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programing codes for rca universal remote - Abbey Badges

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 The interval contains all whole numbers from 1 up to 7, because 7.854 is less than 8.

📌 Thus, the whole numbers in the interval are $ 1, 2, 3, 4, 5, 6, 7 $.

📌 There are $ 7 $ whole numbers.

📌 Question: An ornithologist observes a flock of birds migrating, where the number of birds doubles every day starting from 3 birds on day one. On what day does the total count first exceed 500 birds?

📌 Solution: The number of birds follows a geometric sequence: $ 3, 6, 12, 24, \dots $, with first term $ a = 3 $ and common ratio $ r = 2 $.

📌 The number of birds on day $ n $ is $ 3 \cdot 2^{n-1} $.

📌 \cdot 2^{n-1} > 500

📌 2^{n-1} > \frac{500}{3} \approx 166.67

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We aim to find $ f(x^2 - 2) $.
First, observe that the right-hand side can be expressed in terms of $...
x^4 + 4x^2 + 3 = (x^2)^2 + 4x^2 + 3.
Let $ u = x^2 + 2 $. Then $ x^2 = u - 2 $, and
Substituting into the expression:
x^4 + 4x^2 + 3 = (u^2 - 4u + 4) + 4(u - 2) + 3 = u^2 - 4u + 4 + 4u - 8...
f(u) = u^2 - 1.
Now substitute $ u = x^2 - 2 $ into $ f $:
f(x^2 - 2) = (x^2 - 2)^2 - 1 = x^4 - 4x^2 + 4 - 1 = x^4 - 4x^2 + 3.
\boxed{x^4 - 4x^2 + 3}

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