Question

All the computer work is done. Need help with hand written solution for all questions, thanks.

Freezing pipes. The Problem and Model. The project is to determine an approximation for the indoor temperature u(t) in an unheated builg. The model uses Newton's cooling law, insulation data k and a formula for the ambient outside temperature A(t) (see the background section infra) u'(t) + ku(t) = kA(t) u(0)o Assumptions and Notation. Let the daily temperature in Salt Lake City vary from a low of m = 21 degrees to a high of M-49 degrees with the low and high at 3am and 3pm, respectively usually 0.2 Sks0.5 from midnight 0. The number uo is the temperature at midnight. The building is assumed insulated, the average insulation factor being represented by a Newton cooling constant k . The ambient outside temperature is called A(t) and the inside temperature is called u(t), where t is in hours measured . The model assumes that no heat sources or heat sinks are present inside the building Symbol u(t) refers to the general solution of the homogeneous equation u +ku 0. Symbol up(t stands for a particular solution of u, + k = kA(t) Background Newton Cooling Mol. Newton's law of cooling is: The rate of change of the indoor temperature is proportional to the difference between the ambient and indoor temperatures The cooling law implies that du/dt is proportional to A - Let A(t) be the ambient outside temperature and let k denote the proportionality constant in Newton's cooling law. A model for the indoor temperature u(t) is given by du/dt = k(A-u), u(0) = uo, which can be rearranged as u'(t)+ ku(t)=kA(t), u(0)=uo The number is called the insulation constant

Answer 1

A duriuatom by hand :β 'expedid 、fmth·fanulas unudaboue to an atachud maple urk shut o blem using the bok's intghal tabe

change amiable uex-3 alls u inihal table ehe ill be Set to hs bit Simplty mest studenks kall use maple ?s table lk hand mthod ab n that no change to obtain tha anstwen T thied is awah table. A Coding example ve elo ietoataica example Sinphfiai table Aokup Cl aid ip ara Ubed

h Chuck in maplk is eiganiged as h anse follows s your hand dorived emalat up LHS-RHS) .2 in aboue problem by dropping all l^ 13 k U 35 to chiek th answe Compare it against Ha splayed in sabove unanign ('omga)

an be used to erase asigm limit (exp-k be oded i maple as folloios S- The phase shitt between td an otoit r Alt) haphic, is to be hitd bauge ta

oblem (0nbe 㣺und .in rialle'a.I,un('hon implicit non)-this Plet. and .Jん3D-plot k»0.2 - 045)5 7mm) İnom tlu implicit plot ime domain uachd bho 55Thors please uport answer Freczng 5-5-1hos03c0-45 as many nanges as nudedtodescibe th Situaten, blu sand 1 will be九aquired