A quantity P varies jointly as the square of Q and the cube root of R. If P = 48 when Q = 2 and R = 27, find P when Q = 3 and R = 64.
Answer and explanation
Correct answer: C. 144
- Step 1: Joint variation formula: P = k Q² R^(1/3). Step 2. Substitute initial values: 48 = k(2²)(27^(1/3)) => 48 = k(4)(3) => 48 = 12k => k = 4. Step 3. Calculate P with new values: P = 4(3²)(64^(1/3)) = 4(9)(4) = 144. Answer: 144. Why not the others: 108 uses R^(1/3) = 3; 192 uses Q = 4; 72 halves the result.
Practise more Algebraic Processes, Equations and Graphs.
Free questions with an explanation for every one, and full timed NECO Senior School Certificate Examination mock tests.
More Algebraic Processes, Equations and Graphs questions
- Solve for x in the linear algebraic equation: 3(2x - 4) - 2(x + 5) = 16.
- Solve the simultaneous linear equations for x and y: 2x + 3y = 13 and 3x - y = 3.
- Find the roots of the quadratic equation by factorization: 2x² + 5x - 3 = 0.
- Determine the nature of the roots of the quadratic equation: 3x² - 4x + 2 = 0.
- If α and β are the roots of the quadratic equation 2x² - 7x + 4 = 0, find the numerical value of α + β + αβ.
- Solve the quadratic inequality: x² - 5x + 6 < 0.