Respuesta :
Answer:
Part A: A(m(t)) = π(81t²); Part B: 1017.36
Step by step explanation:
Part A:
To find A(m(t)), we substitute our value for m(t), 9t, in place of m:
A(m(t)) = πm² = π(9t)² = π(81t²)
A(m(t)) = π(81t²)
Part B:
Substitute 2 in for t:
A(m(2)) = π(81(2²)) = π(81(4)) = 3.14(324) = 1017.36
Answer:
As per the statement:
The milk flow can be expressed with the function:
[tex]m(t) = 9t[/tex] where, t represents time in minutes and m represents how far the milk is spreading.
The flowing milk is creating a circular pattern on the tile.
The area of the pattern can be expressed as:
[tex]A(m) = \pi m^2[/tex]
Part A.
Find the area of the circle of spilled milk as a function of time, or A[m(t)].
Substitute m(t) = 9t in A[m] we have;
[tex]A[m(t)] = \pi \cdot (m(t))^2 = \pi \cdot (9t)^2 = 81t^2 \pi[/tex] .....[1]
⇒[tex]81t^2 \pi[/tex] is the area of the circle of spilled milk as a function of time, or A[m(t)].
Part B.
How large is the area of spilled milk after 2 minutes
Substitute t = 2 minutes and Use [tex]\pi = 3.14[/tex] in [1] we have;
[tex]A[m(2)] = 81 \cdot (2)^2 \cdot 3.14 = 81 \cdot 4 \cdot 3.14 = 1,017.36[/tex]
Therefore, 1017.36 square unit is the area of spilled milk after 2 minutes
