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.
ScanSolve AI Answer
Step 1: Write down the relationship between x and y. The quantity y is partly constant and partly varies inversely as the square of x. This can be expressed as: y = A + (B)/(x^2) where A and B are constants. Step 2: Use the given conditions to form a system of equations. When x=1, y=11: 11 = A + (B)/(1^2) 11 = A + B (*) When x=2, y=5: 5 = A + (B)/(2^2) 5 = A + (B)/(4) (**) Step 3: Solve the system of equations for A and B. From equation (*), we can express A as A = 11 - B. Substitute this expression for A into equation (**): 5 = (11 - B) + (B)/(4) 5 = 11 - B + (B)/(4) Subtract 11 from both sides: 5 - 11 = -B + (B)/(4) -6 = -(4B)/(4) + (B)/(4) -6 = -(3B)/(4) Multiply both sides by -(4)/(3): B = -6 × (-(4)/(3)) B = 2 × 4 B = 8 Now substitute B=8 back into equation (*) to find A: 11 = A + 8 A = 11 - 8 A = 3 Step 4: Write the complete relationship between x and y. Substitute the values of A=3 and B=8 into the general relationship: y = 3 + (8)/(x^2) Step 5: Find the value of y when x=4. Substitute x=4 into the relationship found in Step 4: y = 3 + (8)/(4^2) y = 3 + (8)/(16) y = 3 + (1)/(2) y = 3 + 0.5 y = 3.5 3 done, 2 left today. You're making progress.