1. ## Re: Vectors help

Express t from one equation and substitute in into the other.

2. ## Re: Vectors help

Originally Posted by emakarov
Express t from one equation and substitute in into the other.
I don't know if this is right but I ended up with b= -2a+7

3. ## Re: Vectors help

Yes. Also, you probably got that t = 9 / (4 - a). The latter graph looks like this. So, for a > 4 the time to meeting is negative, which means that the meeting must have been in the past and will not happen in the future (this is natural since if B moves right faster than A, they cannot meet). For a < 4, the function t(a) is increasing. Since we need to find the smallest t, we need to find the smallest allowed a.

Since the maximum speed of B is 8 km/h, the vector (a, b), when its beginning is at (0, 0), lies inside a circle of radius 8. Also, b= -2a+7. The circle carves a segment on the line b = -2a+7, and we need to take the left end of that segment, which corresponds to the smallest a.

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The text passage is a discussion thread about a vectors problem, where a user is seeking help and another user is providing guidance and feedback.
no_question

the passage does not contain a direct mathematical question that requires solving. instead, it is a conversation where a user is guided through a problem-solving process, and the final answer is discussed in a conceptual manner rather than explicitly stated as a solution to a question.
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
1. ## Re: Vectors help

Express t from one equation and substitute in into the other.

2. ## Re: Vectors help

Originally Posted by emakarov
Express t from one equation and substitute in into the other.
I don't know if this is right but I ended up with b= -2a+7

3. ## Re: Vectors help

Yes. Also, you probably got that t = 9 / (4 - a). The latter graph looks like this. So, for a > 4 the time to meeting is negative, which means that the meeting must have been in the past and will not happen in the future (this is natural since if B moves right faster than A, they cannot meet). For a < 4, the function t(a) is increasing. Since we need to find the smallest t, we need to find the smallest allowed a.

Since the maximum speed of B is 8 km/h, the vector (a, b), when its beginning is at (0, 0), lies inside a circle of radius 8. Also, b= -2a+7. The circle carves a segment on the line b = -2a+7, and we need to take the left end of that segment, which corresponds to the smallest a.

Page 2 of 2 First 12
user
The text passage is a discussion thread about a vectors problem, where a user is seeking help and another user is providing guidance and feedback.

TYPE: NO_QUESTION

The passage does not contain a direct mathematical question that requires solving. Instead, it is a conversation where a user is guided through a problem-solving process, and the final answer is discussed in a conceptual manner rather than explicitly stated as a solution to a question.