A stone dropped into a still pond sends out a circular ripple whose radius increases at a constant rate of 2 meters per second. How rapidly is the area enclosed by the ripple increasing at the end of 20 seconds?

Q: A board 10 feet long slides down a wall. At the instant the bottom end is 8 feet from the wall, the…

A: Pythagoras theorem: Hypotenuse2=Base2+Perpendicular2 Product rule of differentiation: (fg)'=fg'+gf'…

Q: Example Air is being pumped into a spherical balloon at a rate of 5 cm'/min. Determine the rate at…

A: Air is being bumped into the balloon at a rate of 5 cm3/min. The volume V of the balloon change at a…

Q: A cable is to be run from a power plant on one side of a river 600 m wide to the factory on the…

A: Note: According to the guideline only one question will be answered please upload remaining one…

Q: A circle is inside a square. The radius of the circle is increasing at a rate of 3 meters per minute…

A: Given:- A circle is inside a square. The radius of the circle is increasing at a rate of 3 meters…

Q: nt) A spherical balloon is inflated so that its volume is increasing at the rate of 3.3 ft/min. How…

A:

Q: Water is flowing into a pyramidal water tank with a square top 3 meters on a side and 7 meters in…

A:

Q: A tank contains 90 kg of salt and 1000 L of water. A solution of a concentration 0.045 kg of salt…

A:

Q: 1. A spherical balloon is being inflated so that its volume is increasing at a rate of 5 cubic feet…

A: Authoring guidelines: As per the authoring guidelines, we can solve only the first question.Please…

Q: A water tank is in the shape of an inverted cone. The height of the cone is 10 meters and the…

A:

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

A: We have to find the change of surface area of a cube while it is given that all edges of a cube are…

Q: cm3 A spherical snowball is melting at a rate of 9.3- min How rapidly is the radius decreasing when…

A: Radius is decreasing by 0.009 cm/min.

Q: A tank is initially filled to the brim with 1500 L of pure water. Brine containing 0.35 kg of salt…

A: !st we will make differential equation for amount of salt the will solve it to get total amount of…

Q: Sand is falling in a pile at the rate of 12'., Imin: It piles up in such a way that the diameter of…

A:

Q: 34) The volume of a rectangular box with a square base remains constant at 1200 cm3 as the area of…

A: Let the length of each side of the base= x  Height = y  time=t Area of the base= A= x2 So,…

Q: A ladder is leaning against a wall. The ladder is 5 feet long. The top of ladder slides down the…

A: Let the horizontal distance be x and the vertical distance be y . According to the given problem we…

Q: 6. A tank contains 40 liters of a chemical solution prepared by dissolving 80 g of a soluble…

A: Given:      Since initially there are 40 l of solution prepared by 80 g of substance. So, V0=40…

Q: A tank contains 80 kg of salt and 2000 L of water. A solution of a concentration 0.02 kg of salt per…

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

Q: Water is flowing at the rate of50 m3/min from a shallow concrete conical reservoir (vertexdown) of…

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Q: 9. A rectangle initially has dimensions 2 cm by 4 cm. All sides begin increasing at a rate of 1…

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Q: A five-gallon bucket is full of pure water. Suppose we begin by dumping salt into the bucket at a…

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Q: Ripples in the form of coincentric circles are formed when a pebble is dropped in a pond. the radius…

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Q: 32. An experiment starts and the population of a bacteria culture increases by 10% in the first…

A: According to the question, experiment starts and the population of bacteria culture increases by 10%…

Q: A rectangle initially has dimensions 4 cm by 7 cm. All sides begin increasing in length at a rate of…

A:

Q: Sand is falling from a chute at the rate of 24 - in and forming a conical pile on min 3 the ground…

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Q: circle is inside a square. The radius of the circle is decreasing at a rate of 3 meters per hour…

A: Here we have to use the concept of derivatives

Q: Draining a tank Water is drained from a 3000-gal tank at a rate that starts at 100 gal/hr and…

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: fungal colony grows on a flat surface starting with a single spore. The shape of the colony edge is…

A: Given query is to find the rate of change of area.

Q: A tree trunk is approximated by a circular cylinder of height 50 meters and diameter 4 meters. The…

A: Volume of cylinder = πr2h r = radius of cylinder h= height of cylinder

Q: Disappearing triangle An equilateral triangle initially has sidesof length 20 ft when each vertex…

A: Given that: An equilateral triangle initially has sides of length 20 ft when each vertex moves…

Q: A tank contains 100 kg of salt and 1000 L of water. A solution of a concentration 0.05 kg of salt…

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Q: Gravel is being dumped from a conveyor belt at a rate of 30 ft^3/min. It forms a pile in the shape…

A:

Q: Air is being pumped into a spherical balloon at a rate of 5 cm/min. Determine the rate at which the…

A:

Q: Gravel is being dumped from a conveyor belt at rate of 10 ft°/min. It forms a pile in the shape of a…

A: We will solve the problem

Q: Gravel is being dumped from a conveyor belt at a rate of 10 ft/min. It forms a pile in the shape of…

A:

Q: area of a square is increasing at a rate of 1 sq cm/s. How fas diagonal increasing when the area of…

A:

Q: Optimization: A circular oil slick of uniform thickness is caused by a spill of 1 m3 of oil. The…

A:

Q: Surface Area All edges of a cube are expanding at a rate of 8 centimeters per second. How fast is…

A:

Q: The radius of a sphere, initially zero, increases at rate 6 ft per seconds. Find how fast the volume…

A: By using differentation and integration and rate of change

Q: A ladder is leaning against a wall. The ladder is 17 feet long. The top of ladder slides down the…

A: We will find out the required value.

Q: 5. Sand is pouring from a hole at the rate of 25 cubic feet per second and is forming a conical pile…

A: Solution ) dv/dt = 25 ft3/ sec  h = d/4  d = 4h  [ d = r/2 ] r/2 = 4h  r = 2 × 4h  r = 8h  h = 5…

Q: A tank holds 300 gal of brine solution with 50 pounds of dissolved salt. A brine solution containing…

A: We know that ∵dAdt=Rin-Rout ....(i) So, let's find Rin and Rout ∵ Rin= (concentration of salt in…

Q: Bacteria population initially contains 130 bacteria and the population grows at a rate of 6% every…

A: We can model the bacteria population using an exponential equation.     According to the data…

Q: Consider a tank used in certain hydrodynamic experiments. After one experiment the tank contains 200…

A: Consider Q(t) be the amount of dye present in the tank at any time t.Given that initial the tank…

Q: A big frozen blood (yes, blood...) cube with sides 2 feet is suspended from the ceiling and it’s…

A: Given : the side of the cube is 2 feet the volume of the cube =a3 Now take derivative of the volume…

Q: 2. [Growth of a tumor] When the radius of a spherical tumor is 6 mm, it is growing at a rate of 0.1…

A: To determine how fast the volume is changing.

Q: A circle is inside a square. The radius of the circle is decreasing at a rate of 3 meters per day…

A:

Q: A board 20 feet long slides down a wall. At the instant the bottom end is 16 feet from the wall, the…

A: Given: Length of ladder is 20 ft. sliding down a wall. Distance of the bottom end from the wall is…

Q: Water at the rate of 10 cm3/ min is pouring into the leaky cistern whose shape is a cone 16 cm. deep…

A:

Q: 3. A snowball is rolling down a hill, getting bigger as it goes. Assume the snowball remains a…

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Q: A circle is inside a square. The radius of the circle is decreasing at a rate of 2 meters per day…

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.