Question: Find the body surface area of a child in square meters with each weight by applying the formula Upper S equals StartFraction 4 k plus 7 Over k plus 90 EndFraction, where S is the child's body surface area in square meters and k is the child's weight in kilograms.
a) 14 kg
b) 29 kg
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Part 1
a) The body surface area of a child weighing 14 kg is enter your response here m squared.
(Simplify your answer. Round to the nearest hundredth as needed.)
1. **State the problem:** We need to find the body surface area $S$ of a child given their weight $k$ in kilograms using the formula:
$$S = \frac{4k + 7}{k + 90}$$
2. **Apply the formula for $k = 14$ kg:**
$$S = \frac{4(14) + 7}{14 + 90}$$
3. **Calculate the numerator:**
$$4 \times 14 = 56$$
$$56 + 7 = 63$$
4. **Calculate the denominator:**
$$14 + 90 = 104$$
5. **Write the fraction:**
$$S = \frac{63}{104}$$
6. **Simplify the fraction if possible:**
The numerator and denominator share a common factor of 1 only, so the fraction is already in simplest form.
7. **Convert to decimal and round to nearest hundredth:**
$$S = \frac{63}{104} \approx 0.605769... \approx 0.61$$
**Final answer:** The body surface area of a child weighing 14 kg is approximately $0.61$ square meters.