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Combine: \( 2x^2 + 12x + 36 = 225 \)
Subtract 225: \( 2x^2 + 12x - 189 = 0 \)
Divide by 2: \( x^2 + 6x - 94.5 = 0 \)
\( x = \frac{-6 \pm \sqrt{6^2 - 4(1)(-94.5)}}{2} = \frac{-6 \pm \sqrt{36 + 378}}{2} = \frac{-6 \pm \sqrt{414}}{2} \)
\( \sqrt{414} \approx 20.35 \), so \( x = \frac{-6 + 20.35}{2} \approx 7.175 \)
Shorter leg ≈ 7.18 cm (rounded to two decimals).
#### 7.18
A scientist measures the concentration of a chemical in a solution, which decreases exponentially by 10% per hour. If the initial concentration is 200 mg/L, what will it be after 5 hours?
Decay factor = \( 1 - 0.10 = 0.9 \).
After 5 hours: \( 200 \times (0.9)^5 \)