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Home » $24 = 2^3 imes 3$, - 500apps

$24 = 2^3 imes 3$, - 500apps

📅 March 13, 2026 👤 scraface

Mar 13, 2026

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📌 b_3 = \frac{768 - 81}{1024} = \frac{687}{1024}

📌 \boxed{\frac{687}{1024}}.

📌 \]Question: An environmental educator in Toronto is planning a circular garden with a diameter of 10 meters for a school project. A straight walking path of 6 meters is to be laid across the garden, not passing through the center. What is the shortest distance from the center of the garden to this path?

📌 Let the circular garden have center $ O $ and radius $ r = 5 $ meters (since the diameter is 10 meters). The walking path is a chord $ AB $ of length 6 meters. We are to find the perpendicular distance from the center $ O $ to this chord.

📌 Let $ M $ be the midpoint of the chord $ AB $. Then triangle $ OMA $ is a right triangle, with hypotenuse $ OA = 5 $ meters and leg $ AM = \frac{6}{2} = 3 $ meters. Let $ d $ be the distance from the center to the chord, which is $ OM $.

📌 OM^2 + AM^2 = OA^2

📌 d^2 + 3^2 = 5^2

📌 d^2 + 9 = 25

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2x = 9
x = rac{9}{2}
Since \( x = rac{9}{2}
e -5 \), the solution is valid.
oxed{rac{9}{2}}
A mechanical engineer in California develops energy-efficient heating...
The function \( H(t) = 4t^2 - 12t + 9 \) is a quadratic in standard fo...
t = -rac{b}{2a} = -rac{-12}{2 \cdot 4} = rac{12}{8} = rac{3}{2}
Substitute \( t = rac{3}{2} \) into \( H(t) \):
H\left(rac{3}{2}

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