Suppose that a drop of mist is a perfect sphere and that, through condensation, the drop picks up moisture at a rate proportional to its surface area. Show that under these circumstances the drop’s radius increases at a constant rate.

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 1.2 in/s while its height is…

A: Differentiate volume wrt t

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

A: Formula of volume V=43πr3 Given: Radius, r=8 mm drdt=-1mm/month

Q: The ice cream in a sugar cone (conically shaped) has all melted and is dripping out a hole in the…

A: To express r in terms of h, use the the ratio between the height and radius of the cone is constant…

Q: Suppose that a given moment, the radius of a right circular cylinder is 2 cm and increasing at a…

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Q: Find the volume of a hemispherical shell having outer radius a and inner radius b if the density…

A: Mass density is defined as the mass per unit volume. gm/cm3 is, therefore, a unit of mass density.…

Q: A right cylindrical can has a radius and height of 50 and 120 cm, respectively. Find the approximate…

A: Let  r  and h be the radius and height of the cylinder .Then the volume of the cylinder  V(r,h) =…

Q: A conical vessel 12 cm deep and with a radius of 6 cm at the top, is being filled with water. If the…

A: A conical vessel 12 cm deep and with a radius of 6 cm at the top. That is, the height of the cone is…

Q: 2. A water heater that has the shape of a right cylindrical tank with a radius of 2 ft and a height…

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Q: A cube has sides that are increasing at a rate of 10 cm/s. At what rate is the volume increasing…

A: Valur=?

Q: If the volume of a cube is decreasing at a rate of 24 in sec, then find the rate at which the length…

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Q: Suppose a l-m cylindrical bar has a constant density of 1 g/cm for its left half and a constant…

A: Given, Suppose a 1-m cylindrical bar has a constant density of 1g/cm for its left half and a…

Q: Suppose the radius of a sphere is increasing at a rate of 5 in/second.  At what rate is the surface…

A: Given that radius of a sphere is increasing at an of 5 in/sec. Let r be the initial radius of the…

Q: Suppose at the end of the d perature stays constant at M furnace/air conditioner rate A

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Q: The radius of the base of a right circular cone is decreasing at the rate of 4 cm/min, and the…

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Q: 2. A water tank is in the form of an inverted right circular cone h feet deep and d feet wide across…

A: At any time t, let the height of the water be h ft and the radius of the cone formed by the volume…

Q: The original 24 m edge length x of a cube decreases at the rate of 3 m/min. a. When x = 4 m, at what…

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Q: 11. If the original 24 m edge length x of a cube decreases at the rate of 5 m/min, when x = 3 m at…

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Q: A spherical balloon is being deflated at a rate of 80 cm3/min. At what rate is the radius decreasing…

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Q: Suppose that a mass weighing 10 lb stretches a spring 2 in. If the mass is displaced an additional 2…

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Q: At what rate is the diagonal of a cube increasing if its edges are increasing at a rate of 2 cm/s?

A: To find the rate at diagonal of a cube is increasing

Q: 1. A car is travelling at 50 mi/hr when the breaks are fully applied, producing a constant…

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Q: The altitude of a certain circular cone is the same as the radius of the base, and is measured as 5…

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Q: Suppose a 1-m cylindrical bar has a constant density of 1 g>cm for its left half and a constant…

A: Given-  a 1-m cylindrical bar has a constant density of 1 g>cm for its left half and a constant…

Q: Suppose that a drop of mist is a perfect sphere and that, through condensation, the drop picks up…

A:

Q: The original 24 m edge length x of a cube decreases at the rate of 2 m/min. a. When x = 1 m, at what…

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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: Imagine a sphere whose radius r increases at a rate of 3 cm/s. At what rate is the volume V of the…

A: Note the results : Volume of the sphere is 43πr3 . Suppose F is a function of x and x is a function…

Q: With what initial velocity must an object be thrown upward from a height of 8 feet to reach a…

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Q: Suppose div F = 0 in a region enclosed by two concentricspheres. What is the relationship between…

A: Apply the divergence theorem for the hollow region which is bounded by 2 surfaces. Consider D as the…

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: . Suppose that an air-filled cone-shaped balloon has a leak causing air to escape at a rate of 24…

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Q: 11. At what rate is the volume of the cube changing if the edge is 8 cm and is changing at 4 cm/s?

A: As we know that; The expression for the volume of the cube with the edge length ''a'' is: v=a3…

Q: The original 24 m edge length x of a cube decreases at the rate of 2 m/min. a. When x = 4 m, at what…

A: As Given :                   The length x of Cube decrease at a rate of 2 m/min.…

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: 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: Show that the period of motion of an undamped vibration of a mass hunging from a vertical spring is…

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Q: A comet loses material when it gets close to the Sun at a rate of 100 cubic meters per minute.…

A: Given Comet is a sphere Its radius is 200 meters Let V be the volume of the comet then r be the…

Q: If a ball is thrown vertically upward and with an initial velocity of 10 m/s, it’s velocity at the…

A: To find: The velocity at the highest point reached by the stone. Given: The initial velocity of the…

Q: A conical glass, 10cm high and 8cm in diameter at the top is filled with an exquisite wine to a…

A: Find the sum of volume of the wine and ice cube and compare with the total volume of the conical…

Q: The dimensions of a closed rectangular box are measured as 89 cm, 61 cm, and 35 cm, respectively,…

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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: 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: 2. A cylindrical tank standing upright (with one circular base on the ground) has radius 1 meter.…

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Q: All the edges of a cube are expanding at a rate of 1/6 cm/sec. Determine the rate of change of the…

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Q: 5 If a snowball melts so that its surface area decreases at a rate of 10 cm2/min, find the rate at…

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Q: Consider a thin plate of constant density d lying in the regionbounded by the graphs of y = √x and x…

A: First find the intersection points of the given curve, by equating the y of both curves…

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.