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04 Aug 2025, 11:29
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Increased Efficiency: \(48 - 0.2R\)
Decreased Efficiency: \(45 - 0.15R\)
A machine operates at an efficiency of 36 units per liter of fuel when running at exactly 60 rotations per minute (RPM). Its efficiency decreases by 1.2 units for every 8 RPM increase above 60, and increases by 0.8 units for every 4 RPM decrease below 60.
Select for Increased Efficiency a formula for the machine’s efficiency when running at R RPM, where \(0 < R < 60\) and select for Decreased Efficiency a formula for the machine’s efficiency when running at R RPM, where \(R > 60\). Make only two selections, one in each column.
Select for Increased Efficiency a formula for the machine’s efficiency when running at R RPM, where \(0 < R < 60\) and select for Decreased Efficiency a formula for the machine’s efficiency when running at R RPM, where \(R > 60\). Make only two selections, one in each column.
| Increased Efficiency | Decreased Efficiency | |
| \(36 - 0.3R\) | ||
| \(36 + 0.2R\) | ||
| \(45 - 0.15R\) | ||
| \(48 - 0.2R\) | ||
| \(48 + 0.2R\) | ||
| \(60 - 0.25R\) |
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Official Answer
Increased Efficiency: \(48 - 0.2R\)
Decreased Efficiency: \(45 - 0.15R\)
04 Aug 2025, 11:29
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Official Solution:
Increased Efficiency (\(R < 60\)):
Efficiency increases by 0.8 units for every 4 RPM below 60.
So, number of 4-RPM drops \(= \frac{60 - R}{4}\)
Increase \(= 0.8 * \frac{60 - R}{4}\)
Efficiency \(= 36 + 0.8 * \frac{60 - R}{4} = 48 - 0.2R\)
Decreased Efficiency (\(R > 60\)):
Efficiency decreases by 1.2 units for every 8 RPM above 60.
So, number of 8-RPM increases \(= \frac{R - 60}{8}\)
Decrease \(= 1.2 * \frac{R - 60}{8}\)
Efficiency \(= 36 - 1.2 * \frac{R - 60}{8} = 45 - 0.15R\)
Correct answer:
Increased Efficiency "\(48 - 0.2R\)"
Decreased Efficiency "\(45 - 0.15R\)"
Bunuel
Increased Efficiency (\(R < 60\)):
Efficiency increases by 0.8 units for every 4 RPM below 60.
So, number of 4-RPM drops \(= \frac{60 - R}{4}\)
Increase \(= 0.8 * \frac{60 - R}{4}\)
Efficiency \(= 36 + 0.8 * \frac{60 - R}{4} = 48 - 0.2R\)
Decreased Efficiency (\(R > 60\)):
Efficiency decreases by 1.2 units for every 8 RPM above 60.
So, number of 8-RPM increases \(= \frac{R - 60}{8}\)
Decrease \(= 1.2 * \frac{R - 60}{8}\)
Efficiency \(= 36 - 1.2 * \frac{R - 60}{8} = 45 - 0.15R\)
Correct answer:
Increased Efficiency "\(48 - 0.2R\)"
Decreased Efficiency "\(45 - 0.15R\)"
