Nhiệt độ ngoài trời ở một thành phố vào các thời điểm khác nhau trong ngày có thể được mô phỏng bởi công thức \(h(t)=29+3 \sin \frac{\pi}{12}(t-9)\) với \(h\) tính bằng \({ }^{\circ} C\) và \(t\) là thời gian trong ngày tính bằng giờ. Thời gian nhiệt độ cao nhất trong ngày là:
Hãy suy nghĩ và trả lời câu hỏi trước khi xem đáp án
Phương pháp giải
Sử dụng tập giá trị của hàm số sin để tìm nhiệt độ cao nhất trong ngày,
Sau đó giải điều kiện để tìm thời gian nhiệt độ cao nhất.
Lời giải
Do \(-1 \leq \sin \frac{\pi}{12}(t-9) \leq 1, \forall t\) nên
\(-3 \leq 3 \sin \frac{\pi}{12}(t-9) \leq 3\)
\(\Leftrightarrow 26 \leq 29+3 \sin \frac{\pi}{12}(t-9) \leq 32\).
\(\Leftrightarrow 26 \leq h(t) \leq 32\).
Do đó nhiệt độ cao nhất trong ngày là \(32^{\circ} \mathrm{C}\).
Dấu bằng xảy ra
\(\Leftrightarrow \sin \frac{\pi}{12}(t-9)=1 \Leftrightarrow \frac{\pi}{12}(t-9)=\frac{\pi}{2}+k 2 \pi \Leftrightarrow t=15+24 k(k \in \mathbb{Z})\)
Do \(0 \leq t \leq 24 \Leftrightarrow 0 \leq 15+24 k \leq 24 \Leftrightarrow-\frac{15}{24} \leq k \leq \frac{9}{24}\). Mà \(k \in \mathbb{Z}\) nên \(k=0\).
Khi đó \(t=15\).
Vậy lúc 15 h là thời gian nhiệt độ cao nhất trong ngày.
Đề Thi Tham Khảo Đánh Giá Năng Lực Năm 2025 – ĐHQG Hà Nội – Đề Số 1 là tài liệu ôn tập quan trọng giúp học sinh làm quen với cấu trúc và dạng câu hỏi của kỳ thi ĐGNL do Đại học Quốc gia Hà Nội tổ chức. Đề thi bao gồm các câu hỏi đa dạng, đánh giá toàn diện năng lực tư duy, kiến thức tổng hợp và khả năng giải quyết vấn đề. Tài liệu này giúp thí sinh rèn luyện kỹ năng làm bài, nâng cao hiệu suất làm bài thi và chuẩn bị tốt nhất cho kỳ thi chính thức năm 2025.
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https://tvsthpt.dlib.vn/app/doc-sach-ebook/d00ddd794efd
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