Oil spilled from a ruptured tanker spreads in a circle whose area increases at a constant rate of 7 mi2/hr. How rapidly is radius of the spill increases when the area is 11 mi2/hr

Q: The length of the rectangle is increasing at a rate of 5 cm per second, and its width is decreasing…

A: topic - application of derivatives

Q: A balloon is rising vertically at a constant speed of 3 m=sec: A boy is cycling along a straight…

A: Given: dxdt=7 and dydt=3

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

A:

Q: The width of a rectangle increases at a rate of 2 cms. The length is five times its width. Find the…

A:

Q: The length of the rectangle is increasing at a rate of 5 cm per second, and its width is decreasing…

A: Area of rectangle = Length * Width

Q: A cylindrical pool has a height of 8 feet and a radius of 6 feet. How fast is the volume of the…

A: Here we solve the given problem of calculus.

Q: A high-speed bullet train accelerates and decelerates at therate of 4 fts 2 . Its maximum cruising…

A:

Q: ick is increasing at a rate of 3 meters per minute. How quickly is the area changing when the oil…

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Q: The sides of a square decrease in length at a rate of 1 m/s. At what rate is the area of the square…

A:

Q: The area of an equilateral triangle is decreasing at a rate of 4 sq. cm. per minute. Find the rate…

A: Given,dAdt=-4 cm2/minA=100cm2Let,x=side of the equilateral triangle find dxdt when dAdtis decreased…

Q: The altitude of a triangle is increasing at a rate of 3 cm/minute while the area of the triangle is…

A:

Q: Water is flowing at the rate of 2 m3/min into a tank in the form of an inverted cone having an…

A: The given question can be depicted as follows:Now, the volume of a cone is given by V = 13πr2h

Q: A 20 m tank is full of brine with 40 kg of dissolved salt. Pure water enters the tank at a rate of…

A: In this question, we find the amount of solt when the takl half full. given that  Initial amount of…

Q: Oil spilled from a ruptured tanker spreads in a circle whose area increases at a constant rate of…

A: We have to find the rate of radius increasing when Area, A=8 mi2 and rate of area increasing,…

Q: Water is being poured at the rate of 27 m³/min. into an inverted conical tank that is 12-meter deep…

A: Given that a canonical tank that had radius is 6meter and height is 12 meter and dh/dt= 1/6…

Q: A tank contains 100 liters of brine, with 50 kg total dissolved salt. Saltwater, with a…

A:

Q: The length of a rectangle is increasing at a rate of 5 cm per second and its width is decreasing at…

A: Given: Rate of increase in length of a rectangle, dldt=5 cm/s Rate of decrease in width of a…

Q: A man 2 mts high walks at a uniform speed of 6 km / h away from a lamp post 6 mts high. Find the…

A: According to the question,   To sketch the figure of the given condition,

Q: The length of the rectangle is increasing at a rate of 5 cm per second, and its width is decreasing…

A:

Q: The radius of the circle is increasing at a rate of 3 meters per minute and the sides of the square…

A: Since the circle is enclosed inside the square, the area between the circle and the square will be…

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

A: Here  radius of bubble is given and rate of change of radius of bubble is also given

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: A ladder is slipping down a vertical wall. If the ladder is 13 ft long and the top of it is slipping…

A: Given ,dydt=-2ft/s     negative sign because as ladder is slipping down, y decreasesby Pythagor…

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 patient's blood is traveling at a rate of 16 mL/sec while conveying a medicine into the liver and…

A: so, initially, liver is full at t = 0, but has no medicine,  medicine rich blood comes in, mixes…

Q: A plate in the shape of an equilateral triangle expands with time. The length of a side increases at…

A: Given that the length of side increases at a constant rate of 2 cm/h find out at what rate is the…

Q: The length of a rectangle is increasing at a rate of 5 cm per second and its width is decreasing at…

A: Let x be the length, y be the width and A be the area of the rectangle. Then we get, A = xy The rate…

Q: Water is being poured at the rate of 27 m²/min. into an inverted conical tank that is 12-meter deep…

A:

Q: Oil spilled from a ruptured tanker spreads in a circle whose area increases at a constant rate of 8…

A:

Q: A rectangle's length is increasing at the rate of 5 inches/sec, its width at 2 inches/sec. At what…

A:

Q: air containing 30% oxygen passes slowly into a 3 gallon flask initially filled with pure oxygen and…

A:

Q: A spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.2 cm/min.…

A: Please refer the attached image for complete solution.

Q: A fire has started in an open field and is spreading in the form of a circle, with its radius…

A:

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

A:

Q: The length of a rectangle is increasing at a rate of 8 cm/s and its width is increasing at a rate of…

A:

Q: A swarm of bees is spreading from an original region of 1 square mile. The region the swarm occupies…

A: Given that the original region of 1 square mile.  After 1 year area will be 2(1)=2=21 square miles…

Q: The length of the rectangle is increasing at a rate of 5 centimeters per second, and its width is…

A:

Q: Oil spilled from a ruptured tanker spreads in a circle whose area increases at a constant rate…

A:

Q: A cylindrical pool has a height of 8 feet and radius of 6 feet. How fast is the volume (in cubic…

A: Volume of cylindrical shape V=πr2h ------------------(1)

Q: Two parallel sides of a rectangle are lengthened at a rate of 3 cm/sec, while the other sides are…

A:

Q: A right circular cylinder has a 4 inch diameter and is filling with water at a constant rate.  The…

A: Consider the volume of right circular cylinder V. Differentiate it w.r.t time t.…

Q: A tank originally contains 385 litres of brine holding 470 N of dissolved salt. Eight litres/min of…

A: We will find out the required solution.

Q: The length of the rectangle is decreasing at a rate of 5 cm per second, and its width is increasing…

A:

Q: The altitude of a triangle is increasing at a rate of 1 cm/min while the area of the triangle is…

A: The altitude of a triangle is increasing at a rate of 1 cm/min while the area of the triangle is…

Q: How many kilometers can a train moving at an average velocity of 25 m/s southwest be displaced in 2…

A: Given, average velocity of train = 25 m/s 2 hours = 2x60x60 = 7200 seconds

Q: Water is flowing out of a cylindrical storage tank at a rate of 2 m3/min . If the tank has a radius…

A:

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: A 30 m³ tank is full of brine with 40 kg of dissolved salt. Pure water enters the tank at a rate of…

A: Volume of the tank is 30 m3 The tank is full of brine with 40 kg of dissolved salt. Pure water…

Q: Water is pouring into an inverted cone at the rate of 8 cubic meters per minute. If the height of…

A: Given: Water is pouring into an invented cone at the rate of 8 cubic meters per minute. Height of…

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.