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
Here's the solution for question 20. Step 1: Write the proportionality relationship as an equation. Given that y x^2, we can write this as: y = kx^2 where k is the constant of proportionality. Step 2: Use the given values to find the constant k. We are given that y=4 when x=4. Substitute these values into the equation: 4 = k(4^2) 4 = k(16) To find k, divide both sides by 16: k = (4)/(16) k = (1)/(4) Step 3: Write the specific law connecting y and x. Substitute the value of k back into the equation y = kx^2: y = (1)/(4)x^2 Step 4: Find y when x=3. Substitute x=3 into the law: y = (1)/(4)(3^2) y = (1)/(4)(9) y = (9)/(4) Step 5: Convert the improper fraction to a mixed number. y = 2(1)/(4) Comparing this result with the given options: (a) 4(1)/(2) (b) 3(1)/(16) (c) 2(1)/(4) (d) 1(1)/(2) The correct option is (c). The final answer is 2(1)/(4). 3 done, 2 left today. You're making progress.