The movement of the particle on the circle is its displacement.
The value of dy/dt at this time is -9/2.
Differentiation is a process, in Maths, where we find the instantaneous rate of change in function based on one of its variables.
A particle moves on the circle x^2 + y^2=25 in the XY-plane for time t≥0. At the time when the particle is at the point (3,4), dxdt=6.
The equation of the circle is given as:
[tex]\rm x^2 + y^2=25[/tex]
Differentiate with respect to time
[tex]\rm 2x \times \dfrac{dx}{dt}+2y \times \dfrac{dy}{dt}=0[/tex]
Substitute all the values in the equation
[tex]\rm 2x \times \dfrac{dx}{dt}+2y \times \dfrac{dy}{dt}=0\\\\2(3) \times 6+2(4)\times \dfrac{dy}{dt}=0\\\\ 6 \times 6+8 \times \dfrac{dy}{dt}=0\\\\ 36+8\times \dfrac{dy}{dt}=0\\\\ 8\times \dfrac{dy}{dt}=-36\\\\ \dfrac{dy}{dt}= \dfrac{-36}{8}\\\\ \dfrac{dy}{dt}= \dfrac{-9}{2}[/tex]
Hence, the value of dy/dt at this time is -9/2.
Learn more about differentiation here;
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