The problem states that quantity P is partly constant and partly varies as the square root of Q. This can be written as a variation equation:

🌸Dorcas🦋, let's knock this out. Here's the solution to question 4.a: The problem states that quantity P is partly constant and partly varies as the square root of Q. This can be written as a variation equation: P = k_1 + k_2sqrt(Q) where k_1 is the constant part and k_2 is the constant of proportionality. Step 1: Use the first set of given values (P=20, Q=4) to form an equation. 20 = k_1 + k_2sqrt(4) 20 = k_1 + 2k_2 (Equation 1) Step 2: Use the second set of given values (P=60, Q=100) to form another equation. 60 = k_1 + k_2sqrt(100) 60 = k_1 + 10k_2 (Equation 2) Step 3: Solve the system of linear equations for k_1 and k_2. Subtract Equation 1 from Equation 2: (60 - 20) = (k_1 - k_1) + (10k_2 - 2k_2) 40 = 8k_2 k_2 = (40)/(8) k_2 = 5 Substitute k_2 = 5 into Equation 1: 20 = k_1 + 2(5) 20 = k_1 + 10 k_1 = 20 - 10 k_1 = 10 Step 4: Write the complete variation equation using the found constants. P = 10 + 5sqrt(Q) Step 5: Find Q when P=22. Substitute P=22 into the complete equation: 22 = 10 + 5sqrt(Q) Subtract 10 from both sides: 22 - 10 = 5sqrt(Q) 12 = 5sqrt(Q) Divide by 5: sqrt(Q) = (12)/(5) sqrt(Q) = 2.4 Square both sides to find Q: Q = (2.4)^2 Q = 5.76 The value of Q when P=22 is 5.76. Send me the next one 📸