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Home » Thus, solutions are $30^\circ, 90^\circ, 150^\circ$. - Blask

Thus, solutions are $30^\circ, 90^\circ, 150^\circ$. - Blask

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 \[ \cos^2(\theta) = 1 - \frac{9}{25} = \frac{16}{25} \]

📌 \[ \cos(\theta) = \frac{4}{5} \]

📌 A company's revenue follows the model \(R(t) = 5000e^{0.03t}\), where \(t\) is in years. Calculate the revenue after 5 years.

📌 Substitute \(t = 5\):

📌 \[ R(5) = 5000e^{0.03 \times 5} = 5000e^{0.15} \approx 5000 \times 1.161834 = 5809.17 \]

📌 #### 5809.17Question: A paleobotanist is analyzing a fossilized leaf imprint and models its boundary as an ellipse centered at the origin. If the major axis is $ 10 $ units long and lies along the $ x $-axis, and the minor axis is $ 6 $ units long, find the distance from the center to a focus of the ellipse.

📌 Solution: The standard form of the ellipse centered at the origin is $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$, where $a > b$. Given the major axis is $10$, we have $2a = 10 \Rightarrow a = 5$. The minor axis is $6$, so $2b = 6 \Rightarrow b = 3$. The distance from the center to a focus is given by $c = \sqrt{a^2 - b^2}$. Substituting $a = 5$ and $b = 3$, we get $c = \sqrt{25 - 9} = \sqrt{16} = 4$.

📌 Question: A pharmacologist is modeling the concentration of a drug in the bloodstream over time with the function $ C(t) = \frac{3t}{t^2 + 4} $. Find the time $ t \geq 0 $ at which the concentration is maximized.

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