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Home » Shorter leg ≈ 7.18 cm (rounded to two decimals). - Parker Core Knowledge

Shorter leg ≈ 7.18 cm (rounded to two decimals). - Parker Core Knowledge

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 A solution contains 40% alcohol. How much of a 70% alcohol solution must be added to 100 mL of the 40% solution to obtain a 50% alcohol solution?

📌 Let \(x\) be the amount of 70% solution added.

📌 Equation: \(0.4 \times 100 + 0.7 \times x = 0.5 \times (100 + x)\).

📌 Simplify: \(40 + 0.7x = 50 + 0.5x\).

📌 Rearrange: \(0.2x = 10\).

📌 Solve: \(x = 50\) mL.

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So the expression becomes:
\frac{b^2(x^2 + 1)}{b^2(x^2 - 1)} + \frac{b^2(x^2 - 1)}{b^2(x^2 + 1)}...
Let $ y = \frac{x^2 + 1}{x^2 - 1} $, then the expression becomes:
y + \frac{1}{y}
We compute $ y + \frac{1}{y} $. First, recall that $ x + \frac{1}{x} =...
x^2 + 2 + \frac{1}{x^2} = 25 \Rightarrow x^2 + \frac{1}{x^2} = 23
Now compute $ x^2 + 1 $ and $ x^2 - 1 $:
Let $ A = x^2 + 1 $, $ B = x^2 - 1 $. Then:
\frac{A}{B} + \frac{B}{A} = \frac{(x^2 + 1)^2 + (x^2 - 1)^2}{(x^2 - 1)...
Compute numerator:

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