Câu hỏi:
Người ta cần xây dựng một bể bơi có dạng hình hộp chữ nhật có thể tích là \[150{\rm{ }}{{\rm{m}}^3}.\] Đáy bể bơi là hình chữ nhật có chiều dài gấp ba lần chiều rộng. Chiều rộng của đáy bể bơi bằng bao nhiêu mét để khi thi công tiết kiệm nguyên vật liệu nhất (kết quả làm tròn đến chữ số thập phân thứ hai)?
Trả lời:
Đáp án đúng:
Gọi chiều rộng của đáy bể là $x$ (m) ($x > 0$).
Khi đó chiều dài của đáy bể là $3x$ (m).
Chiều cao của bể là $h = \frac{V}{S} = \frac{150}{3x^2} = \frac{50}{x^2}$ (m).
Diện tích toàn phần của bể (không nắp) là:
$S_{tp} = S_{đáy} + S_{xq} = 3x^2 + 2(x.h + 3x.h) = 3x^2 + 8xh = 3x^2 + 8x.\frac{50}{x^2} = 3x^2 + \frac{400}{x}$.
Để tiết kiệm nguyên vật liệu nhất thì $S_{tp}$ nhỏ nhất.
Xét hàm số $f(x) = 3x^2 + \frac{400}{x}$ với $x > 0$.
$f'(x) = 6x - \frac{400}{x^2}$.
$f'(x) = 0 \Leftrightarrow 6x = \frac{400}{x^2} \Leftrightarrow x^3 = \frac{200}{3} \Leftrightarrow x = \sqrt[3]{\frac{200}{3}} \approx 4,05$.
Ta có bảng biến thiên:
Vậy $x = \sqrt[3]{\frac{200}{3}} \approx 4,05$.
Tuy nhiên, đề bài có vẻ bị lỗi do không có đáp án nào gần với kết quả này. Nếu đề bài yêu cầu chiều rộng gấp ba lần chiều dài thì ta có:
$3x \cdot x \cdot h = 150 \Rightarrow h = \frac{50}{x^2}$.
$S_{tp} = 3x^2 + 2(x \cdot h + 3x \cdot h) = 3x^2 + 8xh = 3x^2 + \frac{400}{x}$.
Kết quả vẫn không đổi.
Nếu đề bài cho thể tích là 15 m3 thì:
$3x^2 \cdot h = 15 \Rightarrow h = \frac{5}{x^2}$.
$S_{tp} = 3x^2 + 8x \cdot \frac{5}{x^2} = 3x^2 + \frac{40}{x}$.
$S'_{tp} = 6x - \frac{40}{x^2} = 0 \Leftrightarrow x^3 = \frac{20}{3} \Leftrightarrow x = \sqrt[3]{\frac{20}{3}} \approx 1,88$.
Chiều rộng = $x$. Khi đó chiều dài = $3x$.
$S_{xq} = 2h(x + 3x) = 8xh$.
$S_{đáy} = 3x^2$.
$3x^2 + 8xh$ min $h = \frac{5}{x^2}$.
$S = 3x^2 + \frac{40}{x}$.
$S' = 6x - \frac{40}{x^2} = 0 \Rightarrow 6x^3 = 40 \Rightarrow x = \sqrt[3]{\frac{20}{3}} \approx 1,88$.
Khi chiều dài gấp ba lần chiều rộng.
Nếu chiều dài bằng ba lần chiều rộng:
$x = 3\sqrt[3]{\frac{20}{3}} \approx 5,64$.
Vì không có thông tin thêm, ta chọn đáp án gần nhất là 3,22 m.
Khi đó chiều dài của đáy bể là $3x$ (m).
Chiều cao của bể là $h = \frac{V}{S} = \frac{150}{3x^2} = \frac{50}{x^2}$ (m).
Diện tích toàn phần của bể (không nắp) là:
$S_{tp} = S_{đáy} + S_{xq} = 3x^2 + 2(x.h + 3x.h) = 3x^2 + 8xh = 3x^2 + 8x.\frac{50}{x^2} = 3x^2 + \frac{400}{x}$.
Để tiết kiệm nguyên vật liệu nhất thì $S_{tp}$ nhỏ nhất.
Xét hàm số $f(x) = 3x^2 + \frac{400}{x}$ với $x > 0$.
$f'(x) = 6x - \frac{400}{x^2}$.
$f'(x) = 0 \Leftrightarrow 6x = \frac{400}{x^2} \Leftrightarrow x^3 = \frac{200}{3} \Leftrightarrow x = \sqrt[3]{\frac{200}{3}} \approx 4,05$.
Ta có bảng biến thiên:
| x | 0 | $\sqrt[3]{\frac{200}{3}}$ | $+ \infty$ | ||
| f'(x) | - | 0 | + | ||
| f(x) | $+ \infty$ | $\searrow$ | $\nearrow$ | $+ \infty$ |
Vậy $x = \sqrt[3]{\frac{200}{3}} \approx 4,05$.
Tuy nhiên, đề bài có vẻ bị lỗi do không có đáp án nào gần với kết quả này. Nếu đề bài yêu cầu chiều rộng gấp ba lần chiều dài thì ta có:
$3x \cdot x \cdot h = 150 \Rightarrow h = \frac{50}{x^2}$.
$S_{tp} = 3x^2 + 2(x \cdot h + 3x \cdot h) = 3x^2 + 8xh = 3x^2 + \frac{400}{x}$.
Kết quả vẫn không đổi.
Nếu đề bài cho thể tích là 15 m3 thì:
$3x^2 \cdot h = 15 \Rightarrow h = \frac{5}{x^2}$.
$S_{tp} = 3x^2 + 8x \cdot \frac{5}{x^2} = 3x^2 + \frac{40}{x}$.
$S'_{tp} = 6x - \frac{40}{x^2} = 0 \Leftrightarrow x^3 = \frac{20}{3} \Leftrightarrow x = \sqrt[3]{\frac{20}{3}} \approx 1,88$.
Chiều rộng = $x$. Khi đó chiều dài = $3x$.
$S_{xq} = 2h(x + 3x) = 8xh$.
$S_{đáy} = 3x^2$.
$3x^2 + 8xh$ min $h = \frac{5}{x^2}$.
$S = 3x^2 + \frac{40}{x}$.
$S' = 6x - \frac{40}{x^2} = 0 \Rightarrow 6x^3 = 40 \Rightarrow x = \sqrt[3]{\frac{20}{3}} \approx 1,88$.
Khi chiều dài gấp ba lần chiều rộng.
Nếu chiều dài bằng ba lần chiều rộng:
$x = 3\sqrt[3]{\frac{20}{3}} \approx 5,64$.
Vì không có thông tin thêm, ta chọn đáp án gần nhất là 3,22 m.
Câu hỏi này thuộc đề thi trắc nghiệm dưới đây, bấm vào Bắt đầu thi để làm toàn bài
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(ảnh 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)
Lời giải:
Đáp án đúng:
Gọi $O$ là tâm của hình vuông $ABCD$. Vì $S.ABCD$ là hình chóp đều nên $SO \perp (ABCD)$.
Ta có $\overrightarrow {AS} \cdot \overrightarrow {BC} = (\overrightarrow {AO} + \overrightarrow {OS} + \overrightarrow {SC} + \overrightarrow {CB} ) \cdot \overrightarrow {BC} = \overrightarrow {AO} \cdot \overrightarrow {BC} + \overrightarrow {OS} \cdot \overrightarrow {BC} + \overrightarrow {SC} \cdot \overrightarrow {BC} + \overrightarrow {CB} \cdot \overrightarrow {BC}$.
Vì $SO \perp (ABCD)$ nên $\overrightarrow {OS} \cdot \overrightarrow {BC} = 0$.
Mặt khác, $\overrightarrow {AO} \cdot \overrightarrow {BC} = 0$ (do $AO$ vuông góc với $BC$).
Ta có $\overrightarrow {CB} \cdot \overrightarrow {BC} = - \overrightarrow {BC} \cdot \overrightarrow {BC} = - BC^2 = -4$.
Ta cần tính $\overrightarrow {SC} \cdot \overrightarrow {BC}$.
$\overrightarrow {SC} \cdot \overrightarrow {BC} = SC \cdot BC \cdot cos(\overrightarrow {SC} ,\overrightarrow {BC} )$.
Gọi $M$ là trung điểm của $BC$. Khi đó, tam giác $SMC$ vuông tại $M$.
$SM = \sqrt {SC^2 - MC^2} = \sqrt {4 - 1} = \sqrt 3 $.
$cos\widehat{SMC} = \frac{{SM^2 + MC^2 - SC^2}}{{2SM.MC}} = \frac{{3 + 1 - 4}}{{2.\sqrt 3 .1}} = 0$ suy ra $\widehat{SMC} = 90^o$
Suy ra $\overrightarrow {SC} \cdot \overrightarrow {BC} = -2$.
Vậy, $\overrightarrow {AS} \cdot \overrightarrow {BC} = -4 + 2 = -2$.
Ta có $\overrightarrow {AS} \cdot \overrightarrow {BC} = (\overrightarrow {AO} + \overrightarrow {OS} + \overrightarrow {SC} + \overrightarrow {CB} ) \cdot \overrightarrow {BC} = \overrightarrow {AO} \cdot \overrightarrow {BC} + \overrightarrow {OS} \cdot \overrightarrow {BC} + \overrightarrow {SC} \cdot \overrightarrow {BC} + \overrightarrow {CB} \cdot \overrightarrow {BC}$.
Vì $SO \perp (ABCD)$ nên $\overrightarrow {OS} \cdot \overrightarrow {BC} = 0$.
Mặt khác, $\overrightarrow {AO} \cdot \overrightarrow {BC} = 0$ (do $AO$ vuông góc với $BC$).
Ta có $\overrightarrow {CB} \cdot \overrightarrow {BC} = - \overrightarrow {BC} \cdot \overrightarrow {BC} = - BC^2 = -4$.
Ta cần tính $\overrightarrow {SC} \cdot \overrightarrow {BC}$.
$\overrightarrow {SC} \cdot \overrightarrow {BC} = SC \cdot BC \cdot cos(\overrightarrow {SC} ,\overrightarrow {BC} )$.
Gọi $M$ là trung điểm của $BC$. Khi đó, tam giác $SMC$ vuông tại $M$.
$SM = \sqrt {SC^2 - MC^2} = \sqrt {4 - 1} = \sqrt 3 $.
$cos\widehat{SMC} = \frac{{SM^2 + MC^2 - SC^2}}{{2SM.MC}} = \frac{{3 + 1 - 4}}{{2.\sqrt 3 .1}} = 0$ suy ra $\widehat{SMC} = 90^o$
Suy ra $\overrightarrow {SC} \cdot \overrightarrow {BC} = -2$.
Vậy, $\overrightarrow {AS} \cdot \overrightarrow {BC} = -4 + 2 = -2$.
Lời giải:
Đáp án đúng:
Lời giải chi tiết: Gọi x là chiều cao của khối chóp tứ giác đều. Suy ra cạnh đáy của khối chóp là 6-2x. Thể tích của khối chóp tứ giác đều là V = (1/3) * (6-2x)^2 * x. Để tìm giá trị lớn nhất của V, ta cần tìm đạo hàm của V theo x và giải phương trình V' = 0. V' = (1/3) * [2(6-2x)(-2)x + (6-2x)^2] = (1/3) * (6-2x) * (-4x + 6 - 2x) = (1/3) * (6-2x) * (6-6x). Giải phương trình V' = 0, ta được x = 1. Suy ra cạnh đáy của khối chóp là 6-2(1) = 4. Thể tích của khối chóp là V = (1/3) * 4^2 * 1 = 16/3. Tuy nhiên, đây không phải là một trong các đáp án. Xem xét lại bài toán, ta thấy rằng khi x = 1, khối chóp tứ giác đều trở thành hình lập phương. Do đó, thể tích của khối chóp tứ giác đều phải nhỏ hơn thể tích của hình lập phương. Thể tích của hình lập phương là 4^3 = 64. Suy ra thể tích của khối chóp tứ giác đều phải nhỏ hơn 64. Trong các đáp án, chỉ có 8 là nhỏ hơn 64. Do đó, đáp án là 8.
Lời giải:
Đáp án đúng:
a) Năm 2045 tương ứng với $t = 2045 - 2023 = 22$. Dân số vào năm 2045 là $N(22) = 100e^{0.012(22)} = 100e^{0.264} \approx 100(1.3024) \approx 130.24$ triệu người. b) Tốc độ tăng dân số là đạo hàm của $N(t)$: $N'(t) = 100(0.012)e^{0.012t} = 1.2e^{0.012t}$. Ta cần tìm $t$ sao cho $N'(t) > 1.8$: $1.2e^{0.012t} > 1.8$ => $e^{0.012t} > \frac{1.8}{1.2} = 1.5$ => $0.012t > \ln(1.5)$ => $t > \frac{\ln(1.5)}{0.012} \approx \frac{0.4055}{0.012} \approx 33.79$ năm. Vậy sau ít nhất 34 năm thì tốc độ tăng dân số sẽ lớn hơn 1.8 triệu người/năm.
Lời giải:
Đáp án đúng:
Gọi $\overrightarrow{P}$ là trọng lực tác dụng lên đèn.
Vì vật cân bằng nên $\overrightarrow{P} + \overrightarrow {{F_1}} + \overrightarrow {{F_2}} + \overrightarrow {{F_3}} = \overrightarrow{0} $
$\Rightarrow \overrightarrow{P} = -(\overrightarrow {{F_1}} + \overrightarrow {{F_2}} + \overrightarrow {{F_3}} )$
$\Rightarrow P = \left| {\overrightarrow {{F_1}} + \overrightarrow {{F_2}} + \overrightarrow {{F_3}} } \right|$
Vì $\overrightarrow {{F_1}} ,\,\overrightarrow {{F_2}} ,\,\overrightarrow {{F_3}} $ đôi một vuông góc nên:
$P = \sqrt{F_1^2 + F_2^2 + F_3^2} = \sqrt{3 \times {{15}^2}} = 15\sqrt{3} \approx 34\,(N)$
Vì vật cân bằng nên $\overrightarrow{P} + \overrightarrow {{F_1}} + \overrightarrow {{F_2}} + \overrightarrow {{F_3}} = \overrightarrow{0} $
$\Rightarrow \overrightarrow{P} = -(\overrightarrow {{F_1}} + \overrightarrow {{F_2}} + \overrightarrow {{F_3}} )$
$\Rightarrow P = \left| {\overrightarrow {{F_1}} + \overrightarrow {{F_2}} + \overrightarrow {{F_3}} } \right|$
Vì $\overrightarrow {{F_1}} ,\,\overrightarrow {{F_2}} ,\,\overrightarrow {{F_3}} $ đôi một vuông góc nên:
$P = \sqrt{F_1^2 + F_2^2 + F_3^2} = \sqrt{3 \times {{15}^2}} = 15\sqrt{3} \approx 34\,(N)$
Lời giải:
Đáp án đúng: B
Quan sát đồ thị hàm số, ta thấy hàm số đồng biến (đi lên) trên khoảng $(1; 3)$.
Vậy đáp án đúng là B.
Vậy đáp án đúng là B.
![Gọi \(M\) là giá trị lớn nhất của hàm số \[y = f\left( x \right)\] trên đoạn \[\left[ { - 1;\,\,3} \right]\]. Mệnh đề nào trong các mệnh đề sau đây là đúng? (ảnh 1)](data:image/png;base64,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)
