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Home » How Dig Digged Uncovered the Most Unexpected Treasure in Town - Leaselab

How Dig Digged Uncovered the Most Unexpected Treasure in Town - Leaselab

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 #### 30 and 20

📌 A rectangular garden is 20 meters long and 15 meters wide. A path 1 meter wide runs around the inside edge of the garden. What is the area of the path?

📌 Total garden area: 20 * 15 = 300 square meters.

📌 Inner dimensions after path: (20 - 2) * (15 - 2) = 18 * 13 = 234 square meters.

📌 Area of the path: 300 - 234 = 66 square meters.

📌 #### 661. A rectangle's length is 3 times its width, and its perimeter is 64 cm. What is the area of the rectangle?

📌 Perimeter formula for a rectangle: \( 2(\text{length} + \text{width}) = 64 \).

📌 Substitute the expressions: \( 2(3w + w) = 64 \).

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Thus, the points of intersection are \( x = 0 \) and \( x = 2 \).
The area \( A \) between the curves from \( x = 0 \) to \( x = 2 \) is...
A = \int_0^2 \left((4x - x^2) - x^2\right) \, dx = \int_0^2 (4x - 2x^2...
Evaluating the integral:
A = \left[ 2x^2 - \frac{2}{3}x^3 \right]_0^2 = \left( 2(2)^2 - \frac{2...
Calculating each term:
= \left( 8 - \frac{16}{3} \right) = \frac{24}{3} - \frac{16}{3} = \fra...
\boxed{\frac{8}{3}}.
Find the remainder when \( v^4 + 3v + 1 \) is divided by \( v^2 + 1 \)...
To find the remainder of \( v^4 + 3v + 1 \) when divided by \( v^2 + 1...

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