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Home » How Much Will Your Concrete Project Cost? Concrete Cost Per Yard Revealed—Start Here! - Upplift

How Much Will Your Concrete Project Cost? Concrete Cost Per Yard Revealed—Start Here! - Upplift

📅 February 28, 2026 👤 scraface

Feb 28, 2026

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📌 $$ 12a + 8b = 156 $$

📌 From the first equation, $ b = 15 - a $. Substitute into the second:

📌 $$ 12a + 8(15 - a) = 156 $$

📌 $$ 12a + 120 - 8a = 156 $$

📌 $$ 4a = 36 $$

📌 $$ a = 9 $$

📌 The lab purchased $ \boxed{9} $ units of reagent A.Question: Find all angles $ \theta \in [0^\circ, 360^\circ] $ that satisfy $ \sin(2\theta) = \frac{\sqrt{3}}{2} $.

📌 Solution: The equation $ \sin(2\theta) = \frac{\sqrt{3}}{2} $ implies $ 2\theta = 60^\circ + 360^\circ k $ or $ 2\theta = 120^\circ + 360^\circ k $ for integer $ k $. Solving for $ \theta $, we get $ \theta = 30^\circ + 180^\circ k $ or $ \theta = 60^\circ + 180^\circ k $. Within $ [0^\circ, 360^\circ] $, the solutions are $ 30^\circ, 60^\circ, 210^\circ, 240^\circ $. Thus, the answer is $ \boxed{30^\circ}, \boxed{60^\circ}, \boxed{210^\circ}, \boxed{240^\circ} $.

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