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Home » And $2\sin x \cos x$ remains. - Londonproperty

And $2\sin x \cos x$ remains. - Londonproperty

📅 March 13, 2026 👤 scraface

Mar 13, 2026

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📌 Other terms match. Thus, $ h(x) = rac{1}{2}x^2 + bx $. Verify that $ h(x + y) = rac{1}{2}(x + y)^2 + b(x + y) = rac{1}{2}x^2 + xy + rac{1}{2}y^2 + bx + by $, which equals $ h(x) + h(y) + xy $. The general solution is $ h(x) = rac{1}{2}x^2 + bx $, where $ b $ is a constant. The function is $ oxed{h(x) = rac{1}{2}x^2 + bx} $.1.

📌 A train travels from City A to City B at a constant speed of 80 km/h. After a 1-hour stop in City B, it returns to City A at a speed of 100 km/h. The round trip takes 9 hours. What is the distance between City A and City B?

📌 The time taken to travel from City A to City B is \( rac{d}{80} \) hours.

📌 The time taken to return from City B to City A is \( rac{d}{100} \) hours.

📌 The total travel time is \( rac{d}{80} + rac{d}{100} + 1 = 9 \).

📌 Combine the fractions:

📌 \( rac{5d + 4d}{400} + 1 = 9 \)

📌 \( rac{9d}{400} = 8 \)

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