Worked solutions for example 3 Workshop 3 - Powers and Quadratics OES Contextual problems

1. 3a Express the heat flow equation in the form 0 = ax2 + bx +
c and state what a, b and c are.
푇 = −
퐴
2푘
푧2 +
(푄푑+퐴푑)
푘
푧

2. 3a • Subtract T from both sides:

3. 3a • Subtract T from both sides:
ퟎ = −
퐀
ퟐ퐤
퐳ퟐ +
(퐐퐝+퐀퐝)
퐤
퐳 + 퐓

4. 3a • Subtract T from both sides:
ퟎ = −
퐀
ퟐ퐤
퐳ퟐ +
(퐐퐝+퐀퐝)
퐤
퐳 + 퐓
• State a, b and c:

5. 3a • Subtract T from both sides:
ퟎ = −
퐀
ퟐ퐤
퐳ퟐ +
(퐐퐝+퐀퐝)
퐤
퐳 + 퐓
• State a, b and c:
퐚 =
퐀
ퟐ퐤
퐛 =
퐐퐝 + 퐀퐝
퐤
퐜 = 퐓

6. 3b Write an expression for z in terms of A, k, Qd, d and T by
substituting a, b and c into the quadratic formula.

7. 3b • Recall the quadratic formula:

8. 3b • Recall the quadratic formula:
z =
−b ± b2 − 4ac
2a

9. 3b • Recall the quadratic formula:
z =
−b ± b2 − 4ac
2a
• Substitute in a, b and c:

10. 3b • Recall the quadratic formula:
z =
−b ± b2 − 4ac
2a
• Substitute in a, b and c:
퐳 =
−
퐐퐝 + 퐀퐝
퐤
±
퐐퐝 + 퐀퐝
퐤
ퟐ
− ퟒ
퐀
ퟐ퐤
퐓
ퟐ
퐀
ퟐ퐤