The coordination of a particle in the xy-plane are differentiable functions of t with dx/dt=-1m/sec and dy/dt=-5m/sec. How fast is particle's distance form the origin changing as it pass through the point(5,12)? I desperately need help with these problem

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Answer 1 · 2018-05-19T13:32:26

#- 5 \ ms^(-1)#

#s = sqrt( x^2 + y^2) #

#dot s = s_x dot x + s_y dot y#

# = ( x dot x + y dot y)/sqrt( x^2 + y^2) #

# = ( 5* (-1) + 12* (-5))/sqrt( 5^2 + 12^2) = - 5#