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Home » \[ A = 2(lw + lh + wh) \] - Coaching Toolbox

\[ A = 2(lw + lh + wh) \] - Coaching Toolbox

📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 So the inequality becomes:

📌 rac{-3x + 11}{x - 2} < 0.

📌 We analyze the sign of this rational expression by identifying the critical points where the numerator or denominator is zero:

📌 Numerator zero: $ -3x + 11 = 0 \Rightarrow x = rac{11}{3} $.

📌 Denominator zero: $ x - 2 = 0 \Rightarrow x = 2 $.

📌 These divide the real line into intervals:

📌 We test the sign of $ rac{-3x + 11}{x - 2} $ in each interval:

📌 For $ x < 2 $, say $ x = 0 $: numerator $ -3(0) + 11 = 11 > 0 $, denominator $ 0 - 2 = -2 < 0 $ â negative.

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From \( f(2) = 10 \):
8a + 4b + 2c + d = 10 \quad \text{(3)}
From \( f(3) = 19 \):
27a + 9b + 3c + d = 19 \quad \text{(4)}
Substitute \( d = 1 \) into (1), (3), and (4):
Now solve the system:
From (1): \( -a + b - c = 3 \)
From (3): \( 8a + 4b + 2c = 9 \) → divide by 2: \( 4a + 2b + c = 4.5 \...
From (4): \( 27a + 9b + 3c = 18 \) → divide by 3: \( 9a + 3b + c = 6 \...
Now add (1) and \( 4a + 2b + c = 4.5 \):

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