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Home » Interest earned is \(0.05 \times 1,000 = 50\) dollars. - High Altitude Science

Interest earned is \(0.05 \times 1,000 = 50\) dollars. - High Altitude Science

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 Solution: Let the four terms be $ a - \frac{3d}{2},\ a - \frac{d}{2},\ a + \frac{d}{2},\ a + \frac{3d}{2} $. This ensures the terms are in arithmetic progression with common difference $ d $. The first term is $ a - \frac{3d}{2} $, and the last term is $ a + \frac{3d}{2} $. Their sum of squares is:

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So \( u = 0 \), \( u = 2 \), or \( u = 3 \). Since \( v = u^2 \), the...
\( u = 0 \Rightarrow v = 0 \)
\( u = 2 \Rightarrow v = 4 \)
\( u = 3 \Rightarrow v = 9 \)
All roots are non-negative, so valid. The sum of the roots is \( 0 + 4...
Thus, the sum is \( \boxed{13} \).
Question: Let \( x, y, z \) be positive real numbers such that \( x +...
Solution: Apply the **Cauchy-Schwarz Inequality** in the Engel form (a...
\frac{x^2}{y} + \frac{y^2}{z} + \frac{z^2}{x} \geq \frac{(x + y + z)^2...
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Total time = 5 + 2.5 = 7.5 hours.
Average speed = \( \frac{500}{7.5} \approx 66.67 \) mph.
If \( \log_2(x) + \log_2(8) = 5 \), what is the value of \( x \)?
Use the property: \( \log_2(x) + \log_2(8) = \log_2(8x) \).
So, \( \log_2(8x) = 5 \).
Convert to exponential form: \( 8x = 2^5 \).
Calculate \( 2^5 = 32 \).
Solve for \( x \): \( 8x = 32 \) implies \( x = 4 \).
A mixture contains 20% alcohol and the rest water. If 10 liters of wat...
Original alcohol = \( 0.2 \times 30 = 6 \) liters.

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