Respuesta :
Answer
As per the statement:
The oil flow can be expressed with the function
n(t) = 8t ....[1]
where,
t represents the time in minutes and
n represents how far the oil is spreading
The flowing oil is creating a circular pattern on the concrete.
The area of the pattern can be expressed as
[tex]A(n) = \pi n^2.[/tex] .....[2]
A.
Area of the circle of spilled oil as a function of time:
[tex]\text{A[n(t)]}= \pi (n(t))^2[/tex]
then;
Substitute equation [1] we get;
[tex]\text{A[n(t)]}= \pi (8t)^2[/tex]
⇒[tex]\text{A[n(t)]}= 64 \pi t^2[/tex] .....[3]
B.
We have to find how large is the area of spilled oil after 5 minutes.
Substitute t = 5 minutes and [tex]\pi = 3.14[/tex] in [3] we have;
⇒[tex]\text{A[n(5)]}= 64 \cdot 3.14 \cdot 5^2[/tex]
⇒[tex]\text{A[n(5)]}= 200.96 \cdot 25[/tex]
Simplify:
[tex]\text{A[n(5)]}= 5,024[/tex]
Therefore, 5,024 large is the area of spilled oil after 5 minutes.
