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Please help! 30 points! I need help with Algebra 1!!




A bucket of paint has spilled on a tile floor. The paint flow can be expressed with the function p(t) = 5t, where t represents time in minutes and p represents how far the paint is spreading.

The flowing paint is creating a circular pattern on the tile. The area of the pattern can be expressed as A(p) = πp2.

Part A: Find the area of the circle of spilled paint as a function of time, or A[p(t)]. Show your work. (6 points)

Part B: How large is the area of spilled paint after 2 minutes? You may use 3.14 to approximate π in this problem. (4 points)

Respuesta :

Riia

Part a.

It is given in the question that, The area of the pattern can be expressed as

[tex] A(p) = \pi p^2 [/tex]

And

[tex] p(t)=5t [/tex]

So for A(p(t)), we have to substitute 5t for p in A(p), that is

[tex] A(P(t)) = \pi(5t)^2
\\
A(p(t)) =25 \pi t^2 [/tex]

Part b .

At t=2minutes,

[tex] A(p(2)) = 25 \pi(2^2) = 25 \pi(4) = 314 [/tex]

And that's the required area at t=2 minutes .

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