一道数学题,英文好的有实力的来LetH(t)betheHeavisideunitstepfunctionasdenedinthelectures(seealsothetextbookpage170.(a)SketchthegraphofH(t-2)-H(t-4).(b)TheBrownshaveanairconditioningunitthatrunsataa

Question

一道数学题,英文好的有实力的来
Let H(t) be the Heaviside unit step function as dened in the lectures (see also the textbook page 170.
(a) Sketch the graph of H(t- 2) - H(t - 4).
(b) The Browns have an air conditioning unit that runs at a
at rate of 67c per hour. They only use
the unit so baby Barry can have a comfortable 2-hour nap between 2pm and 4pm every day. Using
the Heaviside unit step function, determine a periodic formula for the hourly cost of running the air
conditioner unit at any point in a 24 hour day (let noon be t = 0).
(c) The Smiths' house has an air conditioning unit whose hourly cost starts at $1.60, but then decreases
on a linear scale until after two hours it reaches a rate of 60c per hour. It remains at a rate of 60c
per hour for every hour after that. Using the Heaviside unit step function, determine a formula for
the hourly cost of running the air conditioner at t hours, assuming it is turned on when t = 0 and
left on permanently. What is the hourly cost at the 80 minute mark?

Answer 1

H(t)是课上定义的单位阶跃函数 (见课本170页)
(a) 作函数H(t-2)-H(t-4)的图像