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Home » The area is \(x(x + 50) = 6000\). - Veritas Home Health

The area is \(x(x + 50) = 6000\). - Veritas Home Health

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 To rationalize the denominator of \( h(x) = \frac{3x + 5}{\sqrt{2x + 1}} \), we multiply both the numerator and the denominator by \( \sqrt{2x + 1} \) to eliminate the square root in the denominator:

📌 h(x) = \frac{3x + 5}{\sqrt{2x + 1}} \cdot \frac{\sqrt{2x + 1}}{\sqrt{2x + 1}} = \frac{(3x + 5) \sqrt{2x + 1}}{2x + 1}

📌 The rationalized form is:

📌 \boxed{\frac{(3x + 5) \sqrt{2x + 1}}{2x + 1}}

📌 Consider the sequence defined by the recursive formula \( a_n = 2a_{n-1} - 3 \) with the initial term \( a_1 = 4 \). Find the explicit formula for the \( n \)-th term of the sequence.

📌 To find the explicit formula, we first solve the homogeneous part of the recurrence relation \( a_n = 2a_{n-1} \), which gives \( a_n = C \cdot 2^n \) for some constant \( C \). Next, we find a particular solution for the non-homogeneous recurrence. Trying a constant solution \( a_n = A \):

📌 A = 2A - 3 \im

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