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Home » = k \cdot 8 \Rightarrow k = 1 - 500apps

= k \cdot 8 \Rightarrow k = 1 - 500apps

📅 March 13, 2026 👤 scraface

Mar 13, 2026

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📌 Solving for \( r_2 \), we get \( r_2 = 7 - 3 = 4 \).

📌 The difference between the squares of two consecutive integers is 31. Find the smaller integer.

📌 The difference is \( (n+1)^2 - n^2 = 31 \).

📌 Expanding, we get \( n^2 + 2n + 1 - n^2 = 31 \).

📌 Simplifying, \( 2n + 1 = 31 \).

📌 Solving for \( n \), \( 2n = 30 \) so \( n = 15 \).

📌 A circle has a circumference of \( 31.4 \) cm. Calculate the radius of the circle. Use \( \pi pprox 3.14 \).

📌 Given \( C = 31.4 \), we have \( 2 imes 3.14 imes r = 31.4 \).

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a₁ = 1.2 → a(1)² + b(1) + c = a + b + c = 1.2
a₂ = 1.8 → 4a + 2b + c = 1.8
a₃ = 2.5 → 9a + 3b + c = 2.5
Subtract first from second: (4a + 2b + c) − (a + b + c) = 1.8 − 1.2 →...
Subtract second from third: (9a + 3b + c) − (4a + 2b + c) = 2.5 − 1.8...
Now subtract: (5a + b) − (3a + b) = 0.7 − 0.6 → 2a = 0.1 → a = 0.05
Then 3(0.05) + b = 0.6 → 0.15 + b = 0.6 → b = 0.45
Then a + b + c = 1.2 → 0.05 + 0.45 + c = 1.2 → c = 0.7
So aₙ = 0.05n² + 0.45n + 0.7
a₄ = 0.05(16) + 0.45(4) + 0.7 = 0.8 + 1.8 + 0.7 = <<0.8+1.8+0.7=3.3>>3...

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