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Home » To determine the type of conic, compute the discriminant: - Portal da AcÃºstica

To determine the type of conic, compute the discriminant: - Portal da AcÃºstica

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 \(55 \div 11 = 5\), so \(55 \equiv 0 \pmod{11}\).

📌 Then \(55^2 \equiv 0^2 = 0 \pmod{11}\).

📌 Thus, \(3025 \equiv 0 \pmod{11}\).

📌 Alternatively, since \(55 \equiv 0 \mod 11\), the square is divisible by \(11^2\), hence by 11.

📌 Therefore, the remainder is \(\boxed{0}\).

📌 An emerging technology researcher exploring base systems in quantum computing asks: What is the base-ten number represented by the base-nine number \(321_9\)?

📌 To convert \(321_9\) to base ten, expand using powers of 9:

📌 321_9 = 3 \times 9^2 + 2 \times 9^1 + 1 \times 9^0

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Let $ A = x^2 + 4 $, $ B = y^2 + 2 $, and $ C = y^2 - 2 $, then:
A^2 - 16BC = (A - 4\sqrt{BC})(A + 4\sqrt{BC})
But this factoring is not ideal over real numbers. Instead, observe th...
So the full expression becomes:
Now factor the remaining terms:
Letâs try factoring by grouping. Try factoring $ x^4 + 8x^2 + 16 $ a...
x^4 + 8x^2 + 16 = (x^2 + 4)^2
-16y^4 + 64 = -16(y^4 - 4) = -16(y^2 - 2)(y^2 + 2)
Letâs now expand and factor directly:
x^4 + 8x^2 + 16 - 16y^4 + 64 = x^4 + 8x^2 + 80 - 16y^4

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