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\frac2701140 = \frac938 - Silent Sales Machine

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 Question: A robot arm moves in 3D space and its position at time $ t $ is given by $ \vec{r}(t) = \langle t^2, \sin(t), e^t \rangle $. What is the velocity vector at time $ t $?

📌 A. $ \vec{v}(t) = \langle 2t, \cos(t), e^t \rangle $

📌 B. $ \vec{v}(t) = \langle 2t, -\cos(t), e^t \rangle $

📌 C. $ \vec{v}(t) = \langle t, \cos(t), e^t \rangle $

📌 D. $ \vec{v}(t) = \langle 2t, \cos(t), 0 \rangle $

📌 Correct: A $ \vec{v}(t) = \langle 2t, \cos(t), e^t \rangle $

📌 Question: Let $ f(x, y) = x^2 + xy + y^3 $. What is the partial derivative $ \frac{\partial f}{\partial y} $?

📌 A. $ x + 3y^2 $

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