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Home » Together, they fill \( \frac14 + \frac16 \) of the tank per hour. - High Altitude Science

Together, they fill \( \frac14 + \frac16 \) of the tank per hour. - High Altitude Science

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 Let $x = \sin z$. Then:

📌 2x^2 - 3x + 1 = 0

📌 Solve the quadratic:

📌 x = \frac{3 \pm \sqrt{9 - 8}}{4} = \frac{3 \pm 1}{4} \Rightarrow x = 1, \frac{1}{2}

📌 Now solve for $z$:

📌 $\sin z = 1 \Rightarrow z = 90^\circ$

📌 $\sin z = \frac{1}{2} \Rightarrow z = 30^\circ, 150^\circ$

📌 Thus, the solutions are:

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