Aparticle is moving along the parabola x^2=4(y+6). as the particle passes through the point (8,10), the rate of change of its y-coordinate is 5 units per second. how fast, in units per second, is the x-coordinate changing at this instant?

The instantaneous rate of change is the rate of change at a particular instant.

The rate of change per second in the x-coordinate is 1.25 units per second

The parabola is given as:

The rate of change of y is given as:

Start by differentiating both sides, implicitly

Divide both sides by 2x

From the question, we have:

Substitute 8 for x in

Substitute

Hence, the rate of change per second in the x-coordinate is 1.25 units per second

Read more about rates of change at:

link

answer: the price of one pound cabbage = $ 0.8

the point (10,8) represents that the cost of 10 pounds cabbage is $ 8

step-by-step explanation:

since, here is a proportional relation between the number of pounds of cabbage (x) and the price in dollars (y).

therefore, we can write,

⇒ y = k x

where k is the constant of proportionality.

now, point (5,4) is in the line.

thus, it will satisfies the above equation of line.

⇒ 4 = 5 k

⇒ k = 0.8

thus, the equation of the line is,

y = 0.8 x

a) for x = 1,

y = 0.8

therefore, the cost of one pound of cabbage is 0.8 dollars.

b) in the below graph (10,8) represents that the cost of 10 pounds of cabbage is 8 dollars.