Question

Your physics class decides to perform an experiment on circular waves. First, make sure

The water in the school swimming pool is level with no waves. Next, a volunteer tosses a small
marble near the centre of the pool.
Your teacher tells you the radius in feet, r(t), of the outer ripple.
is given by r(t) = 0.73t, where t is the time in seconds after the marble hits the water. The
area of the circle is given by the function Ar = mra, where A(r) is the area in square feet and r is
the radius in feet. Give an equation for the function.

Answer 1

The equation for the function is A(t) = 0.5329πt^2.

Step-by-step explanation:

The equation for the area of a circle is given by the formula A(r) = πr^2, where A(r) is the area in square feet and r is the radius in feet.

Given the function for the radius of the outer ripple as r(t) = 0.73t, we can substitute this expression into the area equation to find the equation for the function:

A(r(t)) = π(0.73t)^2

Simplifying further:

A(t) = π * 0.5329t^2

So, the equation for the function is A(t) = 0.5329πt^2.