Environmental Concerns: The spread of oil leaking from a tanker is in the shape of a circle. If the radius r (in feet) of the spread after t hours is r(t) = 200sqrt t, find the area A of the oil slick as a function of the time t.
I don't get this at all. could someone please help me figure this out????
A = pi r^2 = pi (200√t)^2 = 40000 pi t
Sure, I'd be happy to help you figure it out! Don't worry, I'm not slick enough to evade this question.
To find the area A of the oil slick as a function of time t, we need to use the formula for the area of a circle, which is A = πr^2.
Given that the radius r(t) of the oil slick at time t is r(t) = 200√t, we can substitute this into the formula to get:
A = π(200√t)^2
Simplifying this further, we have:
A = π(40,000t)
So, the area A of the oil slick as a function of time t is A = 40,000πt.
Now you know the A-B-C's of finding the area of the oil slick! Hope this helps!
To find the area of the oil slick as a function of time, we first need to find the equation that relates the radius of the spread to the area of the oil slick.
The area of a circle is given by the formula A = πr^2, where A is the area and r is the radius.
Given that the radius of the spread after t hours is given by r(t) = 200√t, we can substitute this expression into the formula for the area:
A(t) = π(200√t)^2
Now, let's simplify this equation:
A(t) = π(200^2)√t^2
A(t) = π(40,000t)
Therefore, the area of the oil slick as a function of time is A(t) = 40,000πt.
Certainly! I can help you understand how to approach this problem.
To find the area of the oil slick as a function of time, we can use the formula for the area of a circle, which is A = π * r^2.
In the given problem, we are given that the radius of the spread after t hours is r(t) = 200sqrt(t). To find the area A as a function of time t, we need to substitute this expression for r(t) into our area formula.
Therefore, the area A at any given time t can be calculated as:
A(t) = π * r(t)^2
Substituting the given expression for r(t):
A(t) = π * (200sqrt(t))^2
Simplifying the expression, we have:
A(t) = π * (200^2 * t)
Further simplifying, we get:
A(t) = 40000π * t
So, the area A of the oil slick as a function of time t is given by A(t) = 40000πt.
I hope this explanation helps you understand how to solve the problem. If you have any further questions, feel free to ask!