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Home » \(\sqrt345 \approx 18.57\), so - Tacotoon

\(\sqrt345 \approx 18.57\), so - Tacotoon

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 Question: A robotics engineer is calibrating a sensor whose response curve follows the cubic polynomial $ f(x) $ such that $ f(1) = 3, f(2) = -1, f(3) = 5, f(4) = 11 $. Find $ f(0) $.

📌 Solution: Let $ f(x) = ax^3 + bx^2 + cx + d $. Use the given values to form a system of equations:

📌 f(1) &= a + b + c + d = 3 \\

📌 f(2) &= 8a + 4b + 2c + d = -1 \\

📌 f(3) &= 27a + 9b + 3c + d = 5 \\

📌 f(4) &= 64a + 16b + 4c + d = 11 \\

📌 Subtract consecutive equations to eliminate $ d $:

📌 $ (8a + 4b + 2c + d) - (a + b + c + d) = -1 - 3 \Rightarrow 7a + 3b + c = -4 $

🔥 Popular Posts

#### 1541
An ichthyologist models fish biomass in a reef zone. Initial biomass i...
Annual net growth factor: (1 + 0.10) × (1 – 0.08) = 1.10 × 0.92 = 1.01...
So, biomass grows by 1.012 each year.
After 4 years: 45 × (1.012)^4.
Stepwise:
Year 1: 45 × 1.012 = <<45*1.012=45.54>>45.54
Year 2: 45.54 × 1.012 ≈ <<45.54*1.012=46.08888>>46.089
Year 3: 46.089 × 1.012 ≈ <<46.089*1.012=46.653228>>46.653
Year 4: 46.653 × 1.012 ≈ <<46.653*1.012=47.229516>>47.230

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