Vx. As the particle passes through the point (4, 2), its x-coordinate increases at a rate of A particle is moving along the curve y = 3 cm/s. How fast is the distance from the particle to the origin changing at this instant? cm/s

Q: Suppose a stone is dropped from a height of 100 ft. Its position at time t is s(t) =-6r +100. Find…

A: To find the time t when instantaneous velocity equal to its average velocity.

Q: A bug is moving along the right side of the parabola y=x at a rate such that its distance from the…

A: see the calculation below

Q: A particle moves along a straight line and has acceleration given by s" = 5t. Its initial velocityis…

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Q: 2. Suppose that a particle is moving along the curve 4x? + 16y² = 32. When it reaches the point (2,…

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Q: A particle is moving along a hyperbola xy=8 As itreaches the point  , (4,2 ) t he y -coordinate is…

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Q: A standard cell has an emf "E" of 1.2 volts. If the resistance "R" of the circuit is increasing at…

A:

Q: A particle moves along a hyperbola xy = 12. As it reaches the point (6, 2), the y-coordinate is…

A: Application of differentiation

Q: A particle moves along a hyperbola xy = 12. As it reaches the point (6, 2), the y-coordinate is…

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Q: a) A particle is moving along the curve y lIn x, in the upward direction and heading to the right.…

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Q: Find the displacement of a particle moving in a straight line with velocity v(t) = 4t − 3 m/s over…

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Q: A bug is moving along the right side of the parabola y =x at a rate such that its distance from the…

A:

Q: At any time t, the velocity of a particle moving along the y-axis is given by v(t)= 4t - t^2. The…

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Q: A particle moving along a line has the position s(t) = t* – 1812 at time t seconds. What is the…

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Q: Suppose a stone is dropped from a height of 200 ft. Its position at time t is s(t)=-4r +200. Find…

A:

Q: dv dt    = −kv2 An object moving through the water has an initial velocity of 40 m/s. Two seconds…

A: As the given differential equation is: dvdt=-kv2 Given conditions are:  t=0 , v=40 mst=2s, v=30 ms…

Q: A particle moving along a line has position s(t) = t 4 - 18t2 m at time t seconds. At which times…

A: st=t4-18t2 Substitute 0 for s(t) into above position function. st=0t4-18t2=0t2t2-18=0t=0 or t2=18t=0…

Q: 2. Suppose s(t) is the position of an object moving along a line at time t > 0. Describe a process…

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Q: A particle is moving such that its position after t hours is s(t) =- -measured in meter. 4t +1 Find…

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Q: 3. If the temperature in a room is given by T(x, y, z) = xyz, at what rate will the temperature felt…

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Q: 1. a. Given that x + y = (2x² + 2y² - x*)* Find an equation of tangentline to the curve at point (0,…

A: b) This is Rate of Change of Derative

Q: A particle moves along a straight line from the origin (O) with an initial velocity Va=6ft/sec and…

A:

Q: The radius of the first circle is modeled by w(t)=12-12e^-0.5t at what time t is the radius of the…

A: The given equation of circle is w(t)=12-12e-0.5tUpon differentiating: (As it is given rate, we…

Q: a. Water is flowing into a conical tank at a constant rate of 3 cubic meters per second. The cone…

A: The answer is given by using volume formula of cone. The answer is given as follows:

Q: A particle moves along a hyperbola xy = 12. As it reaches the point (3, 4), the y-coordinate is…

A:

Q: The velocity of a particle moving along a line is given by v(t)=t^3−4t^2 meters per second. Find the…

A: To find the displacement of the particle, velocity should be integrated w.r.t. time.

Q: Jim is driving at a constant 75.0 mi/hr (33.5 m/s) along a straight section of Route 3 North. The…

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Q: 4) For the function p = x2y+ yz at the point (1,2,-1), find its rate of change with distance in the…

A: Given data: Function:

Q: A particle moves along a straight line and has acceleration given by s"(t) = 5t +3- Its initial…

A: Given,  s''(t)=5t+3, s'(0)=-4, s(0)=7

Q: 6. If a rock is thrown upward on the planet Mars with a velocity of 10 m/s, its height in meters t…

A: We have given function y=10t-1.86t2 where, y represent height in meteres after t second. We have to…

Q: A 32-lb weight stretch a spring 2ft. At t = 0, the mass is released 1 ft above the cquilibrium…

A: The solution is given below

Q: Suppose a stone is dropped from a height of 200 ft. Its position at time t is s(t) =-12r +200. Find…

A: To find the time t when instantaneous velocity equal to average velocity.

Q: The velocity function (in meters per second) is given by v(t) = t2 - 2t - 3, for a particle moving…

A: We will use formula for the Displacement and distance in terms of Velocity function

Q: Suppose an object moving along a straight line has position (measured in ft)…

A: We have  to find velocity

Q: The population ( in hundreds ) of fish in a pond is given by P(t) = 2t + sin(2t – 10) t months from…

A:

Q: A point moves along the curve y = √x in such a way that the y-component of the position of the point…

A: y=xdifferentiating with respect to t we gwt,dydt=12x.dxdxIt is given that dydx=2 units per second

Q: – 4.9 + 15t + 8 meters above the ground. What is An object is thrown upward at timet = 0. After t…

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Q: A 5-m ladder leans against a wall. Assume the bottom slides away from the wall at a rate of 0.7 m/s.…

A: At t=0, x=1.5 m dxdt=0.7 m/s ∴xt=tdxdt+x0x2=2×0.7+1.5=>x2=2.9 m

Q: What is the position at time t of a car that is accelerating at a rate of 5 meters per second…

A: To determine the position of the car from the given data. (note that s =20 when t=2, not as given)

Q: Suppose the position function for a free-falling object on a certain planet is given by s(t) = - 131…

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Q: An object moves along straight like so that after t minutes , its distance from its starting point…

A: Given equation is: xt=10t+5t+1-5 (a) At the end of 4th minutes we get,…

Q: Ithe particle is at the point (1, ) at time t 0, how far is the particle from the origin at time t=…

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Q: The radius r and height h of a cylinder are changing with time. At the instant in question, r = 3…

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Q: A particle moving along a line has position s(t) = t4 − 18t2 m at time t seconds. At which times…

A: St=t4-18t2The particle passes through the origin when St=0t4-18t2=0t2t2-18=0t2=0   t2-18=0⇒t=0…

Q: If the distance y from the origin at time t is given by y = -16t² + 3000t + 50,000, find the initial…

A: Given: The distance y from the origin at time t is given by  y = -16t2+3000t+50,000 To find: The…

Q: The height (in centimeters) at time t (in seconds) of a small mass oscillating at the end of a…

A: Height is given by ht=3 sin 2πt→1instantaneous velocity=dhdt⇒Differentiate eqn 1 , w.r.t 't' , we…

Q: A particle moves along a hyperbola xy = 12. As it reaches the point (6, 2), the y-coordinate is…

A:

Q: The position of a body moving along s-axis at any time 't is given by s(t) = 4t- 12t, then the…

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Q: A car moves in a straight line. At time t (measured in seconds), its position (measured in meters)…

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Q: At time t seconds, the center of a bobbing cork is 2sin(2t) centimeters above or below water level.…

A: ft=2sin2t Now velocity is the derivative of position with respect to time. So differentiating…