Answered step by step
Verified Expert Solution
Link Copied!

Question

1 Approved Answer

ress and answer for part D, read the question carefully please (10 significant figures) The air in a 57 cubic metre kitchen is initially clean,

ress and answer for part D, read the question carefully please (10 significant figures)

image text in transcribed
The air in a 57 cubic metre kitchen is initially clean, but when David burns his toast while making breakfast, smoke is mixed with the room's air at a rate of 0.06 mg per second. An air conditioning system exchanges the mixture of air and smoke with clean air at a rate of 8 cubic metres per minute. Assume that the pollutant is mixed uniformly throughout the room and that burnt toast is taken outside after 46 seconds. Let 3(t) be the amount of smoke in mg in the room at time t (in seconds) after the toast first began to burn. a. Find a differential equation obeyed by S(t). b. Find S(t) for 0 S t S 46 by solving the differential equation in (a) with an appropriate initial condition. c. What is the level of pollution in mg per cubic meter after 46 seconds? d. How long does it take for the level of pollution to fall to 0.007 mg per cubic metre after the toast is taken outside? You can confirm that you are on the right track by checking numerical answers to some parts dS(t) a. The differential equation is 0.06-S(t)/427.5 a n [E (Enter your expression using Maple syntax and use S(t) rather than just S.) b. As a check that your solution is correct, test one value. 3(11) : 06515811351 9 n [a mg (Enter your answer correct to at least 10 signicant figures. Do not include units.) c. Check the level of pollution in mg per cubic metre after 46 seconds by entering your answer here, correct to at least 10 signicant gures (do not include the units): 00459069215 9 n [E mg m'3 d. The time, in seconds, when the level of pollution falls to 0.007 mg per cubic metre is 6702264937 0 l [E seconds (correct to at least 10 significant figures). Note that this check asks for the time since if : 0 but the question part (d) asks for a time since the toast was taken outside

Step by Step Solution

There are 3 Steps involved in it

Step: 1

blur-text-image

Get Instant Access to Expert-Tailored Solutions

See step-by-step solutions with expert insights and AI powered tools for academic success

Step: 2

blur-text-image

Step: 3

blur-text-image

Ace Your Homework with AI

Get the answers you need in no time with our AI-driven, step-by-step assistance

Get Started

Recommended Textbook for

Linear Algebra Step By Step

Authors: Kuldeep Singh

1st Edition

0191507768, 9780191507762

More Books

Students also viewed these Mathematics questions

Question

600 lb 20 0.5 ft 30 30 5 ft

Answered: 1 week ago