3 years ago

PLEASE HELP ME WITH THIS WILL GIVE 30 POINTS

Mathematics

1 answer:

maxonik [38]3 years ago

8 0

Answer:

i think the area is 21 srry if im wrong

Step-by-step explanation:

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Step-by-step explanation:

Given functions:

$\begin{cases}p(t)=6t \\ A(p)=\pi p^2 \end{cases}$

Part A

To find the area of the circle of spilled paint as a function of time, substitute the function p(t) into the given function A(p):

$\begin{aligned}A(p) & = \pi p^2\\\\ \implies A[p(t)] & = \pi [p(t)]^2\\& = \pi (6t)^2\\& = \pi 6^2 t^2\\& = 36\pi t^2\end{aligned}$

Part B

Given

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Substitute the given values into the equation for A[p(t)} found in part A:

$\begin{aligned}A[p(8)] & = 36\pi t^2\\& = 36 \cdot 3.14 \cdot 8^2\\& = 36 \cdot 3.14 \cdot 64\\& = 113.04 \cdot 64\\& = 7234.56\:\: \sf square\:units\end{aligned}$

Therefore, the area of spilled paint after 8 minutes if 7234.56 square units.

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