The volume V of a given mass of gas varies directly as the temperature T and inversely as the pressure P. If V=220in^3 when T= 200 degrees and P= 10lb/in^2, what is the volume when T=300 degrees and P=15lb/in^2?

Q: The height of a triangle is increasing at a rate of 2 cm/min while the area of the triangle is…

A:

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: A man 6 ft tall walks away from the base of a street light at a rate of 4.2 ft min⁻¹. If the light…

A: Given a man 6 ft tall walks away from the base of a street light at a rate of 4.2 ft min⁻¹. the…

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

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Q: A spotlight on the ground shines on a wall 12 m away. If a girl 1.2 m tall walks from the spotlight…

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Q: the area of a circle is decreasing at a constant rate of 181 square centimeters per second. at the…

A: Given, dAdt=181cm2sec now we know area of circle is: A=πr2 now derivate both side w.r.t t…

Q: Each side of a square is increasing at a rate of 2 cm/s. At what rate is the area of the square…

A: Let the side of the square be 'x' cm. Therefore the area of the square is given by: A=x2

Q: The altitude of a triangle is increasing at a rate of 1.5 centimeters/minute while the area of the…

A: Let height of triangle = h Base = b Then, we are given that:

Q: The continuous rain causes the current of the water of the river to increase its rate. After each…

A: Initial current of the water = 12 km/hAfter every hour current increases by 2%.Current after 1 hour…

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: What is the velocity (in ft/s) of a sandbag 0.25 s after it is released from a hot-air balloon that…

A:

Q: A right triangle has legs of 9 inches and 12 inches whose sides are changing. The short leg is…

A: Given: A right triangle has legs of 9 inches and 12 inches whose sides are changing. The short leg…

Q: The volume of a cube decreases at a rate of 0.6 ft° /min. What is the rate of change of the side…

A: Since you have not mentioned I am answering 2nd Question. Given:Volume of a cube decreases at a rate…

Q: If the radius of a circle increases at a rate of o.01 inch per second, find the rate of change of…

A: Let the radius be r, The rate of change of radius , drdt=0.01 inch per secondArea of the circle is…

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

A: Let, a be the spotlight and “ed” be the wall on which the spotlight shines.Therefore, “ad” is the…

Q: The volume of a cube is increasing at 24 cubic inches per minute. What is the rate of change of its…

A: volume of cube = side3 V= volume  x= side dVdt=24 in3/minutedxdt=? at x=2

Q: The original 24 m edge length of a cube decreases at the rate of 2 m divided by two minutes When x=1…

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Q: The volume of a sphere is changing at a constant rate. Show that the surface area changes at a rate…

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Q: Each of two sides of a triangle are increasing at the rate of 1⁄2 foot per second, and the included…

A: Rate of increase in side lengths = 0.5 ft/s Rate of decrease in angle = -2 degree/s Angle between…

Q: A helicopter flies parallel to the ground at an altitude of 1/2 kilometer and at a speed of 2…

A: Definition used -        Pythagorean theorem - In a right angle triangle, The Square of the…

Q: The altitude of a triangle is increasing at a rate of 2 centimeters/minute while the area of the…

A: Given that increasing altitude of the triangle dh=2cm/min The increasing area of the triangle dA =…

Q: The radius of a right circular cone is increasing at a rate of 5 inches per second and its height is…

A:

Q: The altitude of a triangle is increasing at a rate of 1.5 centimeters/minute while the area of the…

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Q: What is the average rate of change of the height of water in the vase with respect to the volume of…

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Q: When a constant force is applied to an object, the acceleration of the object varies inversely with…

A: Given  mass m=4 kgaccelration a=5 m/s2we know that F=maF=4*5F=20NNow same force applied on anather…

Q: A spotlight on the ground shines on a wall 10 m away. If a man 3 m tall walks from the spotlight…

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

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Q: Suppose that the magnitudes of two earthquakes differ by 1 on the Richter scale. Find the ratio of…

A: Earthquake A be the larger earthquake and earthquake B be the smaller one. The difference in the…

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

A: Given: Resistance R1=0.422 ohm Diameter D1=0.01 inches Given resistance offered by a fixed length…

Q: Suppose the side of a cube is decreasing at a rate of 2 feet per hour. What is the rate of change of…

A: Given: ds/dt=2 side=4ft

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

A: Given: , Where the radius r = 5 cm, Force F=3N. To find the work required to move the magnets from a…

Q: A helicopter flies parallel to the ground at an altitude of 1/2 kilometer and at a speed of 2…

A:

Q: The time required to empty a tank varies inversely as the rate of pumping. If a pump can empty a…

A: Where k is constant of variation.

Q: the length of a rectangle is increasing at a rate of 2 feet per minute, and its width is decreasing…

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

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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: The altitude of a triangle is increasing at a rate of 2 centimeters/minute while the area of the…

A: Formula of area of triangle 12bhWhere b is the base and h is the altitude Chain rule (uv)'= u'v+uv'

Q: A stone is dropped from the edge of a roof, and hits the ground with a velocity of -105 feet per…

A: Given,           A stone is dropped from the edge of a roof, and hits the ground with            a…

Q: triangle

A:

Q: After an hour, the population of bacteria with a number of P0 found that their number became 3 /…

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Q: A light sits on the ground 20 feet away from a very tall wall. A 5-foot-tall person walks toward the…

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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: A right triangle has legs of 18 inches and 24 inches whose sides are changing. The short leg is…

A: Given: A right triangle has legs of 18 inches and 24 inches whose sides are changing. The short leg…

Q: The processing of raw sugar has a step called “inversion” that changes the sugar’s molecular…

A: Let y denote the amount of raw sugar remaining in the processing.Since the rate of change is…

Q: A rectangle has a length that is increasing at a rate of 16 mm per second with the width being held…

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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.