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Home » To find $\cos \theta$, we use the formula for the dot product: - American Beagle Club

To find $\cos \theta$, we use the formula for the dot product: - American Beagle Club

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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egin{cases}
k \equiv 3 \pmod{5} \
k \equiv 4 \pmod{7} \
k \equiv 2 \pmod{9}
We apply the Chinese Remainder Theorem step by step.
First, solve the first two congruences:
Let \( k = 5a + 3 $. Substitute into the second:
5a + 3 \equiv 4 \pmod{7} \implies 5a \equiv 1 \pmod{7}
Multiply both sides by the modular inverse of 5 modulo 7. Since \( 5 \...
a \equiv 3 \cdot 1 = 3 \pmod{7} \implies a = 7b + 3

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