In a grid of wires, the temperature at exterior meshpoints is maintained at constant values (in °C), as shownin the accompanying figure. When the grid is in thermalequilibrium, the temperature T at each interior meshpoint is the average of the temperatures at the fouradjacent points. For example, T 2 = T 3 + T 1 + 200 + 0 4 . Find the temperatures T 1 , T 2 , and T 3 when the grid isin thermal equilibrium.
In a grid of wires, the temperature at exterior meshpoints is maintained at constant values (in °C), as shownin the accompanying figure. When the grid is in thermalequilibrium, the temperature T at each interior meshpoint is the average of the temperatures at the fouradjacent points. For example, T 2 = T 3 + T 1 + 200 + 0 4 . Find the temperatures T 1 , T 2 , and T 3 when the grid isin thermal equilibrium.
In a grid of wires, the temperature at exterior meshpoints is maintained at constant values (in °C), as shownin the accompanying figure. When the grid is in thermalequilibrium, the temperature T at each interior meshpoint is the average of the temperatures at the fouradjacent points. For example,
T
2
=
T
3
+
T
1
+
200
+
0
4
. Find the temperatures
T
1
,
T
2
,
and
T
3
when the grid isin thermal equilibrium.
A cup of water at an initial temperature of 81°C is placed in a room at a constant temperature of 24°C. The temperature of the water is measured every 5 minutes during a half-hour period. The results are recorded as ordered pairs of the form (t, T), where t is the time (in minutes) and T is the temperature (in degrees Celsius).
(0, 81.0°), (5, 69.0°), (10, 60.5°), (15, 54.2°), (20, 49.3°), (25, 45.4°), (30, 42.6°)
(a) Subtract the room temperature from each of the temperatures in the ordered pairs. Use a graphing utility to plot the data points (t, T) and (t, T − 24).
(b) An exponential model for the data (t, T − 24) is T − 24 = 54.4(0.964)t. Solve for T and graph the model. Compare the result with the plot of the original data.
(c) Use a graphing utility to plot the points (t, ln(T − 24)) and observe that the points appear to be linear.
Use the regression feature of the graphing utility to fit a line to these data. This resulting line has the form ln(T − 24) = at + b, which is…
In a grid of wires, the temperature at exterior mesh point is maintained at constant values. When the grid is in thermal equilibrium, the temperature at each interior mesh point is the average of the temperatures at the four adjacent points. For instance,
T1 = (T2 + T3 + 0 -70)/ 4
find the temperatures T1, T2, T3, T4 when the grid is in thermal equilibrium
In your Capstone software create a table with the following variables:
Position x, m: 1, 2, 3, 4
Coefficient of friction μ: 0.36
Velocity v, m/s: v=V 2. u.9.8.x
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