Question

HELP PLEASE ASAP!!!

Answer 1

Answer:

The area of the circle of spilled paint as a function of time is $A(p(t)) = 25 \pi t^2$. The area of spilled paint after 2 minutes is 314.

Step-by-step explanation:

Consider the provided statement.

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: $A(p) = \pi p^2$.

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

Substitute $p = 5t$ in $A(p) = \pi p^2$.

$A(p(t)) = \pi (5t)^2$

$A(p(t)) = 25 \pi t^2$

Hence, the area of the circle of spilled paint as a function of time is $A(p(t)) = 25 \pi t^2$.

Part B: How large is the area of spilled paint after 2 minutes?

Substitute t = 2 in $A(p(t)) = 25 \pi t^2$.

$A(2) = 25 \pi (2)^2$

$A(2) = 100 \pi$

Use π = 3.14 in above equation.

$A(2) = 100 \times 3.14$

$A(2) = 314$

Hence, the area of spilled paint after 2 minutes is 314.

Answer 2

A. It's a composite function, so basically, wherever you see a p, replace it with 5t, because we are given that information. So, your answer is:
$A[p(t)] = 5t \pi 2=10t \pi$

B. Let's use the function we created, and just plug in 2 for t:
$A[p(2)] = 10(2) \pi$
$A[p(2)] = 62.83$

So, your answer is (approximately) 62.83 units².