Question: Find the value of
k =a2+ 9(b−2)/4c
when a =−2.4, b = 3.3 and c = −1.9.
Give your answer correct to three significant figures
1. **State the problem:** We need to find the value of $$k = a^2 + \frac{9(b-2)}{4c}$$ given $$a = -2.4$$, $$b = 3.3$$, and $$c = -1.9$$.
2. **Write the formula:** $$k = a^2 + \frac{9(b-2)}{4c}$$
3. **Calculate each part:**
- Calculate $$a^2$$:
$$a^2 = (-2.4)^2 = 5.76$$
- Calculate $$b-2$$:
$$b-2 = 3.3 - 2 = 1.3$$
- Calculate numerator $$9(b-2)$$:
$$9 \times 1.3 = 11.7$$
- Calculate denominator $$4c$$:
$$4 \times (-1.9) = -7.6$$
4. **Calculate the fraction:**
$$\frac{9(b-2)}{4c} = \frac{11.7}{-7.6}$$
5. **Simplify the fraction:**
$$\frac{11.7}{-7.6} = -\frac{11.7}{7.6}$$
6. **Calculate the fraction value:**
$$-\frac{11.7}{7.6} \approx -1.53947$$
7. **Add $$a^2$$ and the fraction:**
$$k = 5.76 + (-1.53947) = 5.76 - 1.53947 = 4.22053$$
8. **Round to three significant figures:**
$$k \approx 4.22$$
**Final answer:** $$k = 4.22$$