Solve the following IBVP using appropriate extensions of the functions o and w: x > 0, t>0, u(x, 0) = 0(x) =x² + x, x20, u(x, 0) = v(x) = 1 – 2.x, x > 0, Uz (0, t) = 0, t> 0. Utt = Ur, %3D %3D %3D
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- 2. Suppose that in Example 2.27, 400 units of food A, 500 units of B, and 600 units of C are placed in the test tube each day and the data on daily food consumption by the bacteria (in units per day) are as shown in Table 2.7. How many bacteria of each strain can coexist in the test tube and consume all of the food? Table 2.7 Bacteria Strain I Bacteria Strain II Bacteria Strain III Food A 1 2 0 Food B 2 1 3 Food C 1 1 1Prove that if both y and z are solutions to x' = Ax, then for any c1, c2, the function c1y + c2z is also a solution to x' = AxFind x1, x2, x3 with gauss jordan
- Consider the following LPmax x1 + x2s.t. x1 −x2 ≤2 (y1)−2x1 + 3x2 ≤2 (y2)−x1 −2x2 ≤−1 (y3)x1, x2 ≥01. Write down the dual of the primal LP.2. Based on complementary slackness, argue whether x1 = 2, x2 = 2 is an optimal solution to the primalLP.a)X ∼ exp (λ). Under the condition {X> 3} fX | {X> 3} (x | X> 3) =? and E [X | X> 3] =?A manufacturing company employs two devices to inspect output for quality control purposes. The first device is able to accurately detect 99.3% of the defective items it receives, whereas the second is able to do so in 99.7% of the cases. Assume that four defective items are produced and sent out for inspection. Let X and Y denote the number of items that will be identified as defective by inspecting devices 1 and 2, respectively. Assume that the devices are independent. Determine fxy(X=3,Y=4).