Find a cycle in the graph K₁ and reduce the flow by 1 on each edge. Show that the flow in and out of each node in the cycle is still equal. a 15 b S 14 16 c 2 00 17 d K₁ 21 a
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- Find the general flow pattern of network shown in figure. Assuming that all flows are non-negative, what is largest possible value for x3. where n=9.For each graph shown below, determine if it is Hamiltonian.Which of the graph/s above contains an Euler Trail? Which of the graph/s above is/are Eulerian? Which of the graph/s above is/are Hamiltonian?
- a.Find the general flow pattern of the network shown in the figure. b. Assuming that the flow must be in the directions indicated, find the minimum flows in the branches denoted byGraph z(t) = 4eitA natural cubic spline S is defined byS0(x) = 1+B(x −1)−D(x −1)3, if 1 ≤ x < 2 S1(x) = 1+b(x−2) −3/4(x−2)2 + d(x−2)3, if 2 ≤ x ≤ 3If S interpolates the data (1, 1), (2, 1), and (3, 0), find B, D, b, and d.
- Determine whether the given DE is separable, linear, exact, or Bernoulli. Please do part A b C and EA 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…For each pair of vertex, give the vertex sequence of the longest path connecting them that repeat no edges. Is there a longest path connecting them? a.)S & Zb.)S & Vc.) U & YD.) U & Xe.) V & W