mirror of
https://github.com/zenlm/zen-blog.git
synced 2026-11-03 14:11:45 +00:00
zeekay
a30ff37468
b3b6eb0 ran a find-and-replace over the posts forked from the QwenLM
blog that turned "Qwen2" and "Qwen2.5" into "zen": Qwen2-57B-A14B read
as zen7B-A14B, Qwen2-72B as zen-72B, Qwen2AudioForConditionalGeneration
as a class that does not exist, and links such as
github.com/QwenLM/Qwen2 and the qianwen-res image paths pointed at
nothing. Every token is put back from the original post, aligned
against the rewritten one: 536 lines across 29 posts, and 116 of the
example files under public/cases.
These 44 posts are about another lab's releases and now say so with
"upstream: true" in their frontmatter. Two Zen posts lose the
base-model names they carried, and the Zen 3 post stops calling itself
the next generation.
13 lines
2.0 KiB
JSON
13 lines
2.0 KiB
JSON
{
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"title": "Mathematical Reasoning",
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"messages": [
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{
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"role": "User",
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"content": "As shown in the figure, the straight lines AB and CD intersect at point O, OD bisects ∠AOE, ∠BOC = 50.0, then ∠EOB = ()\n"
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},
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{
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"role": "Qwen2.5-VL-32B",
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"content": "### Problem Analysis\nWe are given the following information:\n1. Straight lines $ AB $ and $ CD $ intersect at point $ O $.\n2. $ OD $ bisects $ \\angle AOE $.\n3. $ \\angle BOC = 50^\\\\circ $.\n4. We need to find $ \\angle EOB $.\n\n### Step-by-Step Solution\n\n#### Step 1: Understand the given information and relationships\n- Since $ AB $ and $ CD $ are straight lines intersecting at $ O $, the angles around point $ O $ sum up to $ 360^\\\\circ $.\n- The vertically opposite angles are equal. Therefore:\n $$\n \\angle AOD = \\angle BOC \\\\quad \\text{and} \\\\quad \\angle DOB = \\angle COA.\n $$\n Given $ \\angle BOC = 50^\\\\circ $, we have:\n $$\n \\angle AOD = 50^\\\\circ.\n $$\n\n#### Step 2: Use the angle bisector property\n- It is given that $ OD $ bisects $ \\angle AOE $. This means:\n $$\n \\angle AOD = \\angle DOE.\n $$\n Since $ \\angle AOD = 50^\\\\circ $, we have:\n $$\n \\angle DOE = 50^\\\\circ.\n $$\n\n#### Step 3: Determine $ \\angle AOE $\n- The angle $ \\angle AOE $ is the sum of $ \\angle AOD $ and $ \\angle DOE $:\n $$\n \\angle AOE = \\angle AOD + \\angle DOE = 50^\\\\circ + 50^\\\\circ = 100^\\\\circ.\n $$\n\n#### Step 4: Use the straight line property\n- Since $ AB $ is a straight line, the angles on a straight line sum up to $ 180^\\\\circ $. Therefore:\n $$\n \\angle AOE + \\angle EOB = 180^\\\\circ.\n $$\n Substituting $ \\angle AOE = 100^\\\\circ $, we get:\n $$\n 100^\\\\circ + \\angle EOB = 180^\\\\circ.\n $$\n Solving for $ \\angle EOB $:\n $$\n \\angle EOB = 180^\\\\circ - 100^\\\\circ = 80^\\\\circ.\n $$\n\n### Final Answer\n$$\n\\boxed{80}\n$$\n"
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}
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]
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} |