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Art [367]
3 years ago
8

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 ti

me 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)
Mathematics
1 answer:
jeka57 [31]3 years ago
7 0

Answer:

<u>Part A:</u>  A[m(t)]=100\pi t^2

<u>Part B:</u> Area is 2826

Step-by-step explanation:

<u />

<u>Part A:</u>

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)=\pi m^2

<em>*We basically plug in 10t into m of A(m) formula*</em>

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

<u>Part B:</u>

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,

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

Area is 2826

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