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  # Tutor profile: Jason C.
  
  Inactive
  Jason C.
  Tutor from MIT
  Tutor Satisfaction Guarantee
  
  ## Questions
  
  ### Subject:Python Programming
  
  TutorMe
  Question:
  
  Write a function that takes two integers and returns their greatest common divisor.
  
  Inactive
  Jason C.
  
  The greatest common divisor is at most the smallest of the two inputs. Therefore, we can just loop up to the minimum of the two inputs and check: $$\verb|def f(a, b):|$$ $$\verb| common_divisors = []|$$ $$\verb| for d in range(1, min(a, b) + 1):|$$ $$\verb| if a%d == 0 and b%d == 0:|$$ $$\verb| common_divisors.append(d)|$$ $$\verb| return max(common_divisors)|$$
  
  ### Subject:Pre-Calculus
  
  TutorMe
  Question:
  
  Evaluate $$(1+i\sqrt 3) e^{-i \pi/3}$$.
  
  Inactive
  Jason C.
  
  First, we will convert $$e^{-i \pi/3}$$ to rectangular form: $( e^{-i \pi/3} = \cos (-\pi/3) + i \sin (-\pi/3) = \frac{1}{2} - \frac{\sqrt 3}{2}.$) Then, we take the product of the two terms: (\begin{align*} (1 + i \sqrt 3) \left( \frac{1}{2} - i \frac{\sqrt 3}{2} \right) &= \left( \frac{1}{2} - i \frac{\sqrt 3}{2} \right) + i \sqrt 3 \left( \frac{1}{2} - i \frac{\sqrt 3}{2} \right) \\ &= \frac{1}{2} - i \frac{\sqrt 3}{2} + i \frac{\sqrt 3}{2} + \frac{3}{2} \\ &= 2. \end{align*})
  
  ### Subject:Calculus
  
  TutorMe
  Question:
  
  Evaluate $( \oint_C [(x^2 - y^2)\,dx + (x^2 + y^2)\,dy],$) where $$C$$ is the boundary of the square with vertices $$(0, 0)$$, $$(1, 0)$$, $$(1, 1)$$, and $$(0, 1)$$, oriented counterclockwise
  
  Inactive
  Jason C.
  
  By Green's theorem, we know that the integral about the boundary of region is equal to the integral of the divergence over the region. (\begin{align*}\oint_C [(x^2 - y^2)\,dx + (x^2 + y^2)\,dy] &= \iint_{[0, 1]^2} \left[\frac{d}{dx}(x^2 + y^2) - \frac{d}{dy}(x^2 - y^2)\right] \,dA \\ &= \int_0^1 \int_0^1 [2x + 2y] \,dx\,dy = 2.\end{align*})
  
  ## Contact tutor
  
  Send a message explaining your
  needs and Jason will reply soon.
  ContactÂ Jason
  
  Start Lesson
  
  ## FAQs
  
  What is a lesson?
  A lesson is virtual lesson space on our platform where you and a tutor can communicate. You'll have the option to communicate using video/audio as well as text chat. You can also upload documents, edit papers in real time and use our cutting-edge virtual whiteboard.
  How do I begin a lesson?
  If the tutor is currently online, you can click the "Start Lesson" button above. If they are offline, you can always send them a message to schedule a lesson.
  Who are TutorMe tutors?
  Many of our tutors are current college students or recent graduates of top-tier universities like MIT, Harvard and USC. TutorMe has thousands of top-quality tutors available to work with you.
explanation: The document contains a profile of a tutor named Jason C. from MIT, along with three questions and their corresponding answers in different subjects: Python Programming, Pre-Calculus, and Calculus. Each question is presented in a structured format, followed by the tutor's detailed response.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: Enable contrast version
  
  # Tutor profile: Jason C.
  
  Inactive
  Jason C.
  Tutor from MIT
  Tutor Satisfaction Guarantee
  
  ## Questions
  
  ### Subject:Python Programming
  
  TutorMe
  Question:
  
  Write a function that takes two integers and returns their greatest common divisor.
  
  Inactive
  Jason C.
  
  The greatest common divisor is at most the smallest of the two inputs. Therefore, we can just loop up to the minimum of the two inputs and check: $$\verb|def f(a, b):|$$ $$\verb| common_divisors = []|$$ $$\verb| for d in range(1, min(a, b) + 1):|$$ $$\verb| if a%d == 0 and b%d == 0:|$$ $$\verb| common_divisors.append(d)|$$ $$\verb| return max(common_divisors)|$$
  
  ### Subject:Pre-Calculus
  
  TutorMe
  Question:
  
  Evaluate $$(1+i\sqrt 3) e^{-i \pi/3}$$.
  
  Inactive
  Jason C.
  
  First, we will convert $$e^{-i \pi/3}$$ to rectangular form: $( e^{-i \pi/3} = \cos (-\pi/3) + i \sin (-\pi/3) = \frac{1}{2} - \frac{\sqrt 3}{2}.$) Then, we take the product of the two terms: (\begin{align*} (1 + i \sqrt 3) \left( \frac{1}{2} - i \frac{\sqrt 3}{2} \right) &= \left( \frac{1}{2} - i \frac{\sqrt 3}{2} \right) + i \sqrt 3 \left( \frac{1}{2} - i \frac{\sqrt 3}{2} \right) \\ &= \frac{1}{2} - i \frac{\sqrt 3}{2} + i \frac{\sqrt 3}{2} + \frac{3}{2} \\ &= 2. \end{align*})
  
  ### Subject:Calculus
  
  TutorMe
  Question:
  
  Evaluate $( \oint_C [(x^2 - y^2)\,dx + (x^2 + y^2)\,dy],$) where $$C$$ is the boundary of the square with vertices $$(0, 0)$$, $$(1, 0)$$, $$(1, 1)$$, and $$(0, 1)$$, oriented counterclockwise
  
  Inactive
  Jason C.
  
  By Green's theorem, we know that the integral about the boundary of region is equal to the integral of the divergence over the region. (\begin{align*}\oint_C [(x^2 - y^2)\,dx + (x^2 + y^2)\,dy] &= \iint_{[0, 1]^2} \left[\frac{d}{dx}(x^2 + y^2) - \frac{d}{dy}(x^2 - y^2)\right] \,dA \\ &= \int_0^1 \int_0^1 [2x + 2y] \,dx\,dy = 2.\end{align*})
  
  ## Contact tutor
  
  Send a message explaining your
  needs and Jason will reply soon.
  ContactÂ Jason
  
  Start Lesson
  
  ## FAQs
  
  What is a lesson?
  A lesson is virtual lesson space on our platform where you and a tutor can communicate. You'll have the option to communicate using video/audio as well as text chat. You can also upload documents, edit papers in real time and use our cutting-edge virtual whiteboard.
  How do I begin a lesson?
  If the tutor is currently online, you can click the "Start Lesson" button above. If they are offline, you can always send them a message to schedule a lesson.
  Who are TutorMe tutors?
  Many of our tutors are current college students or recent graduates of top-tier universities like MIT, Harvard and USC. TutorMe has thousands of top-quality tutors available to work with you.
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a profile of a tutor named Jason C. from MIT, along with three questions and their corresponding answers in different subjects: Python Programming, Pre-Calculus, and Calculus. Each question is presented in a structured format, followed by the tutor's detailed response.
  
  Label: multiple-question-and-answer