the radius is 30m? ITm/s

Q: Suppose the edges of a cube are increasing at a constant rate of 8 m/hr. Then, the volume of the…

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Q: 7. A triangle with a base of 20 inches has a height that is decreasing at a rate of 3 inches per…

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Q: Suppose that a spherical balloon is being inflated and the radius of the balloon is increasing at a…

A: The increasing rate of radius of ballon is

Q: Suppose oil spills from a ruptured tanker and spreads in a circular pattern. If the radius of the…

A: Suppose that the radius of circular pattern is “r” and area of the pattern is “A” then, The area of…

Q: 3. The radius of a spherical balloon is increasing at the rate of 2 cm per minute. How fast is the…

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Q: All edges of a cube are expanding at a rate of 9 centimeters per second. (a) How fast is the volume…

A: GivenAll edges of a cube are expanding at a rate of 9 centimeters per second

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

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

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Q: A trough filled with liquid is 2 m long and has a cross section of an isosceles trapezoid 30 cm wide…

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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: Suppose the edges of a cube are increasing at a constant rate of 11 m/hr. Then, the volume of the…

A: Let the side of the cube = x Edges of the cube increasing rate dx/dt = 11 m/hr

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

A: Let the length be: l Let the width be: w

Q: If the population of bacteria in a certain region triples in 30 days. In how many days will be three…

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Q: A sperical snowball is melting in such a way that its volume is decreasing at a rate of 1 cm^3/min.…

A: Volume of the sphere formula:‘r’ is the radius of the sphere

Q: Suppose that a mothball loses volume by evaporation at a rate propotional to its instataneous area.…

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Q: hypothetical cube shrinks so that the length of its sides are decreasing at a rate of 3 ft/min. At…

A: we have to find

Q: A thin sheet of ice is in the form of a circle. If the ice is melting in such a way that the area of…

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Q: All edges of a cube are expanding at a rate of 5 centimeters per second. (a) How fast is the volume…

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Q: Find the rate of change. Volume of a cube with respect to its sides when s = 5

A: The volume of a cube with side s is V=s3 Differentiate with respect to s dVds=ddss3=3s2

Q: How fast is the circumference of a circle changing if the radius is changing at the rate of 3 mm/s?

A: Solution

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

A:

Q: If the sides of an equilateral triangle are increasing at a rate of 6 m/min. How fast is the area of…

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Q: A rectangle is expanding such that its length is always 4 times its width. If the width is…

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

A: It is given that dsdt=6 cms. It is known that V=s3. Differentiate the above equation with respect to…

Q: A perfectly spherical balloon is losing volume at a rate of 3 in3 per sec. How fast is the balloon’s…

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Q: A hypothetical square grows so that the length of its diagonals are increasing at a rate of 8…

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Q: A fire has started in an open field and is spreading in the form of a circle, with its radius…

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Q: 4 THE LENGTH OF A TRIANGLE LL INCREASING ATA RATE OF 8cm/s AND ITS WIDTH IS INCREASING AT A RATE OF…

A: SOLUTION-

Q: Suppose the amount of oil pumped from one of canyon near the beach of island decreases at the…

A: Given query is to find the time when output will become one fifth of initial value.

Q: A mold grows at a rate proportional to its present size. If the original amount doubles in one day,…

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Q: a spherical snowball is melting in such a way that its surface area decrease at the rate of…

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Q: If the radius of a right circular cylinder is increasing at a rate of 1 inch per minute, and the…

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Q: 3. The volume of a cube is increasing at the rate of 6 cm³/min. How fast is the surface increasing…

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

A:

Q: Suppose oil spills from a ruptured tanker and spreads in a circular pattern. If the radius of the…

A: Given oil is spilled from tank and it flowing  in a circular path with increasing radius of 2m/s .…

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: The length of a rectangle is decreasing at the rate of 5 cm/s and its width is increasing at the…

A: Area of a rectangle = length× width Rate of change with respect to time is D/Dt

Q: All edges of a cube are expanding at a rate of 9 centimeters per second. (a) How fast is the volume…

A: To find how fast the volume changing  when edge is 5cm and 12cm :

Q: A rectangle has a length of 7 inches and a width of 8 inches, whose sides are changing. The length…

A: Given: A rectangle has a length of 7 inches and a width of 8 inches, whose sides are changing.The…

Q: The radius of a sphere is increasing at a rate of 4 meters per minute. When the radius is 11 meters,…

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Q: All edges of a cube are expanding at a rate of 7 centimeters per second. (a) How fast is the volume…

A: Let , the edges of a cube=a cmall edges of a cube are expanding at a rate of 7 centimetres per…

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

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Q: Suppose that a cube's volume increases at a constant rate of 2 m. How fast are it's sides growing at…

A:

Q: Suppose oil spills from a ruptured tanker and spreads in a circular pattern. If the radius of the…

A: The calculation are as follows

Q: A rectangle is expanding such that its length is always 4 times its width. If the width is…

A: Let's find.

Q: Suppose that a spherical balloon is being inflated and the radius of the balloon is increasing at a…

A:

Q: A bacterial cell is spherical in shape. If the radius of the cell is increasing at the rate of 0.01…

A: Given , Bacterial cell is in spherical shape.Let radius be 'r' μm . ∴ Volume of cell, v v = 43π…

Q: 2. The diagonal of a square increases at the rate of 3 m/sec. How fast is the area changing when the…

A: Let the length of diagonal be y. so that, Now, Length of the side of a square be x. Using the…

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

A: Given that, All edges of a cube are expanding at a rate of 6 centimeters per second. Thus, dxdt=6…