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Home » Substitute back to find \(y\): \(y = 4(1.5) - 5 = 1\). - Abu Waleed Tea

Substitute back to find \(y\): \(y = 4(1.5) - 5 = 1\). - Abu Waleed Tea

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 g(3) = 3^2 - 4(3) + 9k = 9 - 12 + 9k = -3 + 9k

📌 Set them equal since \( f(3) = g(3) \):

📌 + k = -3 + 9k

📌 Subtract \(-3\) from both sides:

📌 Subtract \( k \) from both sides:

📌 = 8k \quad \Rightarrow \quad k = 0

📌 A science fiction writer models the growth of a resource-dependent colony on Mars using the equation \( a + b = 12 \) and \( a^2 + b^2 = 80 \). Find \( a^3 + b^3 \).

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But that's identity. So instead, suppose the intended equation is:
\cos(\theta + 60^\circ) + \cos(\theta - 60^\circ) = \sqrt{3}
\Rightarrow \cos\theta = \sqrt{3} \quad \text{(impossible)}
Thus, no solution. But to fix, suppose the equation is:
2\cos\theta = \sqrt{3} \Rightarrow \cos\theta = \frac{\sqrt{3}}{2}
\Rightarrow \theta = 30^\circ \text{ or } 330^\circ
Smallest positive is $30^\circ$. But not matching. Re-express the iden...
\cos(\theta + 60^\circ) + \cos(\theta - 60^\circ) = 2\cos\theta\cos 60...
So equation is $\cos\theta = \sqrt{3}$ — impossible. Therefore, the on...
\Rightarrow \cos\theta = 1 \Rightarrow \theta = 0^\circ

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