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Home » We use trigonometric identities to simplify and analyze the expression. Recall: - AMAZONAWS

We use trigonometric identities to simplify and analyze the expression. Recall: - AMAZONAWS

📅 March 6, 2026 👤 scraface

Mar 06, 2026

We use trigonometric identities to simplify and analyze the expression. Recall:

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📌 A scientist measures the concentration of a solution at 0.5 M. She dilutes the solution by adding 200 mL of water to 300 mL of the original solution. What is the new concentration of the solution?

📌 Solution: Assume $ f $ is quadratic: $ f(x) = ax^2 + bx + c $. Substitute into equation: $ a(x + y)^2 + b(x + y) + c = ax^2 + bx + c + ay^2 + by + c + 2xy $. Expand left: $ ax^2 + 2axy + ay^2 + bx + by + c $. Right: $ ax^2 + ay^2 + bx + by + 2c + 2xy $. Equate coefficients: $ 2a = 2 \Rightarrow a = 1 $, and $ 2c = c \Rightarrow c = 0 $. Thus, $ f(x) = x^2 + bx $. Check: $ (x + y)^2 + b(x + y) = x^2 + y^2 + 2xy + bx + by $, which matches. Any $ b $ works, so infinitely many solutions. \boxed{\infty}<think1. A train travels at a constant speed of 90 miles per hour. If it travels for 2.5 hours, how far does the train travel?

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📌 For an equilateral triangle, the radius \( r \) of the inscribed circle is given by:

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