A particle moves along the curve ln x2 = sq. root (y+1). As it arrives at the point (e, 3), the x-coordinate is changing at a rate of 4 units per second. How fast is the y-coordinate changing at that instant?

Q: A particle is moving along the curve ? = ? 2 . As the particle passes through the point ( 1,?), its…

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Q: A 13ft ladder rests against a vertical wall. If the bottom of the ladder is sliding away from the…

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Q: A particle moves along the curve below. y = sqt(24 + x^3) As it reaches the point (1, 5), the…

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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 point P is moving along the line whose equation is y=8x. How fast is the distance between P and…

A: Any point on line whose equation is y=8x is P(x,8x) Then , distance between point P and (3,0) is

Q: A balloon is 20 m horizontally away from an observer. At an instant, the balloon rises vertically at…

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Q: A balloon is rising straight up from a level field, at a constant rate of 0.4 m/ sec. Just when the…

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Q: 2. A 13-foot ladder is leaning against a vertical wall when Jack begins pulling the foot of the…

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Q: A balloon leaves the ground 30 m from an observer. If it rises at the rate of 2 m/s, how fast is it…

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Q: A man whose height is 1.5 m. is walking directly away from a lamp post at a constant rate of 0.8…

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Q: 3. A cylindrical tank of diameter 20ft is being drained with water at the rate of 400ft /min. How…

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Q: A particle moves along the curve y = V1+ x3. As it reaches the point (2, 3), the y-coordinate is…

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Q: A rectangular box has its height increasing at a rate of 1m/s while its volume is decreasing at a…

A: We have to find the  rate of change of length.

Q: A potter forms a piece of clay into a cylinder. As he rolls it, the length, L, of the cylinder…

A: Differentiate volume wrt t

Q: A ladder of length 3 meters is placed on a wall, with the distance from the wall x and the height of…

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Q: 3. A 20 ft ladder is leaning against a wall and begins to slide. How fast is the top of the ladder…

A: A 20ft ladder is leaning against a wall and begins slide.The ladder is 12ft away from the wall and…

Q: 11. The top of a ladder slides down a vertical wall at a rate of 0.15 m/s. At the moment when the…

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Q: A particle is moving along the curve y = 2+ Vx + 1. At the instant that the partical passes through…

A: (15) Find dy/dt from y using the chain rule and dx/dt from the statement given.

Q: A man of height  1.9  meters walks away from a 5-meter lamppost at a speed of  2.1  m/s. Find the…

A: Let distance of the man from the pole=x   Let the length of the shadow =y…

Q: A point P is moving along the line whose equation is y =2x. How fast is the distance between P and…

A: The line is given by y=2x, differentiate w. r. t. t to get: dydt=2dxdt Let Px,y be a point on the…

Q: A point P is moving along the line whose equation is y 2x. How fast is the distance between P and…

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Q: 1. Imagine a person standing on the point in the plane (0,0) and starts running along a path traced…

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Q: Under certain conditions, cane sugar in water is converted into dextrose at a rate proportional to…

A: Given that,  At time, t=0, the amount of cane sugar in water =75kg At time, t=30minutes, the amount…

Q: A potter forms a piece of clay into a cylinder. As he rolls it, the length, L, of the cylinder…

A: Here, the amount of the clay is fixed. dVdt=0...(1) Now, the volume of the cylinder is given by:…

Q: 7. The top of a ladder slides down a vertical wall at a rate of 0.15 m/s. At the moment when the…

A: Given data A ladder slides a vertical wall at rate of 0.15 m/s  find the length of ladder = ?

Q: A 25 ft ladder is leaning against a vertical wall. 25 ft At what rate (with respect to time) is the…

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Q: Under certain conditions, cane sugar in water is converted into dextrose at a rate proportional to…

A: Given: when the initial time t=0 amount of the cane sugar is 75 kg, and the time t=30 minutes amount…

Q: At 12-ft ladder is leaning against a vertical wall when Jack begins pulling the foot of the ladder…

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Q: A particle is moving along the curve y = x². As the particle passes through the point (1,e), its…

A: Given: A particle is moving along the curve y=x2. As the particle passes through the point (1, e),…

Q: A flag is raised vertically from a pole at a constant rate of 1m/s. A point B on the ground level…

A: Given: Vertically raising speed of flag at constant rate=1 m/s……1Horizontal distance from flagpole…

Q: 5. A 6-ft man walks away from a 15-ft lamppost at a speed of 3 ft/s. Find the rate at which his…

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Q: The top of a ladder slides down a vertical wall at a rate of 1.5 m/s. At the moment when the bottom…

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Q: A weather balloon is rising vertically at the rate of 2 m/sec. An observer is standing on the ground…

A: The diagram of the given question will be as follows Given: dydt=2 m/s To find: dxdt

Q: 20. A 13 foot ladder leans against a vertical wall. When the ladder is pulled away from the wall at…

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Q: A man of height 1.9 meters walks away from a 5-meter lamppost at a speed of 1.1 m/s. Find the rate…

A: Given Data: The height of the man is: h=1.9 m The height of the lamppost is: H=5 m The increasing…

Q: A balloon is rising straight up from a level field, at a constant rate of 0.4 m/ sec. Just when the…

A:

Q: The top of a ladder slides down a vertical wall at a rate of 0.15 m/s. At the moment when the bottom…

A: Given,

Q: The top of a ladder slides down a vertical wall at a rate of 0.15m/s. At the moment when the bottom…

A: We have given; the rate of change when ladder slides down i.e 0.15m/s The rate of change when it…

Q: At what rate is the height of the water rising at the instant the tank is half full?

A: To find the rate at water rising

Q: A 15 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 4 ft/s, how…

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Q: A point P is moving along the line whose equation is y = 2x. How fast is the distance between P and…

A: Firstly we find the distance between a random point on the line y = 2x, and then we differentiate…

Q: A point P is moving along the line whose equation is y = 2x. How fast is the distance between P and…

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Q: A 10 m ladder leans against a vertical wall and the bottom of the ladder slides away from the wall…

A: Let L be the length of the ladder, h be the height of the wall and b be the distance between the…

Q: A point P is moving along the curve whose equation is  y=4x. How fast is the distance between P and…

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Q: A balloon leaving the ground 60 ft from an observer rises vertically at the rate of 10ft/sec. How…

A: Given,            A balloon leaving the ground 60 ft from an observer rises vertically at the rate…

Q: A triangle has a base that is decreasing at a rate of 4 cm/s with the height being held constant.…

A: Let b and h be the base and height of the trianglegiven rate at which base is decreasing, dbdt=4cm/s…

Q: A balloon is rising vertically above a level, straight road at a constant rate of 4ft/sec. Just when…

A: See below the answer

Q: The top of a ladder slides down a vertical wall at a rate of 0.25 m/s. At the moment when the bottom…

A: Let the height up of the wall to the top of the ladder is y. let the distance between the bottom of…