1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
svetoff [14.1K]
2 years ago
5

A bucket of paint has spilled on a tile floor. The paint flow can be expressed with the function p(t) = 6t, where t represents t

ime 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.

Part B: How large is the area of spilled paint after 8 minutes? You may use 3.14 to approximate π in this problem.
Mathematics
2 answers:
xenn [34]2 years ago
6 0

A(p(t))

  • π(6t)²
  • π36t²
  • 36t²π

#B

put t=8

A(p(t))

  • 36π(8)²
  • 36π(64)
  • 7234.56units²
Neko [114]2 years ago
4 0

Answer:

A)   A[p(t)] = 36πt²

B)   7234.56 square units

Step-by-step explanation:

               

<u>Given functions</u>:

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

<u>Part A</u>

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}

<u>Part B</u>

Given

  • t = 8 minutes
  • π = 3.14

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.

You might be interested in
Help me plzzzzz I’ll mark Brainly!!!!
garik1379 [7]

Answer:

ASA

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
Please help mee Idk.
Ira Lisetskai [31]

Answer:

x(1.05)+4.00

Step-by-step explanation:

He bought x pens for 1.05 each and you have to add the $4 shipping fee to it

Hope this Helps

8 0
3 years ago
Read 2 more answers
Pls help me answer this!​
Vadim26 [7]

Answer:

someoeneenennene willlll heelellelelleep yyouuouou

Step-by-step explanation:

stan kim namjoon

8 0
2 years ago
Read 2 more answers
Hey can you please me asap!
crimeas [40]

Answer:

It's D

Step-by-step explanation:


6 0
3 years ago
Read 2 more answers
What is f(x)= 13,500 (times) 0.89^4?
SOVA2 [1]
Solution : 8470.202535
7 0
2 years ago
Other questions:
  • Eighteen out of 24 of emil’s cds are country music. five out of 8 of imani’s cds are country. which is a true statement?
    10·2 answers
  • The length of a car is 1/20of the length of the actual car. If the model is 9.3in. long, how long is the actual car?
    5·1 answer
  • Explain how you could use the distribute property and mental math to find 5 times 198
    5·1 answer
  • 6051 m is equal to how many km?
    8·2 answers
  • Erik's disabled sailboat is floating stationary 3 miles east and 2 miles north of Kingston. A ferry leaves Kingston heading towa
    9·1 answer
  • The fifth root of x to the fourth power times the fifth root of x to the fourth power
    7·2 answers
  • Error Analysis jessie incorrectly said the rate 1/5 hour 1/10 acer can be written as the unit rate 1/50 per acer . What is the c
    8·2 answers
  • Find the shortest length of wood that can be cut into equal lengths of 3m. 8<br>and 12m​
    5·1 answer
  • The table shows the projected numbers N (in millions) of people living in the United States.
    11·1 answer
  • Which sets of ordered pairs represent functions?
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!