The area of a rectangle with one of its sides s is A(s) = 6s². What is the rate of change of the area of the rectangle with respect to the sid n when s = 9?

Q: The area of a rectangle with one of its sides s is A(s) = 6s². What is the rate of change of the…

A: Differentiate both sides of the equation, with respect to s to establish a relation between the…

Q: The radius of a sphere is increasing at a rate of 3 mm/s. How fast is the volume increasing when the…

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Q: A cube is heated in such a way that the volume increases at a rate of 1 mm/s. The rate of change of…

A: A cube is heated in way that volume increases at the rate of 1mm/s. the side of the cube is 7mm…

Q: The length of a rectangle is increasing at a rate of 9 cm/s and its width is increasing at a rate of…

A: It would be best to express length, width, and area as functions of time. I’ll set x = width, y =…

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

A: Given that the diameter= 100 mm So the radius is=r=1002=50 mm Given that the radius of a sphere is…

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: Suppose a snowball remains spherical while it melts, with the radius r shrinking at 4 inch(es) per…

A: Let r be the radius of the snowball at any time t. The radius r is decreasing at the rate of 4 in/hr…

Q: A honeybee population starts with 100 bees and increasesat a rate of n'(t) bees per week. What does…

A: Given data: The initial honeybee population is n(0)=100. If n'(t) is the rate at which the…

Q: The edge of an expanding cube is changing at the rate of 2.3 cm/s at the instant its edge is 18.3 cm…

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Q: A tank contains 100 gal of brine made by dissolving 80 lb of salt in water. Pure water runs into the…

A: Many real-life problems can be modeled using differential equations. This is one of the significant…

Q: 9. When a particular plate of metal is heated in an oven, its radius increases at the rate of…

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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: The radius of a circle is increasing at the rate of 4 cm/s. How fast is the area of the circle…

A: Given,           The radius of a circle is increasing at the rate of 4 cm/s. And the radius is 5 cm…

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: The length of a rectangle is increasing at a rate of 4 cm/s and its width is increasing at a rate of…

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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 spherical balloon is increasing at the rate of 2 cm per minute. How fast is the…

A: Let r be the radius of spherical ballon

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: 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: An 8- meter ladder is leaning against a vertical wall. If a the ladder away from the person pulls…

A: Given  Length of the ladder = 8 meter The rate at which ladder is pulled away from the wall =0.7m/s…

Q: 1. If the radius of a spherical balloon is increasing at the rate of 3 cm/s, which of the following…

A: We are only allowed to solve one question at a time so we will answer only the first question.…

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

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Q: Water is discharged from an inverted cone-shaped tank with a height of 12 meters and a radius of 6…

A: Given: The height of the inverted cone-shaped tank, h = 12m. Also, its radius, r = 6m. From the…

Q: A designer develops a cylindrical box with a fixed height of 15 cm. Calculate the instantaneous rate…

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Q: The length of a rectangle is increasing at a rate of 7 cm/s and its width is increasing at a rate of…

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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: 2. The radius and lateral area of a right circular cylinder change at the rates of 1 cm/s and -2…

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Q: A balloon has just been inflated. Calculate the instantaneous rate of change by which the area…

A: Introduction: A geometric shape with a sphere-like appearance. In three dimensions, the sphere is…

Q: 1. Suppose that oil spills from a container and spreads in a circular pattern. If the radius of the…

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Q: A 100-ft long cable of diameter 4 in. is subsequently submerged in seawater. Due to corrosion, the…

A: Given that diameter is 4 inches and height is 100 feet. And rate of decrease in area is 750 in2yr.…

Q: A spherical balloon is inflated so that its volume is increasing at the rate of 2 ft3/minft3/min.…

A: Given: A spherical balloon is inflated so that its volume is increasing at the rate of 2 ft3/min.…

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

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Q: Find the rate Of Chaange the folloewing in Table de. X 1-2)-1 TO fex) F3 -1 3.

A: Given that table values, x -2 -1 0 1 f(x) -3 -1 1 3 Use the formula of the rate of change,…

Q: The length of a rectangle is increasing at a rate of 7 cm/s and its width is increasing at a rate of…

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Q: The length of a rectangle is increasing at a rate of 8 cm/s and its width is increasing at a rate of…

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Q: The length of a rectangle is increasing at a rate of 9 cm/s and it’s width is increasing at a rate…

A: Rectangle: It is a polygon with four side and opposite sides are equal.  Also. the all the four…

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: A rectangle has a length of 12 inches and a width of 6 inches whose sides are changing. The length…

A: The length of a rectangle is l=12 inThe width of a rectangle is w=6 inTo find the rate at width the…

Q: A rectangle has a length of 9 inches and a width of 10 inches whose sides are changing. The length…

A: Length of the rectangle, l =9 inches Width of the rectangle, w = 10 inches The length is increasing…

Q: The radius of semicircle is increasing at the rate of 0.8 cm/s, calculate the rate of change in the…

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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: The length of a rectangle is increasing at a rate of 6 cm/s and its width is increasing at a rate of…

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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: Find the rate of change. Volume V of a cylinder with respect to radius if the height is equal to the…

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Q: The surface area of a cube with sides of length x is given by S = 6x2 . Find the rate of change of…

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Q: The diameter of a sphere is 5(2x+ 5), the rate of change of its surface area with respect to x is

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

A: Given that the radius of a sphere is increasing at a rate of 4mm/s. That is, Now consider the…

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…