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Home » The rationalized form is $ \boxed{\sqrt15 + \sqrt10} $. - NBX Soluciones

The rationalized form is $ \boxed{\sqrt15 + \sqrt10} $. - NBX Soluciones

📅 May 2, 2026 👤 scraface

May 02, 2026

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📌 Check: LHS = |4/3 - 5| = |-11/3| = 11/3, RHS = |2/3 + 3| = |11/3| = 11/3 → valid.

📌 Sum = \( 8 + \frac{2}{3} = \frac{24}{3} + \frac{2}{3} = \frac{26}{3} \)

📌 A circle with center at (2, -3) passes through the point (5, 1). What is the length of the radius?

📌 Use distance formula:

📌 Radius = \( \sqrt{(5 - 2)^2 + (1 - (-3))^2} = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \)

📌 If \( \sin \theta = \frac{3}{5} \) and \( \theta \) is in the second quadrant, what is \( \cos(2\theta) \)?

📌 Use identity: \( \cos(2\theta) = 1 - 2\sin^2\theta = 1 - 2\left(\frac{3}{5}\right)^2 = 1 - 2\cdot\frac{9}{25}

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