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Taya2010 [7]
2 years ago
13

A carton of milk has spilled on a tile floor. The milk flow can be expressed with the function m(t) = 9t, where t represents tim

e 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. (4 points)
Mathematics
2 answers:
____ [38]2 years ago
4 0

Answer:

The area of circle of spilled milk as a function of time, or A[m(t)] is A[m(t)]=81t^2\pi. The area of spilled milk after 2 minutes is 1017.36 square unit.

Step-by-step explanation:

Consider the provided information.

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 area of the pattern can be expressed as A(m) = πm².

Part A:

To find the area of the circle of spilled milk as a function of time, substitute the value of function in area as shown:

A(m)=\pi m^2

A[m(t)]=\pi (9t)^2

A[m(t)]=81t^2\pi

Hence. the area of circle of spilled milk as a function of time, or A[m(t)] is A[m(t)]=81t^2\pi.

Part B:

Substitute t = 2 in the above equation.

A[m(t)]=81(2)^2\pi

A[m(t)]=81\times 4\times 3.14

A[m(t)]=1017.36

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

nataly862011 [7]2 years ago
3 0
Part A)     means that we have to find a composition of functions A and m
A(m(t))=π(9t)²=9πt²
part B)  
A(m(t))=9πt²
A(m(2))=9*3.14*(2)²=113.04
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