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Home » Shocking Tease: Steam Machine Two in the Studio—Release Date Just Dropped! - Upplift

Shocking Tease: Steam Machine Two in the Studio—Release Date Just Dropped! - Upplift

📅 February 28, 2026 👤 scraface

Feb 28, 2026

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📌 \begin{pmatrix} a & b \\ c & d \end{pmatrix} \begin{pmatrix} 1 \\ 2 \end{pmatrix} = \begin{pmatrix} a + 2b \\ c + 2d \end{pmatrix} = \begin{pmatrix} 3 \\ 4 \end{pmatrix}

📌 \Rightarrow a + 2b = 3, \quad c + 2d = 4

📌 Apply the second condition:

📌 \begin{pmatrix} a & b \\ c & d \end{pmatrix} \begin{pmatrix} 0 \\ 1 \end{pmQuestion: A space explorer makes 25 voyages through a wormhole, 60% of which are successful. After 10 more voyages, her success rate increases to 68%. How many additional successful voyages did she achieve?

📌 Solution: Initially, the explorer has $ 25 \times 0.60 = 15 $ successful voyages. After 10 more attempts, the total voyages are $ 25 + 10 = 35 $. With a 68% success rate, total successful voyages become $ 35 \times 0.68 = 23.8 $, which rounds to 24 (since successes are whole numbers). The additional successful voyages are $ 24 - 15 = 9 $.

📌 Question: An epidemiologist models the spread of a virus in a population with the equation $ p(t) = -t^2 + 14t + 30 $, where $ p(t) $ represents the number of infected individuals at time $ t $. What is the maximum number of infected individuals?

📌 Solution: The quadratic $ p(t) = -t^2 + 14t + 30 $ opens downward. The vertex occurs at $ t = -\frac{b}{2a} = -\frac{14}{2(-1)} = 7 $. Substituting $ t = 7 $, $ p(7) = -(7)^2 + 14(7) + 30 = -49 + 98 + 30 = 79 $.

📌 \boxed{79}

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