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Home » Tired of Same-Old Coloring? Grab the Spookiest Halloween Page Now! - Appcentric

Tired of Same-Old Coloring? Grab the Spookiest Halloween Page Now! - Appcentric

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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The solutions for \(\theta\) in the interval \([0^\circ, 360^\circ]\)...
\theta = 30^\circ \quad \text{and} \quad \theta = 150^\circ.
Next, consider the case where \(\cos(\theta) = 0\). This occurs at:
\theta = 90^\circ \quad \text{and} \quad \theta = 270^\circ.
Checking these values in the original equation, we find \(\sin(180^\ci...
Thus, the complete set of solutions is:
\(\theta = 30^\circ, 90^\circ, 150^\circ, 270^\circ\).
\boxed{30^\circ, 90^\circ, 150^\circ, 270^\circ}
Find the vector \(\mathbf{v}\) such that \(\mathbf{v} \times \mathbf{b...
The vector cross product \(\mathbf{v} \times \mathbf{b} = \langle v_1,...

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Final answer: $ \boxed{30 - 12\sqrt{6}} $
Question: Rationalize the denominator of $ \frac{5}{\sqrt{7} + \sqrt{2...
Multiply numerator and denominator by the conjugate $ \sqrt{7} - \sqrt...
\frac{5}{\sqrt{7} + \sqrt{2}} \cdot \frac{\sqrt{7} - \sqrt{2}}{\sqrt{7...
Simplify the denominator using the difference of squares:
\frac{5(\sqrt{7} - \sqrt{2})}{5} = \sqrt{7} - \sqrt{2}
Final answer: $ \boxed{\sqrt{7} - \sqrt{2}} $
Question: Expand the product $ (x^2 + 2x + 3)(x^2 - 2x + 3) $.
Use distributive property (FOIL-like expansion):
x^2(x^2 - 2x + 3) = x^4 - 2x^3 + 3x^2 \\

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