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Home » Substitute \( p = 1 \), \( q = 1 \), \( r = 1 \) into equation (1): - Dachbleche24

Substitute \( p = 1 \), \( q = 1 \), \( r = 1 \) into equation (1): - Dachbleche24

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 A computational biologist is working on a model where the relationship between variables is given by the equation $4x - 7 = 9$. Find the value of $x$ that satisfies this equation.

📌 4x - 7 = 9

📌 Divide both sides by 4:

📌 Thus, the value of $x$ that satisfies the equation is:

📌 \]Question: An anthropologist discovers ancient carvings depicting a regular hexagon with an area of \( 54\sqrt{3} \) square units. If each side is reduced by 2 units, by how many square units does the area decrease?

📌 Solution: The area \( A \) of a regular hexagon with side length \( s \) is \( A = \frac{3\sqrt{3}}{2}s^2 \). Given \( 54\sqrt{3} = \frac{3\sqrt{3}}{2}s^2 \), solving for \( s^2 \) yields \( s^2 = 36 \), so \( s = 6 \). The new side length is \( 6 - 2 = 4 \). The new area is \( \frac{3\sqrt{3}}{2}(4)^2 = 24\sqrt{3} \). The decrease in area is \( 54\sqrt{3} - 24\sqrt{3} = 30\sqrt{3} \). \boxed{30\sqrt{3}}

📌 Question: A renewable energy engineer designs a tidal turbine foundation shaped as a circular sector with radius 12 meters and central angle \( 90^\circ \). If the radius is increased by 4 meters, by how many square meters does the area increase?

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