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📅 May 16, 2026 👤 scraface

May 16, 2026

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📌 Time for first part = 180 miles / 60 mph = 3 hours

📌 Time for second part = 120 miles / 80 mph = 1.5 hours

📌 Total distance = 180 + 120 = 300 miles

📌 Total time = 3 + 1.5 = 4.5 hours

📌 Average speed = Total distance / Total time = 300 / 4.5 = 66.67 mph

📌 #### 66.67 mph

📌 A circle has a circumference of 31.4 cm. What is its area? (Use \( \pi \approx 3.14 \))

📌 Solve for \( r \): \( 31.4 = 2 \times 3.14 \times r \) → \( r = 5 \) cm

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a(1)^2 + b(1) + c &= 6, \\
a(2)^2 + b(2) + c &= 11, \\
a(3)^2 + b(3) + c &= 18.
a + b + c &= 6, \\
4a + 2b + c &= 11, \\
9a + 3b + c &= 18.
Now, we solve the system:
3a + b &= 5, \\
5a + b &= 7.
Substitute \( a = 1 \) back into \( 3a + b = 5 \):

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ec{OA} \cdot ec{OB} = (-1 + \sqrt{7})(-1 - \sqrt{7}) + (1 + \sqrt{7})...
= [(-1)^2 - (\sqrt{7})^2] + [1 - (\sqrt{7})^2] = (1 - 7) + (1 - 7) = -...
Magnitudes:
|ec{OA}| = \sqrt{(-1 + \sqrt{7})^2 + (1 + \sqrt{7})^2} = \sqrt{(1 - 2...
|ec{OB}| = \sqrt{(-1 - \sqrt{7})^2 + (1 - \sqrt{7})^2} = \sqrt{(1 + 2...
\cos heta = rac{-12}{(2\sqrt{6})(2\sqrt{6})} = rac{-12}{24} = -rac...
The area of the circular sector is:
A_{ ext{sector}} = rac{1}{2} r^2 heta = rac{1}{2} \cdot 16 \cdot r...
Area of triangle \(OAB\):
A_{ ext{triangle}} = rac{1}{2} ab \sin heta = rac{1}{2} (2\sqrt{6})...

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