An oil tanker aground on a reef is forming a circular oil slick about 0.1 foot thick (see the figure). To estimate the volumetric rate  (in cubic feet per minute) at which the oil is leaking from the tanker, it was found that the radius of the slick was increasing at 0.32 foot per minute when the radius R was 500 feet.

Q: 2. Oil leaks from a damaged, stationary oil tanker at the rate of 30 m3/hr, forming a circular oil…

A: The instantaneous rate of change is the differential of the variable. The rate of change of one…

Q: The radius r of a right circular cylinder with a fixed height of 48 inches is increasing. Find the…

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Q: The rate (in liters per minute) at which water drains from a tank is recorded at half-minute…

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Q: -10 10 t Water is running into an open conical tank at the rate of 9 cubic feet per minute. The tank…

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Q: dv represent? dt If V represents the volume of an object, what does

A: Given question is "V represents the volume of an object, what does dV/dt represent?:

Q: The radius of a circle is growing at a constant rate of 3 in./sec. (a) What is the area of the…

A: Introduction :

Q: Air is being pumped into a spherical balloon so that its volumeincreases at a rate of 100 cu. cm /s…

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Q: The altitude (,) of a right circular cylinder is always equal to the diameter (a) of the base. Find…

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Q: A faucet is filling a hemispherical basin of diameter 60 cmwith water at a rate of 2L/min . Find the…

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Q: Sand falls from an overhead bin and accumulates in a conical pile with a radius that is always three…

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Q: The volume V of a sphere with surface GUA SE Calculate the rate at which the volume of a sphere is…

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Q: 10. Gas is escaping from a spherical balloon at a rate of 2 cubic feet per minute. How fast is the…

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Q: Suppose a spherical balloon grows in such a way that after t seconds, its volume V is given by V = 4…

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Q: A balloon which maintains the shape of a sphere is being inflated. The rate of change of its volume…

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Q: At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 2…

A: Given data- dvdt=2 ft3/min. diameter (d) = 3h. We have to find the rate of change of height.

Q: Gravel is being dumped from a conveyor belt at a rate of 30 cubic feet per minute. It forms a pile…

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Q: #Ś A spherical balloon is filled with helium at a rate of 200 cmsec.At the moment when the radius is…

A: we have to find the rate change of surface area of the spherical balloon

Q: The volume of a sphere is expanding where r= 2t + 1. What is the rate of change in volume with…

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Q: 2. Find the rate of change of a volume V of a cube with respect to (a) the length w of a diagonal of…

A: Consider a cube of a side a , and diagonals z and w  We know that Pythagorean theorem , Hypotenuse 2…

Q: The volume of a sphere is increasing at the rate of 6 cm3/hr. at what rate is its surface area…

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Q: At noon, a city park manager starts filling a swimming pool. IfV(t) is the volume of water (in ft3)…

A: Given that a city park manager is filling his swimming pool. Volume of the swimming pool is V=43πr3.…

Q: The radius of a sphere decreases at a rate of 2 m/s. when the radius is 6 m, then the rate at which…

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Q: Use the differential dV to estimate the change in volume of a cube when the side length changes from…

A: Given, To determine the change in volume of a cube when the side length changes from 4 to 3.8.…

Q: Use the differential dV to estimate the change in volume of a cube when the side length changes from…

A: We have to estimate the change in volume of a cube. And given that the side length changes from 7 to…

Q: The radius r of a right circular cylinder with a fixed height of 48 inches is increasing. Find the…

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Q: The rate (in liters per minute) at which water drains from a tank is recorded at half-minute…

A:

Q: Gravel is being dumped from a conveyor belt at a rate of 30 cubic feet per minute. It forms a pile…

A:

Q: The radius of a circular oil slick expands at a rate of 8 m/min. (a) How fast is the area of the oil…

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Q: Gravel is being dumped from a conveyor belt at a rate of 50 cubic feet per minute. It forms a pile…

A: Given that dvdt=50,  Given that the base diameter and height are always equal.  So, 2r=h or, r=h2 We…

Q: The radius of a sphere decreases at a rate of 3 m/s. when the radius is 9 m, then the rate at which…

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

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Q: : B1. The radius of a sphere increases at the rate of 4 m/sec. Find the rate at which the volume of…

A: We have to find the rate of volume increase.

Q: Brine containing 3lb/gal of salt enters a tank at the rate of 4gal/min and the solution well-stirred

A: Given that the initial amount of salt is zero( because of pure water) Rate in 4gal/min Rate out…

Q: Use the differential dV to estimate the change in volume of a cube when the side length changes from…

A: We need to use the formula for differential to estimate the change in volume when side of the cube…

Q: hA balloon is being fi ned with helium at the rate Off 4 f+%A Fld the rate in 8quare teet per Minute…

A: The volume of a balloon with radius r will be V=43πr3 and surface area will be S =4πr2 Given: dVdt=…

Q: The rate (in liters per minute) at which water drains from a tank is recorded at half-minute…

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Q: A cancer tissue is in the shape of a sphere whose radius is increasing at the rate of 2 mm per day.…

A: we know that surface area of sphere is S=4πr2   As per our guideline, we supposed to answer only the…

Q: The altitude (,) of a right circular cylinder is always equal to the diameter (a) of the base. Find…

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Q: The rate (in liters per minute) at which water drains from a tank is recorded at half-minute…

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Q: The altitude of a right circular cone is 15 in, and is increasing at 0.2 in/min.  The radius of the…

A: Given, the altitude of a right circular cone,y=15 inch the radius of the cone,x=10 inch rate of…

Q: The rate (in liters per minute) at which water drains from a tank is recorded at half-minute…

A: The given table is: To find total amount of water drained during first 3 minute.

Q: Air is being pumped into a spherical balloon so that its volume increases at a rate of 40 m s1. How…

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Q: The radius of a sphere decreases at a rate of 5 m/s. when the radius is 7 m, then the rate at which…

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Q: A soap bubble has a radius of 6 in and a volume of 288T in. How fast is the volume changing if the…

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Q: The side of a cube increases at the rate of 10 m/sec. The rate at which the volume of the cube…

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Q: The radius of a circular oil slick expands at a rate of 7 m/min. (a) How fast is the area of the oil…

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Q: The rate (in liters per minute) at which water drains from a tank is recorded at half-minute…

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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.