39. Motion along a parabola A particle moves along the top of the parabola y? = 2x from left to right at a constant speed of 5 units per second. Find the velocity of the particle as it moves through the point (2, 2).

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Q: A mass weighing 24 pounds, attached to the end of a spring, stretches it 4 inches. Initially, the…

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Q: A particle is oscillating about a central point such that its displacement x (centimetres) at any…

A: Given that the displacement x at any time t is modeled by the equation x=sint+cost+cost-π3 for t≥0.…

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Q: 6. The ellipsoid + y2 + z2 = 4 and the plane y = 1 intersect to form an ellipse. Find slope of the…

A: Given:

Q: 02. Determine the points of intersection between the circlex+y =3 and the hyperbola xy=1. Use…

A: Given: x2+y2 = 3   ; xy = 1Hence, f1x,y =  x2+y2 -3f2x,y =  xy -1with, x0 = 0.5 ; y0 =…

Q: curves about the x-axis. y = x, y = 0, x = 2, x = 3 O 1 O 13 O 19

A: We will find the volume of the region.

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: Equation of the tangent drawn from the point S(2,4) on the 8x = y^2 parabola ? 2y=2x+2 y=2x+2…

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Q: 5. A particle is moving along the curve y = x² + x in such a way that the y-coordinate is increasing…

A: Given:- A particle is moving along the curve y = x² + x in such a way that the y-coordinate is…

Q: find a parametrization for the curve. the upper half of the parabola  x-9=y^2

A: The given curve is x-9 = y2  ...(a) Putting y = t in (a) then x = 9+ y2…

Q: 1. Elimination of Arbitrary Constant: y= Ax² + Bx+C , A and B are constant, C is a parameter 2.…

A: Note:- These are multiple questions and according to our company guideline we can do maximum one…

Q: 2.) A tank is in the shape of a frustum of a pyramid having a square section. The upper base is 3.0m…

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Q: A bug is moving along the right side of the parabola y=x^2 at a rate such that its distance from the…

A: Differentiate the above expression with respect to t as follows.

Q: When you cough, you are using a high-speed stream of air to clear your trachea (windpipe).  During a…

A: This is what I hope the velocity isV(r) = c(3-r)r^2We don't need to know the constant since we will…

Q: n Progress ch the section of the surface at x = 0. = 1 25 ce: 8. 10 6. 6. 4. 4. 6. 8. -8 -6 6.…

A: topic - conics

Q: 2. A particle moves in a circular orbit x? + y = 16. As it passes through the point (2, 2/3 ), its…

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Q: A force of 640 newtons stretches a spring 4 meters. A mass of 40 kilograms is attached to the end of…

A: Given that a force of 640 newtons stretches a spring 4 meters. A mass of 40 kilograms is attached to…

Q: 78. A particle starts at the origin and moves along the curve y = 2x32/3 in the positive x-direction…

A: According to question,Given curve,y = 2 x323,speed dxdt= 3 cmsec,t = 6

Q: A mass weighing 64 pounds stretches a spring 0.32 foot. The mass is initially released from a point…

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Q: 5. Motion. In a straight-line motion, let the velocity be the reciprocal of the acceleration. Find…

A: As per guidelines at a time only one question is answered Solution of first question is given below:

Q: A line tangent to the hyperbola 4x² −y² = 36 intersects the y-axis at the point (0, 4). Find the…

A: Consider the given hyperbola 4x2-y2=36 Let the point Pα, β be on the the hyperbola. To find the…

Q: (2) Find the equation of the tangent line to y = when x = = 0. 2+ 33 (3) Find the parabola with…

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Q: A force of 480 newtons stretches a spring 2 meters. A mass of 60 kilograms is attached to the end of…

A: From the given information,The weight W = 480 newtons and the spring stretches s = 2 meters.

Q: 1: A fly walks with a speed of 1 cm/sec in every direction of a piece of paper which is considered…

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Q: 40) x+(y-1) = 36 A) Center: (-1, 0) Radius: 6 B) Center: (0, 1) Radius: 36 C) Center: (-1, 1)…

A: Given that, Equation of circle is, x2 + (y - 1)2 = 36 We have to find the center and the radius of…

Q: b. Differentiate both sides of the equation in part (a) with re- 86. The hyperbolic in hyperbolic…

A: (a) We can draw the graph of the sector AOP as shown below. Now,  We observe that the area A(u) of…

Q: 1. An ellipse has equation x?+ 2xy+ 4y2 = 16 (a) Calculate a formula for dy the derivative of y with…

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Q: A particle is traveling along a circualr path defined by x^2 + y^2 = 4, where x and y are measured…

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Q: A weight stretches a spring 6 inches in equilibrium. The weight is initially displaced 6 inches…

A: In this question, concept of Differential Equation is used. Differential Equation A differential…

Q: 13. A point moves along the curve y = x² +2 so that the x-coordinate is increasing at the rate of 3…

A: y=x2+2 since x coordinate is increasing at the rate of 3 units per second.where x and y are…

Q: the moment of inertia of the area bounded by the cubic parabola a^2 y = x3, the y – axis and the…

A: To find the moment of inertia of the area bounded by the below equations about the y-axis.…

Q: 2 Two particles, P and Q, move in a straight line. The velocity of particle P, v, m s", is given by…

A: We need to find  a)time when acceleration of p and q are equal. b)maximum velocity of q  c)time when…

Q: As an engineer at Ghana Atomic Energy, you have been tasked to design a cooling tower in the shape…

A: Hey, since there are multiple questions posted, we will answer the first question. If you want any…

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Q: The tank in the form of a right-circular cone of radius 11 feet and height 15 feet standing on its…

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Q: Find the Area of the Surface obtained by rotating the curve about the x - axis X= (²+2),

A: The objective is to find the surface area.

Q: D The region D above lies between the two red lines and the red parabola y It can be describe in two…

A: Integration is the process of finding the anti-derivative function of a function. The integration…

Q: 3. A point describe parabola y = 4x + 1, with a constant velocity, vy = 4. Find vx and ax at point…

A: vx=dxdy= velocity of x with respect to(w.r.t.) yax=d2xdy2= acceleration of x w.r.t. yTo get dydx…

Q: 2. Rotating around a vertical axis: y = 4x -x2, y = 3 and rotated about x = 1.

A: We have to find point of intersection and draw the region bounded , Then rotate the region about x=1…

Q: 1. Elimination of Arbitrary Constant: y = Ar+ Bx+C, A and B are constant, C is a parameter 2.…

A: Since you have posted multiple questions. As per guidelines we will solve only first question  If…

Q: find the location and value of the absolute maximum and minimum of the f(x,y)=e^x - sin(y) on the…

A: As per the question we have to both maximize and minimize the bivariate function f(x,y) constrained…

Q: A force of 200 newtons stretches a spring 2 meters. A mass of 50 kilograms is attached to the end of…

A: a. From the given information, the value of m=50 kg, s=2 m and W=200 N. By the Hooks Law, the spring…

Q: A force of 640 newtons stretches a spring 4 meters. A mass of 40 kilograms is attached to the end of…

A: Given that a mass of 40 kilograms is attached to the end of the spring and is initially released…

Q: 2 Find the point on the sphere x² + y² + z² = 16 farthest from the point (-1,-1,1). The point is…

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Q: 2. A particle moves in a circular orbit x² + y² = 16. As it passes through the point (2, 2/3 ), its…

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Q: A certain tank of depth 10 ft is a surface of revolution formed by rotating y = x² about its axis.…

A: Work done= mgh

Q: A force of 540 newtons stretches a spring 3 meters. A mass of 45 kilograms is attached to the end of…

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Q: Find the Area of the Surface obtained by rotating the curve about the y -axis y = √x, 1 ≤ y ≤2

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