Question

Oil spills from a tanker in the Gulf of Mexico and surfaces continuously at coordinates(x, y) = (0,0).If oil spreads in a circular pattern for ten hours and the circle's radius increases at arate of 2 inches per hour, write an equation of the circle that models the range of thespill's effect.I

Answer 1

Given the point:

(x, y) ==> (0, 0)

Number of hours the oil spilled for = 10 hours

Rate of increase = 2 inches per hour.

Let's find the equation that models the range of the spill's effect.

Apply the formula:

`(x-h)^2+(y-k)^2=r^2`

Where:

(h, k) is the center ==> (0, 0)

r is the radius

Since the oil spills for 10 hours and increases at the rate of 2 inches per hour, therefore, the radius of the circle will be:

`10*2=20\text{ inches}`

Therefore, the equation of the circle is:

`\begin{gathered} (x-0)^2+(y-0)^2=20^2 \\ \\ x^2+y^2=20^2 \end{gathered}`

ANSWER:

`x^2+y^2=20^2`