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Home » You’ll Learn Free Pattern Making in Minutes—Watch This Breathtaking Hack! - Groen Casting

You’ll Learn Free Pattern Making in Minutes—Watch This Breathtaking Hack! - Groen Casting

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 \frac{1}{4} s^2 = 36 \quad \Rightarrow \quad s^2 = 144 \quad \Rightarrow \quad s = 12 \text{ cm}

📌 The new side length is:

📌 s' = 12 + 2 = 14 \text{ cm}

📌 A' = \frac{\sqrt{3}}{4} (14)^2 = \frac{\sqrt{3}}{4} \cdot 196 = 49\sqrt{3} \text{ cm}^2

📌 \Delta A = A' - A = 49\sqrt{3} - 36\sqrt{3} = 13\sqrt{3} \text{ cm}^2

📌 Thus, the area increases by \(\boxed{13\sqrt{3}}\) square centimeters.Question: Find the area enclosed by the graph of $ |x| + |y| = 4 $.

📌 Solution: The equation $ |x| + |y| = 4 $ describes a diamond (or rhombus) centered at the origin. To find the vertices, consider the four cases for absolute values:

📌 $ x \geq 0, y \geq 0 $: $ x + y = 4 $, intercepts at $ (4, 0) $, $ (0, 4) $

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2a = 6 \Rightarrow a = 3, \quad a + b = 4 \Rightarrow 3 + b = 4 \Right...
Thus, the leading coefficient of $ f(x) $ is $ \boxed{3} $.
Question: A function $ f: \mathbb{R} \to \mathbb{R} $ satisfies $ f(a...
Solution: Let’s plug in $ a = b = 1 $ into the functional equation:
f(2) + f(0) = 2f(1) + 2f(1) = 4
We are given $ f(1) = 1 $, so:
f(2) + f(0) = 4 \quad \text{(1)}
Now plug in $ a = 0, b = 1 $:
f(1) + f(-1) = 2f(0) + 2f(1) \Rightarrow 1 + f(-1) = 2f(0) + 2 \Righta...
Now plug in $ a = 1, b = 0 $:

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