Suppose that a mothball loses volume by evaporation at a rate propotional to its instataneous area. If the diameter of the ball decrease from 2 cm to 1 cm in 3 months,how long will it take until the ball has practically gone.

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: 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 that the sides of a cube are expanding at a rate of 2 inches per minute. How fast i the…

A: We need to find the rate of change of volume of cube when side is 20 inches. Volume of cube=(side)3…

Q: The edges of a cube are expanding at a rate of 5cm per second. How fast is the volume changing when…

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Q: The radius of a right circular cone is increasing at a rate of 1.1 in/s while its height is…

A: Given that, drdt=1.1 in/s and dhdt=-2.7 in/s. Also, it is given that r=102 in. and h=162 in. It is…

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: A spherical snowball is melting in such a way that its radius is decreasing at rate of 0.1 cm/min.…

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Q: The surface area of kelp near Monterrey Bay is 40,000 square acres, but after four years a red sea…

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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: There is a constant outflow of a liquid into a inverted conical vessel 15 m deep and 7.5 m in…

A: Find the rate of change of volume of water in the cone, with respect to time:…

Q: Suppose that the sides of a cube are expanding at a rate of 2 inches per minute. How fast is the…

A: all details are given in below. please check it

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: Suppose the sides of a cube are expanding at a rate of 2 inches per minute, How fast is the volume…

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Q: A block of ice, in the shape of a right circular cone, is melting in such a way that both its height…

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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: the

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Q: A rectangle is growing in such a way that when its length is 5 ft and its width is 2 ft, the length…

A: When length is:= 5 ft; When width is:= 2 ft; Rate of increasing length= 3 ft/s; Rate of increasing…

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: Suppose a liquid is to be cleared of sediment by pouring it through a cone-shaped filter. Assume…

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Q: A balloon, in the shape of a right circular cylinder, is being inflated in such a way that 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: A cylindrical tank with radius 3 m is being filled with water at a rate of 3 m³/min. How fast is the…

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Q: The original 24 m edge length x of a cube decreases at the rate of 2m/min.   When x=2 m, the…

A: Given,           The original 24 m edge length x of a cube decreases at the rate of 2 m/min.We know…

Q: The radius of a right circular cone is increasing at a rate of 1.2 in/s while its height is…

A: To calculate the required rate of change using partial derivatives

Q: If the volume of a cube is increasing at a rate of 24 in'/min and each edge is increasing at 2…

A: The volume of cube is given by V=a3 where a edge of cube. Given that volume of cube increasing at 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: 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: The radius of a right circular cone is increasing at a rate of 5 inches per second and its height is…

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Q: 2. Suppose that the bottom of a conical shaped tank of water has been ruptured. At the instant when…

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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 population of yeast cells can double in 6 hours. Assume an initial population of 4,000 cells. What…

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Q: 17. If the radius of a sphere is increasing at the constant rate of 3 inches per second, how fast is…

A: Given: The radius of the sphere is increasing at the constant rate of 3 inches per second. To find:…

Q: The side of the base of a square prism is decreasing at a rate of 7 km/min and the height of the…

A: Surface area of a square prism is given by- A=2a2+4ah where a is side of prism, h is height of…

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: 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: 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: 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: Suppose the radius of a sphere is expanding at a rate of 3 inches per minute. How fast is the volume…

A: Let V & r be the volume and radius of the sphere at any time t respectively. Given that, the…

Q: If the original 24 m edge length x of a cube decreases at the rate of5 m/min, when x = 3 m at what…

A: Given: S the surface area of the cube, x the length of the cube and the length x of the cube…

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

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Q: Suppose that a tumor in a person's body has a spherical shape and that treatment is causing the…

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Q: A toxic radioactive substance with a density of 9 milligrams per square cm is detected in the…

A: It is given that, A toxic radioactive substance with a density of 9 milligrams per square cm is…

Q: A triangle has a base that is decreasing at a rate of 4 cm/s with the height being held constant.…

A: Let b and h be the base and height of the trianglegiven rate at which base is decreasing, dbdt=4cm/s…

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: If the original 24 m edge length x of a cube decreases at the rate of5 m/min, when x = 3 m at what…

A: If the original 24 m edge length x of a cube decreases at the rate of5 m/min, when x = 3 m at what…

Q: Suppose an elastic rubber band is used to make a square, and is being streched (while keeping the…

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Q: 5) If the radius of a right circular cylinder is increasing at a rate of 1 inch per minute, and the…

A: The volume of cylinder is given by the formula V=πr2h. The given values are as follows: r=40 inches,…

Q: The radius of a sphere, initially zero, increases at the rate of 4 feet per second. Find how fast…

A: Solution :Given  the adius of a sphere, initially zero, increases at the rate of 4 feet per…

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.