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)= 200 square root of t, find the area A of the oil slick as a function of the time t.
You know that the area of a circle is A=pi*r^2. You're told that the radius is a funtion of time and
r(t)=200*sqrt(t). If you compose the function to get
A(r(t))=pi*(200*sqrt(t))^2
you'll have area as a funtion of time, or
A(t) = something you can simplify.
pi*(200^2)^2
Why did the oil slick join a book club? Because it wanted to broaden its "literacy"!
Now, let's get down to business. We know that the radius of the oil slick, r(t), is given as 200 times the square root of t. To find the area of the slick as a function of time, A(t), we can substitute this value of r(t) into the formula for the area of a circle:
A(t) = π * r(t)^2
Substituting r(t) = 200√t, we have:
A(t) = π * (200√t)^2
= π * 200^2 * t
Simplifying this, we get:
A(t) = 40,000πt
So the area of the oil slick as a function of time is A(t) = 40,000πt.
To find the area A of the oil slick as a function of time t, we can substitute the given radius function r(t) = 200√t into the formula for the area of a circle, A = πr^2.
Substituting r(t) into the formula, we have:
A(t) = π * (200√t)^2
Simplifying the expression:
A(t) = π * (200^2) * (√t)^2
A(t) = π * 40000 * t
Therefore, the area A of the oil slick as a function of time t is given by:
A(t) = 40000πt
To find the area A of the oil slick as a function of time t, we can substitute the given expression for the radius r(t) into the formula for the area of a circle.
The formula for the area A of a circle is A = pi * r^2. Substituting the expression for the radius r(t) into the formula, we have:
A(t) = pi * (200 * sqrt(t))^2
Simplifying this expression, we square the term inside the parentheses:
A(t) = pi * (200^2 * t)
Simplifying further, we square 200 to get 40,000:
A(t) = pi * (40,000 * t)
Therefore, the area A of the oil slick as a function of time t is A(t) = 40,000 * pi * t.