A circle has a radius that increases at a rate of 10cm/s. Find the equation of the outermost circle 6 seconds after it starts to expand. Using x2 +y2=r2
To find the equation of the outermost circle, we need to determine the radius of the circle after 6 seconds of expansion.
Given that the radius increases at a rate of 10 cm/s, we can determine the radius at any time using the following formula:
radius = initial radius + rate of increase × time
In this case, the initial radius is the radius at the start of expansion, which we don't have in the given information. However, we can assume it to be zero since the circle is just starting to expand. Therefore, the formula becomes:
radius = 0 + 10 cm/s × 6 s
radius = 60 cm
Now that we have the radius, we can write the equation of the outermost circle using the form x^2 + y^2 = r^2, where r is the radius:
x^2 + y^2 = 60^2
x^2 + y^2 = 3600
So, the equation of the outermost circle 6 seconds after it starts to expand is x^2 + y^2 = 3600.