85. Thermostat Control Energy conservation experts estimate that homeowners can save 5% to 10% on winter heating bills by programming their thermostats 5 to 10 degrees lower while sleeping. In the graph (next page), the temperature T(in degrees Fahrenheit) of a home is given as a function of time t (in hours after midnight) over a 24-hour period. (a) At what temperature is the thermostat set during daytime hours? At what temperature is the thermostat set overnight? (b) The homeowner reprograms the thermostat to y = T ( t ) − 2 . Explain how this affects the temperature in the house. Graph this new function. (c) The homeowner reprograms the thermostat to y = T ( t + 1 ) . Explain how this affects the temperature in the house. Graph this new function. Source: Roger Albright, 547 Ways to Be Fuel Smart, 2000
85. Thermostat Control Energy conservation experts estimate that homeowners can save 5% to 10% on winter heating bills by programming their thermostats 5 to 10 degrees lower while sleeping. In the graph (next page), the temperature T(in degrees Fahrenheit) of a home is given as a function of time t (in hours after midnight) over a 24-hour period. (a) At what temperature is the thermostat set during daytime hours? At what temperature is the thermostat set overnight? (b) The homeowner reprograms the thermostat to y = T ( t ) − 2 . Explain how this affects the temperature in the house. Graph this new function. (c) The homeowner reprograms the thermostat to y = T ( t + 1 ) . Explain how this affects the temperature in the house. Graph this new function. Source: Roger Albright, 547 Ways to Be Fuel Smart, 2000
Solution Summary: Thermostat Control Energy conservation experts estimate that homeowners can save 5 to 10 % on winter heating bills by programming their thermostats 5-10 degrees lower while sleeping.
85. Thermostat Control Energy conservation experts estimate that homeowners can save
to
on winter heating bills by programming their thermostats 5 to 10 degrees lower while sleeping. In the graph (next page), the temperature T(in degrees Fahrenheit) of a home is given as a function of time
(in hours after midnight) over a 24-hour period.
(a) At what temperature is the thermostat set during daytime hours? At what temperature is the thermostat set overnight?
(b) The homeowner reprograms the thermostat to
. Explain how this affects the temperature in the house. Graph this new function.
(c) The homeowner reprograms the thermostat to
. Explain how this affects the temperature in the house. Graph this new function.
Source: Roger Albright, 547 Ways to Be Fuel Smart, 2000
The velocity of a particle moves along the x-axis and is given by the equation ds/dt = 40 - 3t^2 m/s. Calculate the acceleration at time t=2 s and t=4 s. Calculate also the total displacement at the given interval. Assume at t=0 s=5m.Write the solution using pen and draw the graph if needed.
4. Use method of separation of variable to solve the following wave equation
მłu
J²u
subject to
u(0,t) =0, for t> 0,
u(л,t) = 0, for t> 0,
=
t> 0,
at²
ax²'
u(x, 0) = 0,
0.01 x,
ut(x, 0) =
Π
0.01 (π-x),
0
Solve the following heat equation by method of separation variables:
ди
=
at
subject to
u(0,t) =0, for
-16024
ძx2 •
t>0, 0 0,
ux (4,t) = 0, for
t> 0,
u(x, 0) =
(x-3,
\-1,
0 < x ≤2
2≤ x ≤ 4.
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Time Series Analysis Theory & Uni-variate Forecasting Techniques; Author: Analytics University;https://www.youtube.com/watch?v=_X5q9FYLGxM;License: Standard YouTube License, CC-BY