1. **State the problem:** We need to find the horsepower of an automobile engine given the bore, stroke, average pressure, and power strokes per minute. 2. **Given data:** - Bore diameter $d = 2.9000$ inches - Stroke length $L = 2 \frac{3}{16} = 2.1875$ inches - Average pressure $P = 105$ pounds per square inch (psi) - Power strokes per minute $N = 2000$ 3. **Formula for horsepower:** Horsepower (HP) can be calculated using the formula: $$\text{HP} = \frac{P \times A \times L \times N}{33000}$$ where: - $P$ is the average pressure in psi - $A$ is the cross-sectional area of the cylinder in square inches - $L$ is the stroke length in inches - $N$ is the number of power strokes per minute - 33000 is the conversion factor from inch-pounds per minute to horsepower 4. **Calculate the cross-sectional area $A$ of the cylinder:** The bore is the diameter, so the radius $r = \frac{d}{2} = \frac{2.9}{2} = 1.45$ inches. $$A = \pi r^2 = \pi (1.45)^2 = \pi \times 2.1025 = 6.605$ (approx) square inches 5. **Calculate the horsepower:** $$\text{HP} = \frac{105 \times 6.605 \times 2.1875 \times 2000}{33000}$$ 6. **Simplify step-by-step:** Calculate numerator: $$105 \times 6.605 = 693.525$$ $$693.525 \times 2.1875 = 1517.48$$ $$1517.48 \times 2000 = 3,034,960$$ Divide by denominator: $$\text{HP} = \frac{3,034,960}{33000}$$ 7. **Cancel common factors:** $$\text{HP} = \frac{3,034,960}{33,000} = \frac{3,034,960 \div 11}{33,000 \div 11} = \frac{275,905.45}{3,000}$$ 8. **Final division:** $$\text{HP} = 91.97$$ 9. **Round to nearest tenth:** $$\boxed{92.0 \text{ hp}}$$ Thus, the horsepower of the engine is approximately 92.0 hp.