Suppose the water in Example 4 is poured in at the rate of cubic inches per second. How fast is the water level rising when the water is 2 inches deep?

Q: All edges of a cube are expanding at a rate of 8 centimeters per second. (a) How fast is the surface…

A: Surface area of cube = 6x2Where x is the edge of the cube

Q: 7. A triangle with a base of 20 inches has a height that is decreasing at a rate of 3 inches per…

A:

Q: A mold grows at a rate proportional to its present size. Initially there is 2 oz of this mold, and…

A: Let size of mold at time t is yt then according to given condition dydt α yt⇒dydt=kyt where k is…

Q: Assume that the rate of evaporation for water is proportional to the amount of water in a bowl. If…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Car A leaves a parking lot at 9 am and travels eastward at the rate of 60 kph. Another vehicle, car…

A:

Q: All edges of a cube are expanding at a rate of 8 centimeters per second. (a) How fast is the volume…

A:

Q: A rectangular parallelepiped with an altitude of 10cm has its width decreasing by 2 cm/min and…

A: A rectangular parallelepiped with an altitude of 10cm has its width decreasing by 2 cm/min and…

Q: All edges of a cube are expanding at a rate of 8 centimeters per second. (a) How fast is the volume…

A:

Q: The volume of a cube is decreasing at a rate of 24 cubic inches per minute. At the instant when an…

A: Given that  The volume of a cube is decreasing at a rate of 24 cubic inches per minute.…

Q: 2. In a certain bacterial culture where the rate of growth of bacteria is proportional to the number…

A: Solution is given below:

Q: The volume of oil in a cylindrical container is increasing at a rate of 150 cubic inches per second.…

A:

Q: A ladder 25 feet is leaning against a wall. If the foot of the ladder is being pulled away from the…

A: To determine the rate at which the ladder is sliding. Given: Ladder is 25 feet long dx/dt = 14…

Q: A ladder 20 feet long leans against a house. What is the rate at the top of a ladder that is moving…

A: Given that ,      A ladder 20 feet long leans against a house. We have to calculate the rate at the…

Q: A spotlight on the ground shines on a wall 12m away. If a man 2m tall walks from the spotlight…

A:

Q: In the absence of predators the population of mosquitos in a certain area would inccrease at a rate…

A: Let P(t) be the population of mosquitoes in the area with t in weeks, and k be the rate at whichthey…

Q: The rate at which bacteria multiply is proportional to the instantaneous N numbers present. If the…

A: Let y(t) represents the number of bacteria present in the culture after t hours. Let the initial…

Q: A 17 feet ladder is leaning against a wall. if the bottom of the ladder is pulled along the ground…

A: Given:- A 17 feet ladder is leaning against a wall. if the bottom of the ladder is pulled along the…

Q: All edges of a cube are expanding at a rate of 5 centimeters per second. (a) How fast is the volume…

A:

Q: The length of a rectangle is increasing at a rate of 5 meters per hour and the width is decreasing…

A: The length of a rectangle is 11 meters and the width is 20 meters. The length is increasing at a…

Q: A 15-foot teddy bear is leaning against a shelf. The top hand of the teddy bear is sliding down the…

A: Let horizontal distance= x ft , vertical distance= y ft Relation between x and y is: Given that…

Q: Bacteria grown in a certain culture increase at a rate proportional to the amount present. If there…

A: This question is based on application of diffrential equation.

Q: All edges of a cube are expanding at a rate of 6 centimeters per second (a) How fast is the surface…

A: Rate of change of surface area is given by ds/dt = a . dA/dt Where a = edge length dA/dt =rate of…

Q: Water is leaking from a 2 foot tall rectangular tank at 0.1 cubic foot per hour. Suppose that the…

A: Given that water is leaking from a 2 foot tall rectangular tank at 0.1 cubic foot per hour. And the…

Q: 4. A rock thrown into a still pond and causes a circular ripple. If the radius of the ripple is…

A: Follow the procedure given below.

Q: A wet towel hung from a clothesline to dry loses moisture through evap-oration at a rate…

A:

Q: A swimming pool is 20 ft wide, 40 ft long, 3 ft deep at the shallow end, and 9 ft deep at its…

A:

Q: All edges of a cube are expanding at a rate of 2 centimeters per second. (a) How fast is the volume…

A:

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

A:

Q: A bacteria culture is known to grow at a rate proportional to the amount present. If the population…

A: This is a problem of the application of differential equations.

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

A: Given dr/dt = 3

Q: All edges of a cube are expanding at a rate of 2 centimeters per second. (a) How fast is the volume…

A:

Q: edges of a cube are expanding at a rate of 8 centimeters per second. How fast is the volume changing…

A:

Q: An ice cube that is 3 cm on each side is melting at the rate of 2 cubic cm per min. How fast is the…

A:

Q: If the area A = s of an expanding square is increasing at the constant rate of 8 square inches

A:

Q: All edges of a cube are expanding at a rate of 8 centimeters per second. (a) How fast is the volume…

A:

Q: The growth rate of a bacteria culture is proportional to the number of bacteria present. If a…

A:

Q: Sand flows out of an hourglass at a rate of 4 cubic inches per second and forms a conical pile. How…

A: Write the expression for volume of cone take the derivative with respect to time t than put the all…

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: The length of a rectangle is decreasing at the rate of 1 feet per second, but the area remains…

A: Let x and y ( in feet ) be the length and width of rectangle and A ( in ft2) be the area of…

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

A: To find how fast the volume changing  when edge is 5cm and 12cm :

Q: All edges of a cube are expanding at a rate of 7 centimeters per second. (a) How fast is the volume…

A: Let , the edges of a cube=a cmall edges of a cube are expanding at a rate of 7 centimetres per…

Q: A 3.5 cu. inches car air freshener is losing volume at a rate of 1% per day. Find the volume after…

A: If the initial amount of any substance is N0 and it is decreasing at the rate of a% then amount left…

Q: The top of a 18 foot ladder, leaning against a vertical wall, is slipping down the wall at the rate…

A:

Q: All edges of a cube are expanding at a rate of 3 centimeters per second. (a) How fast is the volume…

A:

Q: All edges of a cube are expanding at a rate of 4 centimeters per second. (a) How fast is the surface…

A: From the given data: The rate of expanding of a cube is 4cm/sec

Q: A wet towel hung on a clothesline to dry outside loses moisture at a rate proportional to its…

A:

Q: All edges of a cube are expanding at a rate of 4 centimeters per second. (a) How fast is the surface…

A:

Q: The volume of a cube is increasing at the rate of 2 cubic inches per minute. How fast is the surface…

A:

Q: All edges of a cube are expanding at a rate of 6 centimeters per second. How fast is the volume…

A: Given that, All edges of a cube are expanding at a rate of 6 centimeters per second. Thus, dxdt=6…

Q: 2. The population of a country doubles in 50 years. How many years will be 5 times as much? Assume…

A:

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.