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Home » Two vectors are orthogonal if their dot product is zero: - Dyverse

Two vectors are orthogonal if their dot product is zero: - Dyverse

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 Thus, the value of $ k $ is $\boxed{9}$.

📌 Question: A zoologist models the population growth of a rare species in the Amazon with the function $ P(t) = t^2 + bt + 12 $, where $ t $ is time in years. If the population stabilizes (i.e., reaches zero growth) at $ t = -6 $, what is the value of $ b $?

📌 Solution: Since the population stabilizes at $ t = -6 $, this means $ P(-6) = 0 $. Substituting into the equation:

📌 P(-6) = (-6)^2 + b(-6) + 12 = 0

📌 - 6b + 12 = 0

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