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Home » 2A^2 + 6Ad + 9d^2 = 16A^2 + 48Ad + 36d^2 - AMAZONAWS

2A^2 + 6Ad + 9d^2 = 16A^2 + 48Ad + 36d^2 - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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📌 The second term is \( a - d = 10 - d \), and the fourth term is \( a + d = 10 + d \). Their product is:

📌 \[ (10 - d)(10 + d) = 100 - d^2 = 48. \]

📌 Solve for \( d^2 \):

📌 \[ 100 - d^2 = 48 \Rightarrow d^2 = 52. \]

📌 But we are asked for the third term, which is \( a = 10 \).

📌 \[\boxed{10}.\]1. A science educator is organizing a hands-on chemistry activity involving titration. She needs 0.5 liters of 0.2 M hydrochloric acid for each of 8 student groups. If she has a 2-liter stock solution of 1.0 M HCl, how many liters of water must she add to dilute the stock solution sufficiently for all groups?

📌 Each group requires 0.5 L × 0.2 mol/L = <<0.5*0.2=0.1>>0.1 moles of HCl.

📌 Total moles needed = 0.1 mol/group × 8 groups = <<0.1*8=0.8>>0.8 moles.

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