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A point moves along the curve y = VX in such a way that the y-component...
A curve is such that =-4x. The curve has a maximum point at (2, 12). (i) Find the equation of the curve. [6] A point P moves along the curve in such a way that the x-coordinate is increasing at 0.05 units per second. (ii) Find the rate at which the y-coordinate is changing when x = 3, stating whether the y-coordinate is increasing or decreasing. 127
A particle moves along the curve below. y = sqrt15 + x3 As it reaches the point (1, 4), the y-coordinate is increasing at a rate of 4 cm/s. How fast is the x-coordinate of the point changing at that instant?
4. A particle moves along the curve y = A12 so that its position is given by x = Bt. (a) Find the position vector of the particle in the form 式t) = x(t) + y(t) j (b) Calculate the speed u = of the particle along this path at an arbitrary instant t.
A particle moves along the curve y = x^3/2 such that its distance from the origin, measured along the curve, is given by s = t^3 . Determine the acceleration in vector form when t = 2 seconds. The units are inches and seconds.
Evaluate JF.dr from (0,0) to (9,3) along the curve y=vx if Ē(x, y, z) = x’yi – xy? j -
Use the curve y = VX-2 and the point (5.0) to answer the following. (a) [5 pts) What equation provides the distance, d, between a point on the curve and the point (5,0)? (b) [5 pts) Find the point on the curve y= VX-2 that is closest to the point (5.0).
EX #1: For t > 0, a particle moves along a curve so that its position at time t is (x(t), y(t)), where x(t) = 4t and = 1 - 2t. Find the time t at which the speed of the particle is 5.
Find the line integral along the curve from the origin along the x-axis to the point (4.0) and then counterclockwise around the circumference of the circle x+y? - 16 to the point 4/24/2) A7-vx + 13-17 + n(x + 175
RSS3 points 12. Find the point on the curve y=Vx that is a minimum distance from the point (4,0). Report your answer as an ordered pair in the format (x, y) and round each coordinate to the nearest tenth. 13. Consider all lines in the xy-plane that pass through both the origin and a point (x, y) on the graph of the parabola y = x^2 - x + 16 for (1,8). The figure below shows one such line and...
all questions clearly solved please (2) If the point of application of a force F: R3 R moves along a curve C, then the work done by the force is W F.dr. (a) Find the total work done on an object that traverses the curve c(t) (cos(t), 2 sin(t), (b) Find the total work done on an object that traverses the straight line from (1,0,-2) (c) Explain why the answers in the previous two questions coincide and provide a way...