A vat of milk has spilled on a tile floor. The milk flow can be expressed with the function r(t) = 4t, where t represents time in minutes and r represents how far the milk is spreading.

The spilled milk is creating a circular pattern on the tile. The area of the pattern can be expressed as A(r) = πr2.

Part A: Find the area of the circle of spilled milk as a function of time, or A[r(t)]. Show your work.

Part B: How large is the area of spilled milk after 4 minutes? You may use 3.14 to approximate π in this problem.

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Moralesdanielid Moralesdanielid · Answer 1

Answer:

For a) $A(r(t))=π(4t)^2.$

For b) 803.84

Step-by-step explanation:

For a) we can do a simple substitution on the variable r. Notice that $A=πr^2$ make $A$ a function of $r.$ Then, $A(r(t))=\pi (r(t))^2=\pi (4t)^2.$

For b) you only need to substitute the value $t=4$ on the expresión $A(r(t)).$

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