A particle in the first quadrant is moving along a path described by the equation LaTeX: x^2+xy+2y^2=16x 2 + x y + 2 y 2 = 16 such that at the moment its x-coordinate is 2, its y-coordinate is decreasing at a rate of 10 cm/sec. At what rate is its x-coordinate changing at that time?

cm/sec.

Step-by-step explanation:

We have been given that a particle in the first quadrant is moving along a path described by the equation such that at the moment its x-coordinate is 2, its y-coordinate is decreasing at a rate of 10 cm/sec. We are asked to find the rate at which x-coordinate is changing at that time.

First of all, we will find the y value, when by substituting in our given equation.

Since the particle is moving in the 1st quadrant, so the value of y will be positive that is .

Now, we will find the derivative of our given equation.

We have been given that , and .

Therefore, the x-coordinate is increasing at a rate of cm/sec.

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