Question

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 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. (4 points)

Answer 1

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.

Answer 2

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