Answers: Introduction to rearranging equations
These are the answers to Questions: Introduction to rearranging equations.
Please attempt the questions before reading these answers!
Q1
1.1. \(\quad a = x - 2b\)
1.2. \(\quad b = \dfrac{x-a}{2}\)
1.3. \(\quad z = - \dfrac{x}{4} + \dfrac{y}{2} + 1\)
1.4. \(\quad x = \dfrac{3y}{5} - \dfrac{8z}{5} -\dfrac{2}{5}\)
1.5. \(\quad y = \dfrac{5x}{3} +\dfrac{8z}{3} + \dfrac{2}{3}\)
1.6. \(\quad z = -\dfrac{5x}{8} + \dfrac{3y}{8} - \dfrac{1}{4}\)
1.7. \(\quad x = \pm\sqrt{4-y^2}\)
1.8. \(\quad x = \pm\sqrt{4a - \dfrac{y^2}{4}}\)
1.9. \(\quad y = \pm\sqrt{16a - 4x^2}\)
1.10. \(\quad x = \pm\sqrt{(y+1)^2 + a^2}\)
1.11. \(\quad a = \sqrt[3]{x^3 - (y+1)^3}\)
1.12. \(\quad x = \sqrt[3]{(y+1)^3 - a^3}\)
1.13. \(\quad d = \dfrac{a^3 - x^4y^2}{2bc}\)
1.14. \(\quad a = \sqrt[3]{x^4y^2 - 2bcd}\)
1.15. \(\quad x = \pm\sqrt[4]{\dfrac{a^3 + 2bcd}{y^2}}\)
1.16. \(\quad x = \dfrac{1}{ly^2 - 45}\)
Q2
\(\quad a = \dfrac{5x^3y^3}{4bc^2} + \dfrac{6z}{4bc^2w^4}\)
\(\quad b = \dfrac{5x^3y^3}{4ac^2} + \dfrac{6z}{4ac^2w^4}\)
\(\quad c = \pm\sqrt{\dfrac{5x^3y^3}{4ab} + \dfrac{6z}{4abw^4}}\)
\(\quad y = \sqrt[3]{\dfrac{4abc^2}{5x^3} - \dfrac{6z}{5w^4x^3}}\)
\(\quad z = \dfrac{4abc^2w^4 - 5w^4x^3y^3}{6}\)
\(\quad w = \sqrt[4]{\dfrac{6z}{4abc^2 - 5x^3y^3}}\)
Version history and licensing
v1.0: initial version created 08/23 by Shanelle Advani, tdhc as part of a University of St Andrews STEP project.
- v1.1: edited 05/24 by tdhc.