For the given curve y = 5x – 2x', when x increases at the rate of 2 units / sec, then how fast is the slope of curve changes when x = 3?

Q: A body cools at the rate of 0.5°C per second when it is 500°C above the surroundings. What is 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: The top of a ladder slides down a vertical wall at a rate of 0.375 m/s. At the moment when the…

A: Let the ladder is k meters. (k=constant) Let the distance of the bottom = x m and distance of the…

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: 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: Find the derivative gx) = 4 K) = cost dt

A: Problem is solved using Leibniz rule

Q: A point on the graph of y = is moving along the curve in such a way that its x-coordinate is…

A: Given graph- y=1x Rate of increase of x-coordinate,dxdt= 6 units per second y-coordinate = 5 Then,…

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: The sides of a square decrease in length at a rate of 1 m/s. At what rate is the area of the square…

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Q: A 10-metre ladder is placed against a vertical wall. Suppose the bottom of the ladder slides away…

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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: The length of the rectangle is increasing at a rate of 5 cm per second, and its width is decreasing…

A: Given that, Let length of the ractangle is L and the width is W and area is A. Then according to the…

Q: What is the rate of change of y = In x at x = 10?

A: Explanation: Given that,  y=lnx   Concept Used: To find the rate of change we will find the…

Q: Car B starts 30 miles directly east of car A and begins moving west at 90 mph. At the same moment…

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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: Two parallel sides of a rectangle are being lengthened at the rate of 20 mm/sec, while the other two…

A: Let the sides of rectangle be x and y   since, two parallel sides are increasing at the rate of…

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 cone-shaped tank of water is leaking water at a constant rate of 3 m³/hour. If the base radius of…

A: Using volume  of cone and applications of derivative idea we solve this

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 spherical snowball is melting so that its diameter is decreasing at rate of 0.2 cm/min. At what is…

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Q: A man of height 1.7meters walks away from a 5-meter lamppost at a speed of 1.1 m/s. Find the rate at…

A: Given that a man of height 1.7m walks away from a 5 meters lamp post at a speed of 1.1 m/s. We need…

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 square with side x, is changing with time where x(t) =3t + 1. What is the formula for the rate of…

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Q: The top of a ladder slides down a vertical wall at a rate of 0.375 m/s. At the moment when the…

A: Let the length of the ladder is L.

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 spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.4 cm/min.…

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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: 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 mold grows at a rate that is proportional to the amount present. Initially there is 6oz of this…

A: The amount of mold at time 0 is m0. The amount of mold present after t hours is m. The rate of…

Q: A particle moves along the curve ln x2 = sq. root (y+1). As it arrives at the point (e, 3), the…

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Q: Suppose y=f(x) is a curve that always lies above the x-axis and never has a horizontal tangent,…

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Q: Suppose that the revenue (in dollars) from the sale of a product is given by R = 60x + 0.9x? –…

A: Since you have asked multiple questions in a single request, we would be answering only the first…

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

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Q: A triangle has a base that is decreasing at a rate of 11 cm/s with the height being held constant.…

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Q: A body cools at the rate of 0.5°C per second when it is 500°C above the surroundings. what is the…

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Q: What is the instantaneous rate of change of y=y=−2x^2+2x at x=0 ?

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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: Consider a rectangular metal box without a top lid which, because of being heated, is increasing in…

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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…

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Q: A spherical snowball is melting so that its diameter is decreasing at rate of 0.2 cm/min. At what is…

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Q: A body weighing 64 Ib is dropped from a height of 100 ft with an initial velocity of 10 ft/sec.…

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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 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: The top of a ladder slides down a vertical wall at a rate of 0.375 m/s. At the moment when the…

A: form a triangle with given information : let BC = x   dxdt=0.5 AB = y  dydt=-0.375  AC = z  dzdt=0…

Q: A weather balloon is rising vertically at the rate of 10ft/s. An observer is standing on the ground…

A: Given: -

Q: Assign variables and restate the following problem in terms of known and unknown derivatives (but do…

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Exponential Growth Model

The relation that represents an exponential function is: