Acarton of milk has spilled on a tile floor. the milk flow can be expressed with the function m(t) = 9t, 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 a(m) = πm2. part a: find the area of the circle of spilled milk as a function of time, or a[m(t)]. show your work. (6 points) part b: how large is the area of spilled milk after 2 minutes? you may use 3.14 to approximate π in this problem.

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

As per the statement:

The milk flow can be expressed with the function:

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:

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;

   .....[1]

⇒ 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 in [1] we have;

Therefore, 1017.36 square unit  is the area of spilled milk after 2 minutes

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