This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Hey geraldmusau27 — ready when you are. Question 13: Given vectors: r = i + 2j - 4k s = 4i - j + 3k t = 2i + 3k Step 1: Calculate 3s. 3s = 3(4i - j + 3k) = 12i - 3j + 9k Step 2: Calculate OP = r - 3s + t. Substitute the vector values: OP = (i + 2j - 4k) - (12i - 3j + 9k) + (2i + 0j + 3k) Combine the i components: 1 - 12 + 2 = -9 Combine the j components: 2 - (-3) + 0 = 2 + 3 = 5 Combine the k components: -4 - 9 + 3 = -13 + 3 = -10 So, the resultant vector is: OP = -9i + 5j - 10k Step 3: Determine the coordinates of P. Since O is the origin, the coordinates of P are the components of OP. The coordinates of P are (-9, 5, -10). Question 14: Initial state: Total beads = 14 Number of red beads = x Number of blue beads = 14 - x After removing 4 red beads: Number of red beads = x - 4 Total number of beads = 14 - 4 = 10 The probability of selecting a red bead is given as (2)/(5). Step 1: Set up the probability equation. Number of red beadsTotal number of beads = (2)/(5) (x - 4)/(10) = (2)/(5) Step 2: Solve for x. Multiply both sides by 10: x - 4 = (2)/(5) × 10 x - 4 = 4 Add 4 to both sides: x = 4 + 4 x = 8 The value of x is 8. Send me the next one 📸