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Home » 2a + 3b = 11 \\ - Imagemakers

2a + 3b = 11 \\ - Imagemakers

📅 April 29, 2026 👤 scraface

Apr 29, 2026

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📌 A pyramid has a square base with side length 6 meters and a height of 9 meters. What is its volume?

📌 A piece of wire 60 cm long is bent to form a rectangle with a length twice its width. What are the dimensions of the rectangle?

📌 #### 10 cm by 20 cmQuestion: A GIS analyst is mapping urban heat zones and records temperature data at 7 different locations, each labeled either H for high heat or L for low heat. How many such 7-character sequences contain at least one instance of two consecutive Hs?

📌 Lets first compute the total number of 7-character sequences using only H and L. Since each position has 2 choices:

📌 This is a classic recurrence relation problem. Lets define:

📌 $ a_n $: number of valid sequences of length $ n $ with no two consecutive Hs.

📌 We can build such sequences recursively:

📌 $ a_2 = 3 $: sequences are LL, LH, HL (excluding HH)

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