Is the rate of change of a cube's volume linearly proportional to the rate of change of its side?

Q: assume that an airplane is flying toward you at a constant height, h miles, and at a speed dx/dt.…

A: assume that an airplane is flying toward you at a constant height, h miles, and at a speed dx/dt.…

Q: the velocity of a particle is the rate of change in the position function over time true or false

A: We have to check

Q: An engineer is experimenting with a cylindrical can with a fixed height of 15 in. Find the rate of…

A: GIVEN-  A CYLINDER OF HEIGHTS 15 inch is given AND RADIUS =4 inch TO FIND -  RATE OF CHANGE OF…

Q: One ship, Ship A, is approaching a port from the east, travleing west at 15 miles per hour, and is…

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Q: How fast is the volume of a parallelepiped increasing if the length, width, and height of the…

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Q: The radius of a right circular cylinder is increasing at a rate of 4 inches per minute, and the…

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Q: a snowball melts in such a way that the rate of change in its volume is proportional to its surface…

A: Please see the below pictures for detailed solution.

Q: Find the rate of change of supply price with respect to the number of units supplied.

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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: 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: Can instantaneous velocity be defined as a ratio? If not, how is instantaneous velocity computed?

A: We know that instantaneous velocity is the average velocity between two points on the path in the…

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: Can the instantaneous rate of change be different than the average rate of change in the same…

A: We describe that the instantaneous rate of change be different than the average rate of change in…

Q: A spherical snowball melts at a rate proportional to its surface area. Show that that rate of change…

A: It is given that, the spherical snowball melts at a rate proportional to it’s surface area. This can…

Q: Find the rate of change of the area of a square with respect to the length z of a diagonal. What is…

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Q: Example: Find the rate of change of the volume of a cylinder with respect to r if h = 10m.

A:

Q: If a snowball melts so that its surface area decreases at a rate of 2 cm2/min, find the rate at…

A:

Q: If we know the rate of growth of a patch of moss, how can we calculate the area the moss covers?

A: The rate of growth of a patch of moss is modeled by a complex function A't, where t is measured in…

Q: A spherical snowball is melting so that its diameter is decreasing at a rate of 0.4 cm/min. At what…

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Q: A cone-shaped tank of water is leaking water at a constant rate of 3 m³/hour. If the base radius of…

A: Using volume  of cone and applications of derivative idea we solve this

Q: Find the rate of change of the total surface area of a cylinder of radius r and height h, when the…

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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: The pressure exerted by a certain Iiquid at 0 given point varies directly as the depth of the point…

A: Given pressure of liquid at a point is directly proportional to the depth of the surface at the…

Q: 2. A tank with a shape of a cone is 20 feet deep and has a diameter of 10 feet at the top. Water is…

A: Given; Diameter = 10 feet  Height = 20 feet

Q: the top of a 25 foot ladder is sliding down a vertical wall at a constant rate of 3 feet per minute.…

A: Given  c=25 ft b= 7ft dbdt=3 ft/minute dcdt=0

Q: One airplane is approaching an airport from the north at 203 km/hr. a second airplane approaches…

A: Let in the below figure P represents the airport, Q represents the southbound plane and R represents…

Q: One airplane is approaching an airport from the north at 128 km/hr. A second airplane approaches…

A: Let x be the distance of south bound plane and y be the distance of west bound plane from airport at…

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

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Q: The linear density of a cable wire is the rate of change of its mass with respect to its length. A…

A:

Q: If the radius of a cone increases at a rate of 36 inches per second and the height decreases 2 feet…

A: Given

Q: Assume the learning rate for new skills is proportional to the difference between the maximum…

A: The learning rate for new skills is proportional to the difference between the maximum potential for…

Q: Find the rate of change of the surface area of the cube when the volume is 8 cm". A block of ice in…

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Q: Find the rate of change of volume of a sphere with respect to its surface area when the radius is 2…

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Q: What is the rate of change of distance between the top of the ladder and the ground?

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Q: Show that the rate of change of the area of a circle with respect to its radius is equal to the…

A: Our Aim is to show that the rate of change of area of a circle with respectto its radius is equal…

Q: The temperature at a point in a ball with conductivity K is inversely proportional to the distance…

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Q: The radius of a right circular cone is increasing at 3 cm/min whereas the height of the cone is…

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Q: The volume of a cube decreases at a rate of 0.3 3ft/min. What is the rate of change of the side…

A: Let the length of each side of the cube be a ft. Find the volume of the cube. Differentiate the…

Q: A balloon, in the shape of a right circular cylinder, is being inflated in such a way that the…

A:

Q: A cone-shaped tank of water is leaking water at a constant rate of 2 m3/hour. If the base radius of…

A: Given that

Q: Assume the rate at which the zombies spread is jointly proportional to the number of encounters…

A: Given: Let the total number of student is 300 in the campus.

Q: A spherical balloon is being deflated at the rate of 10 cm/s. What is the rate of change for the…

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Q: An ice cube melts in the sun, causing it to shrink. Use a linear approximation to estimate the…

A: The length of the side of the ice cube changes from 1 inch to 0.9 inch The decrease in the side of…

Q: 2. The height and volume of a right circular cone change at the rates of 1 cm/s and -2 cm^3/s,…

A: Let's find.

Q: What is the velocity of flow in feet per seconds f

A:

Q: How can you relate the rate of change for the surface area of a cube (dSA/dt) as compared with its…

A: we know that surface areaS.A. and volumeV of cube is given by S.A.=6l2…

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

A: