Answer:
The x coordinate of P is [tex]\frac{4}{3}[/tex].
Step-by-step explanation:
Let is find the rate of change of the equation in time, which consists in a composite differentiation. That is:
[tex]\frac{dy}{dt} = 2\cdot x \cdot \frac{dx}{dt} -2\cdot \frac{dx}{dt}[/tex]
According to the statement of the problem, these variables are known:
[tex]\frac{dx}{dt} = 6[/tex] and [tex]\frac{dy}{dt} = 4[/tex]
Hence, the x coordinate of P is found by direct substitution:
[tex]4 = 2\cdot x \cdot (6)-2\cdot (6)[/tex]
[tex]4 = 12\cdot x -12[/tex]
[tex]x = \frac{4}{3}[/tex]
The x coordinate of P is [tex]\frac{4}{3}[/tex].
