A particle on the x-axis is moving to the right at 2 units per second. At a certain instant it is at the point (5,0). How rapidly it the distance between the particle and the point (0,9) on the y-axis changing at that instant

dr/dt = 1.94 units per second

Explanation:

A particle is moving on the x-axis to the right at 2 u/s.

To know how is changing the distance of the particle respect to the point (0,9), on the y-axis, you first take into account that the distance between charge and a point over the y-axis is given by:

         (1)

Next, you calculate implicitly the derivative of the equation (1) respect to t:

      (2)

Next, you solve the previous equation for dr/dx:

      (3)

dx/dt: the speed of the particle on the x-axis = 2

dy/dt: speed of the particle on the y-axis = 0

For the instant given in the statement, you have that:

x = 5

y = 9

Then, you replace the values for x, y, dx/dt and dy/dt in the equation (3):

The speed of change of the distance between particle and point (0,9) is 1.94 units per second

Heyo,

Your answer is West

if this question helped can you mark me brainliest