Continuity equation is derived using the law of conservation of mass

Q: the velocity of a particle is the rate of change in the position function over time true or false

A: We have to check

Q: A fluid is being pumped from a cylinder into a rectangular prism with a square base. The base has…

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Q: Water is draining from a cylindrical tank of water at a rate of 3 m / min . If the radius of the…

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Q: The velocity of a material point that starts moving on a linear trajectory from the point 1 X= 0 is…

A: Given Initial point is x = 0 V = 50-0.5x a = dV/dt = -0.5 dX/dt a = -0.5V

Q: Continuity equation is derived using the law of conservation of mass

A: According to the given information, it is required to tell whether the given statement is true or…

Q: the radius of a circle is increasing at a constant rate of 100 meters per second. at what rate is…

A: First of all, consider the area for the circle.Then differentiate on both sides of equation w.r.t…

Q: 3. A plane flying horizontally at an altitude of 1 mi and a speed of 500 mi/h passes directly over a…

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Q: An eagle flying horizontally at an altitude of 6 m and speed of 4 m/s passes over a beaver standing…

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Q: A rectangular shaped region is changing with time and increasing in the x direction at the rate of 2…

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Q: A spherical snowball melts at a rate proportional to its surface area. Show that that rate of change…

A: It is given that, the spherical snowball melts at a rate proportional to it’s surface area. This can…

Q: Use differentials to estimate the amount of paint needed to apply a coat of paint .05 cm thick to a…

A: Using differential to estimate the amount of paint needed to apply a coat of paint of 0.05cm thick

Q: 4. A man is walking beside a 30-m street lamp. After walking 25 m away from the street lamp, he sunk…

A: As per our guidelines we can solve only one question at a time. Please repost unsolved question…

Q: . A mass of 1 kg is attached to the end of a spring whose restoring force is 180 The mass is in a…

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Q: A point moves along the curve y = √x in such a way that the y-value is increasing at a rate of 2…

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Q: The rate of proliferation (that is, reproduction) for the cells in a tumor varies depending on the…

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Q: The temperature at a point in a ball with conductivity K is inversely proportional to the distance…

A: We know:

Q: 2. A fish is being reeled in by a fishing line that is moving at a rate of - 4 feet per second from…

A: Assume AC=h be the length of the fishing line, BC=x be the distance of fish from the pole and θ be…

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: Define Constant acceleration ?

A: The acceleration of a particle or a body is defined as the rate of change of the particle or the…

Q: The volume of oil in an inverted conical basin is increasing at a rate of 3 cubic inches per second.…

A: The volume of oil in an inverted conical basin is increasing at a rate of 3 cubic inches per second.…

Q: At a certain moment, an object in linear motion has velocity 100 m/s. Estimate the distance traveled…

A: Given that: At a certain moment, an object in linear motion has velocity 100 m/s To estimate the…

Q: An ice cube in a freezer is growing due to accretion, each edge is increasing by 0.2 cm per minute.…

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Q: The linear density of a cable wire is the rate of change of its mass with respect to its length. A…

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Q: A rocket is blasting off from a launch pad and you are going to film the take off. You position…

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Q: A spaceship is moving in a straight line at 36,000 miles per socond. Suddenly it accelerates at a(t)…

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Q: As an object cools, its rate of cooling slows. Explain how this follows from Newton’s Law of…

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Q: How is integral calculus related to differential calculus?

A: Solution

Q: Water is leaking out of an inverted conical tank at a rateof 10,000 cm3/min at the same time that…

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Q: A mothball loses volume by evaporation at a rate proportional to its instantaneous area. If the…

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Q: A leaky 10-kg bucket is lifted from the ground to a heightof 12 m at a constant speed with a rope…

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Q: 4. A solid cylindrical cord of elastic material has length 32 inches and radius 0.5 inch. The cord…

A: Given:        Length  l=32 inches        radius  r=0.5 inch      Volume of a cylinder  V=πr2l…

Q: The rate of proliferation (that is, reproduction) for the cells in a tumor varies depending on the…

A: Here,             We have given  the rate of proliferation for the cells in a tumor varies depending…

Q: A plane flying horizontally at an altitude of Imi and a speed of 500mi/hr passes directly over a…

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Q: A right circular cylinder has a fixed height of 4 meters. Find the rate of change of its volume V…

A: Given: A right circular cylinder has a fixed height of 6 m.

Q: Express the mathematical relationship between stress and strain in case of elastic material.

A: The mathematical expression can be related as:

Q: A leaky 10-kg bucket is lifted from the ground to a height of 12 m at a constant speed with å rope…

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Q: The velocity (in centimeters per second) of blood molecules flowing through a capillary of radius…

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Q: Show that the period of motion of an undamped vibration of a mass hunging from a vertical spring is…

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Q: 2. All edges of a cube are expanding at a rate of 6 centimeters per second. How fast is the volume…

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Q: ladder 5 meters long is leaning against a vertical wall. Due to the smooth floor, the foot of the…

A: Given query is to find the rate of change of y with respect to x.

Q: A leaky 10-kg bucket is lifted from the ground to a height of 12m at a constant speed with a rope…

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Q: Water is being drained at a rate of 50 m3/min from a concrete conical reservoir (vertex down). The…

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Q: The radius of a right circular cone is increasing at the rate of 6 cm/sec while its altitude is…

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Q: Africtionless spring with a 7-kg mass can be held stretched 0.2 meters beyond its natural length by…

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

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Q: The rate of conversion of a certain substance is proportional to the square root of the amount m of…

A: We need to find time.

Q: Speed is the rate of change of velocity over time. True False

A: The given statement is, "Speed is rate of change of velocity over time"

Q: All edges of a cube are expanding at a rate of 6 centimeters per second. (a) How fast is the surface…

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Q: 1. A particle moving along in a straight line with a uniform acceleration covers 72 cm displacement…

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Q: A ball is thrown vertically upward from ground level with an initial velocity of 64 feet per second.…

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