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A carton of milk has spilled on a tile floor. The milk flow can be expressed with the function m(t) = 10t, 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 3 minutes? You may use 3.14 to approximate π in this problem. (4 points)

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Answer:

Part A:  [tex]A[m(t)]=100\pi t^2[/tex]

Part B: Area is 2826

Step-by-step explanation:

Part A:

We want to express the area as A[m(t)], so we plug in m(t)=10t into the Area formula which is A(m)=[tex]\pi m^2[/tex]

*We basically plug in 10t into m of A(m) formula*

Thus, [tex]A[m(t)]=\pi (10t)^2=100\pi t^2[/tex]

Part B:

To find the area of the milk spread after 3 minutes, we plug in 3 into t of the formula we just found in Part A. Thus,

[tex]A[m(t)]=100\pi t^2\\=100(3.14)(3)^{2}\\=2826[/tex]

Area is 2826

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