A particle is moving along the parabola x2 = 4 (y + 5) As the particle passes th

Question

A particle is moving along the parabola x2 = 4 (y + 5) As the particle passes through the point (4, -1), the rate of change of its y-coordinate is 4 units per second. How fast, in units per second, is the x-coordinate changing at this instant? A heap of rubbish in the shape of a cube is being compacted into a smaller cube. Given that the volume decreases at a rate of 3 cubic meters per minute, find the rate of change of an edge, in meters per minute, of the cube when the volume is exactly 64 cubic meters.

Explanation / Answer

1) according to equestion by diffrentiating 2x(dx/dt)=4(dy/dt) dx/dt=(2/x)*(dy/dt) dx/dt=(1/2)*4 dx/dt=2 the rate of change of x co-ordinate is 2 units per second 2) V=a^3 a=edge length V=Volume diffrentiating the equation we get dv/dt=3a^2(da/dt) da/dt=(1/3a^2)*(dv/dt) V=64 ; a=4 da/dt= (1/3a^2)*3 da/dt=1/16=0.0625 rate of change of an edge is 0.0625 metres per minute

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