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mr Goodwill [35]
3 years ago
5

A barrel of tomato sauce has spilled on a tile floor. The sauce flow can be expressed with the function r(t) = 2t, where t repre

sents time in minutes and r represents how far the sauce is spreading.
The spilled sauce 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 sauce as a function of time, or A[r(t)]. Show your work. (6 points)

Part B: How large is the area of spilled sauce after 5 minutes? You may use 3.14 to approximate π in this problem. (4 points)
Mathematics
2 answers:
Reil [10]3 years ago
4 0

Answer:

As per the statement:

The sauce flow can be expressed with the function is given by:

r(t) = 2t

where, t represents time in minutes and r represents how far the sauce is spreading.

The spilled sauce is creating a circular pattern on the tile.

The area of the pattern can be expressed as:

A(r) = \pi r^2

Part A.

To find the area of the circle of spilled sauce as a function of time.

A[r(t)]

then;

A[r(t)] = \pi (r(t))^2

Substitute the function r(t) we have;

A[r(t)] = \pi (2t)^2 = \pi 4t^2 = 4 \pi t^2            .....[1]

therefore, the area of the circle of spilled sauce as a function of time, is:

A[r(t)] = 4 \pi t^2.

Part B:

We have to find how large is the area of spilled sauce after 5 minute.

use  π = 3.14 and t = 5 minutes

Substitutes these in [1] we have;

A[r(5)] = 4 \cdot 3.14 \cdot 5^2

⇒A[r(5)] = 100 \cdot 3.14

Simplify:

A[r(5)] = 314 square unit

therefore, 314 square unit large is the area of spilled sauce after 5 minute.

IrinaVladis [17]3 years ago
3 0
For the answer to the question above, I'll show my solution for the answer below.
Area A = pi r^2 
<span>The rate of change of area = d A/ d t = 2 pi r d r/d t </span>
<span>r= 2t, d r = 2 d t </span>
<span>This gives </span>
<span>d A/ d t = 2 pi 2t 2 d t = 8 pi t dt </span>
<span>Integrate it </span>
<span>A= 4 pi t^2. </span>
<span>After t=5, the area will be 100* 3.14 square= 314 square units.</span>
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