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Home » The area is the magnitude of the cross product $\mathbfr \times \mathbfs$: - Aurero

The area is the magnitude of the cross product $\mathbfr \times \mathbfs$: - Aurero

📅 March 16, 2026 👤 scraface

Mar 16, 2026

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Let \( w \) be the width of the garden. Then the length \( l \) is giv...
\( l = 2w + 3 \)
\( 2l + 2w = 54 \)
Substitute \( l \) into the perimeter equation:
\( 2(2w + 3) + 2w = 54 \)
\( 4w + 6 + 2w = 54 \)
Now, find \( l \):
\( l = 2(8) + 3 = 16 + 3 = 19 \)
The dimensions of the garden are 8 meters by 19 meters.
#### 8 meters width, 19 meters length

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\( D^3 \equiv 1 \pmod{9} \), and
\( D \not\equiv 1 \pmod{9} \)
0^3 &= 0 \\
1^3 &= 1 \\
2^3 = 8 \\
3^3 = 27 \equiv 0 \\
4^3 = 64 \equiv 1 \pmod{9} \quad (64 - 63 = 1) \\
5^3 = 125 \equiv 125 - 13\times9 = 125 - 117 = 8 \\
6^3 = 216 \equiv 0 \\
7^3 = 343 \equiv 343 - 38\times9 = 343 - 342 = 1 \\

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