A spherical drop of liquid evaporates at a rate proportional to tis surface area. If a given drop evaporates to 1/8 of its volume in 5 minutes, in how many minutes will it evaporate completely?

Q: If a snowball melts so that its surface area decreases at a rate of 1cm /min, find the rate at which…

A: Diameter= DRadius = r =D/2Surface area = A= 4pi*r^2Given dA/dt= -1 cm^2/min (negative because…

Q: The volume of an ice cube is decreasing at a rate of 1.5 cm³/ sec. At what rate is a side of the ice…

A: We know that volume of a cube is given by V=a3 here V=volume of cube ,a=edge of cube Rate of change…

Q: 11. If a snowball melts so that its surface area decreases at a rate of 1 cm/min, find the rate at…

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Q: 8. If a snowball melts so that its surface area decreases at a rate of 4 cm2 /min , find the rate at…

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Q: The volume of a cube is increasing at a rate of 64 in/sec. At what rate is the length of each edge…

A:

Q: Each side of a square is 6 ft and is increasing at a rate of 2 ft per second. How fast is the area…

A: By differentiating equation of area of square with respect to time and substituting the value of…

Q: If a ball of candy is covered in chocolate and is melting so that its surface area decreases at a…

A: To find: The rate at which diameter decreases when diameter is 10 cm. Given: The rate of surface…

Q: Each side of a square is increasing at a rate of 6 cm/s. At what is the area of the square…

A: Given that, Area of square is  25cm2    Area A = x2 Where x is the side length. The area of square…

Q: snowball melts so that its surface area decreases ata rate of 1cm^2/min, find the rate at which the…

A: Given query is to find the rate of chnage of diameter.

Q: If a snowball melts so that its surface area decreases at a rate of 6 cm2/min, find the rate at…

A:

Q: A substance evaporates at a rate proportional to the exposed surface. If a sphericalmothball of…

A: The rate of evaporation is proportional to the exposed surface, and the exposed surface is that of a…

Q: If a snowball melts so that its surface area decreases at a rate of 7 cm2/min, find the rate at…

A: Solve using increasing & decreasing function.

Q: If a snowball melts so that its surface area decreases at a rate of 9 cm2/min, find the rate at…

A:

Q: The volume of an ice cube is decreasing at a rate of 1.5 cm³/sec. At what rate is a side of the ice…

A: option A is correct detailed solution with explanations given below

Q: The volume of a cube is increasing at a rate of 60 in/sec. At what rate is the length of each edge…

A: The objective is to find the rate at which the length of each edge of the cube is changing when the…

Q: The width of a rectangle is increasing at a rate of 2 cm/sec, while the length increases at 3…

A: The rate of increase of the width of a rectangle i.e. dwdt=2 cm/sec The rate of increase of the…

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

A:

Q: The width of a rectangle is increasing at a rate of 5 cm/sec, while the length increases at 6…

A:

Q: The side of a cube is increasing at a rate 7m/s, then the rate at which the volume of the cube…

A: Let s be the side of the cube in meter and V be the volume of the cube and t be the time in…

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 a snowball melts so that its surface area decreases at a rate of 9 cm2/min, find the rate at…

A:

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

A: (a)Given:

Q: If a snowball melts so that its surface area decreases at a rate of 7 cm2/min, find the rate at…

A:

Q: The original 24 m edge length x of a cube decreases at the rate of 5 ​m/min.   a. When x=5m, at what…

A:

Q: The volume of a cube is increasing at the rate of 8 cm /sec.How fast is the surface area in creasing…

A: We can find the answer as below

Q: If a snowball melts so that its surface area decreases at a rate of 1 cm²/min, find the rate at…

A: 1) Let A be the surface area  r = radius of the sphere D = diameter of sphere = 10 cm…

Q: at what rate is the volume of the cube changing if the edge is 8cm and is changing at 4cm/sec?

A: The volume of a cube is: Where, a is the edge of the cube. Formula used:

Q: If a snowball melts so that its surface area decreases at a rate of 4 cm2/min, find the rate at…

A: To find the rate at which the diameter decreases when the diameter is 12 cm and surface area…

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

A:

Q: The rate at which bacteria multiply is proportional to the instantaneous Number Present. If the…

A:

Q: a. If a snowball melts so that its surface area decreases at a rate of 1 cm²/min, find the rate at…

A:

Q: A stone dropped in a pond sends out a circular ripple whose radius increases at a constant rate of 2…

A: Given ,  A stone dropped in a pond sends out a circular ripple whose radius increases at a constant…

Q: The radius of a right circular cone is increasing at a rate of 5 in/s while its height is decreasing…

A: Let,  r - radius of the right circular cone h-Height of the right circular cone  V- Volume of the…

Q: How fast is the volume of a cube changing when the edge is 15 cm if the edge is changing at the rate…

A:

Q: If a snowball melts so that its surface area decreases at a rate of 3 cm2/min, find the rate at…

A: Given,Surface area is decreasing at rate = 3 cm2 per minDiameter of the snowball (d) = 11 cm

Q: If the radius of a sphere increases at a rate of 0.5 m/sec, then the rate at which the volume of the…

A: Let the radius of the sphere be r. Then the volume of the sphere is: V=43πr3…

Q: an ice cube is shrinking uniformly at a rate of 8 cubic inches per hour. when the cube has a volume…

A: We are given the rate of change of volume of ice cube is shrinking uniformly at a rate of 8 cubic…

Q: A conical tank 20 feet in diameter and 30 feet tall (with vertex down) leaks water at a rate of 5…

A: To find the rate of water

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: How long (in hours) would it take to fill a city water tank that has an inside diameter of 120 feet…

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Q: The surface area of a balloon that is being filled with helium increases at a rate of 5 square feet…

A:

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

A:

Q: The volume of a cube is increasing at a rate of 56 in/sec. At what rate is the length of each edge…

A: Given that the volume of a cube is increasing at a rate 56 in3/sec and the edges are 8 in. long. It…

Q: The radius of a right circulare cylinder is increasing at the rate of 3 in/sec, while the height is…

A: To determine the change of rate of the volume of cylinder.

Q: The radius of a sphere decreases at a rate of 4 m/s. when the radius is 7 m, then the rate at which…

A:

Q: 7, If a snowball melts so that its surface area decreases at a rate of 3 cm2/min, find the rate at…

A:

Q: A process tank is being filled at a rate of 1200 GPM. If the tank is completely full, how much is…

A: In flow rate is 1200 GPM. Out flow rate is 320 GPM.

Q: The radius of an air bubble is increasing at the rate of 1/2 cm/s.At what rate is the volume of the…

A:

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

A:

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.