Answer:
A) A(p(t)) = 25πt²
B) 314 square units.
Step-by-step explanation:
Part A)
Flow of paint can be expressed by the function:
p(t) = 5t
Area of the pattern is expressed as:
A(p) = πp²
Since area is given in terms of p, we can use the expression of p to express the area of pattern in terms of time(t). Using the value, we get:
A(p(t)) = π (5t)²
A(p(t)) = 25πt²
Part B)
We have to calculate the area of the pattern after time t. Substituting the value of t in above expression, we get:
A(p(2)) = 25 x 3.14 x 4 = 314 square units.
Therefore, the area of spilled paint after 2 minutes will be 314 square units.
