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Home » Two vectors are perpendicular if their dot product is zero. - Blask

Two vectors are perpendicular if their dot product is zero. - Blask

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 A robotics engineer is programming a robotic arm to pick and place components on an assembly line. The arm moves in discrete steps, each step covering 0.15 meters. If the arm must travel a total of 9 meters to complete one full cycle, how many steps are required, and if each step takes 0.4 seconds, how long in seconds does the entire movement take?

📌 First, determine the number of steps: \( \frac{9}{0.15} = 60 \) steps.

📌 Then, calculate the total time: \( 60 \times 0.4 = 24 \) seconds.

📌 2: A paleobotanist examines a fossilized leaf and estimates its surface area was originally 120 cm². Due to preservation, only 65% of the original structure remains intact. Additionally, micro-imaging reveals the visible area is 72 cm²—about what percentage of the remaining structure is actually preserved and visible?

📌 First, compute the expected preserved area: \( 120 \times 0.65 = 78 \) cm².

📌 Then, find the percentage of visible area relative to preserved area: \( \frac{72}{78} \times 100 \approx 92.31\% \).

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