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Home » This Sopapilla Cheesecake Will Change the Way You Bake Forever! 🔥 - Groen Casting

This Sopapilla Cheesecake Will Change the Way You Bake Forever! 🔥 - Groen Casting

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Question: A science policy analyst evaluates energy savings from two initiatives. Initiative X saves $ 5\% $ of energy annually, while Initiative Y saves $ \sqrt{0.81} $ of energy. What is the simplified form of $ \sqrt{0.81} $?

📌 Solution: Simplify $ \sqrt{0.81} $:

📌 $$ \sqrt{0.81} = \sqrt{\frac{81}{100}} = \frac{\sqrt{81}}{\sqrt{100}} = \frac{9}{10} $$

📌 The simplified form is $ \boxed{\dfrac{9}{10}} $.

📌 Question: Solve for $ x $: $ \frac{2}{x - 1} + \frac{3}{x + 2} = 1 $.

📌 Solution: Find a common denominator $ (x - 1)(x + 2) $:

📌 $$ 2(x + 2) + 3(x - 1) = (x - 1)(x + 2) $$

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Multiply both sides by \( 144 = 16 \cdot 9 \):
\cdot \left( \frac{x^2}{16} + \frac{y^2}{9} \right) = 9x^2 + 16y^2 = 1...
So we solve \( 9x^2 + 16y^2 = 144 \) in integers with \( |x| \leq 4 \)...
We try all integer \( x \) from \( -4 \) to \( 4 \), compute \( 9x^2 \...
\( x = 0 \): \( y^2 = \frac{144}{16} = 9 \) → \( y = \pm 3 \) → valid
\( x = \pm 1 \): \( 9(1) = 9 \), \( 144 - 9 = 135 \), \( y^2 = 135/16...
\( x = \pm 2 \): \( 9(4) = 36 \), \( 144 - 36 = 108 \), \( y^2 = 108/1...
\( x = \pm 3 \): \( 9(9) = 81 \), \( 144 - 81 = 63 \), \( y^2 =
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