Find the work done by the gas for the given volume and pressure. Assume that the pressure is inversely proportional to the volume A quantity of gas with an initial volume of 2 cubic feet and a pressure of 1000 pounds per quare foot expands to a volume of 3 cubic feet.

Q: In the electric currect flow, it is found that the resistance (measured in the units called ohms)…

A: Given that resistance offered by a fixed length of wire of a given material varies inversely as the…

Q: 2) If y is inversely proportional to the cube of x, find y when x =5, given y = 2 when x = 7. %3D

A: given y is inversely proportional to x3

Q: According to the Stefan-Boltzmann Law, the thermal radiation energy emitted (per unit time) by a hot…

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Q: The pressure exerted by a certain liquid at a given point varies directly as the depth of the point…

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Q: The gravitational force, F, between an object and the Earth is inversely proportional to the square…

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Q: irectly proportional

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Q: Suppose that y is directly proportional to x.  If y=6 and x=3, find the constant of proportionality…

A: Suppose that y is directly proportional to x. If y=6 and x=3, to find the constant of…

Q: If l represents the intensity of light which has penetrated water to a depth of x feet, then the…

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Q: Find the work done by the gas with an initial volume of 3 cubic feet and a pressure of 1000 pounds…

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Q: If y is directly proportional to x and x is directly proportional to z, then y is directly…

A: To write a variation equation for a given variation statement following things should be kept in…

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

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Q: The drag force (D) of an object falling through air varies directly as the square of its velocity…

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Q: A box weighing 50lbs falls from rest and the air resistance is proportional to his speed V and that…

A: We need to find velocity.

Q: Let y be inversely proportional to x. If y=12 when x=3, find the constant of proportionality k.…

A: We have to find k

Q: With snow on the ground and falling at a constant rate, a snowplow began plowing down a long…

A:

Q: The kinetic energy K of a movingobject varies jointly with its mass m and the square of itsvelocity…

A: Given, The kinetic energy K of a movingobject varies jointly with its mass m and the square of…

Q: The pressure exerted by a certain liquid at a given point varies directly as the depth of the point…

A: Given            The pressure at 70 feet=140

Q: Please see attached

A: Given,Side of cube = 7 inches

Q: It is a fundamental law of Physics that the force the Earth exerts on an object 5) varies inversely…

A: Solving the equation provided in a) gives the value of K.

Q: The rate at which a ceratin disease spreads is proportional to the product of the percentage of the…

A: We have to find the rate R(t) at which disease spreads Constant of  Proportionality = 0.03 Percent…

Q: Suppose you drive your car on a perfectly flat road at a constant speed with no wind. In this case,…

A: As given in the question, The amount of fuel is directly proportional to the distance Travelled. ⇒y…

Q: Let  x(V) = V1/3  be the length of the side of a cube in terms of its volume. As V decreases, does…

A: V is decreasing that is dv/dt is negative  Let dv/dt =-k where k is constant.

Q: Find the rate of change of the total surface area of a cylinder of radius r and height h, when the…

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Q: The velocity of a heavy meteorite enteringEarth’s atmosphere is inversely proportional to √s when it…

A:

Q: In the electric currect​ flow, it is found that the resistance​ (measured in the units called​ ohms)…

A: Resistance R ∝ 1/D2 R = k/ D2; where k is the proportionality constant. A wire 0.01 inches in…

Q: The pressure exerted by a certain Iiquid at 0 given point varies directly as the depth of the point…

A: Given pressure of liquid at a point is directly proportional to the depth of the surface at the…

Q: The intensity of illumination falling on a surface from a given source of lightis inversely…

A:

Q: comparing the surface area of a sphere with its volume and assuming that air resistance is…

A: We will solve the following.

Q: X is inversely proportional to the square root of y and y is inversely proportional to the cube of…

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Q: y is inversely proportional to the square root of (x + 1). When x = 8, y = 2. %3D Find y when x =…

A: y is inversely proportional to the square root of (x+1). Also When x=8, y=2. To find y when x=99.

Q: Assume that r varies directly as P. what is the constant of proportionality if R equals three when P…

A: Given r varies directly as p . we find the constantof proportionality if r ⊂ 3 and p=15

Q: proportional

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

A: We will find in how many year the population of country will be five times as shown below

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

A:

Q: Find the rate of change of y with respect to x when x=3000 and y=100

A: Given data:   The given expression of the function is 180x0.75y0.25=230,734. The given value of…

Q: The population of country doubles in 100 years. How many years will it be five times as much? Assume…

A: Denote T as the total population of the country, denote S as the initial population in the country…

Q: A balloon is deflating at a constant rate of 12 cubic centimeters per second. When the volume of the…

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Q: The strength of magnetic force varies inversely with the square of the distance between the magnets.…

A: Given query is to find the work required to move the magnets.

Q: Suppose that y is inversely proportional to the square of x, and that y=64 when x=5. What is y when…

A: Since  y is inversely proportional to the square of xy ∝1x2y =k 1x2where k is constant

Q: The fuel efficiency,  in miles per gallon,  of an American- made car is it discrete or continuous?

A: We have to identify type of variable.

Q: Find the rate of change of the area of a square with respect to the length z of a diagonal when z =…

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Q: X and Y are inversely proportional with each other. Given that X = 15000 when Y = 162500. Find X…

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Q: find the integrating factor

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Q: rate of change

A: It is given that an increase of 3 units change in t corresponds to 4 unit change in d. We have to…

Q: z is jointly proportional to the square of x and the square of y. If z=364 when x=6 and y=5, find z…

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Q: Find the average rate of change of g(z) = 3z - 2 fromz = - 2 to z = 4 %3D 202.6

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Q: Find the integrating factor.

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Q: Approximate the change in the atmospheric pressure whenthe altitude increases from z = 2 km to z =…

A: Our Aim is to approximate the change in the atmospheric pressure whenthe altitude increases from z=2…

Q: Consider a cylinder with a radius of 1cm and a height of 3cm. Find the change in the volume of the…

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

A: We can find the answer as below.

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.