text: # How did they come to the conclusion of 2/3h? Thanks! How did they come to the...
  
  ###### Question:
  
  How did they come to the conclusion of 2/3h? Thanks!
  
  How did they come to the conclusion of 2/3h? Can someone show me exactly how they got to this number?
  EXAMPLE 26-1 REFLECTING ON A FLOWER to the leit ofa An observer is at table level, a distance d to the left of a flower of height h. The flower itself is a distance d to as shown in the sketch. Note that a ray of light propagating from the top of the flower to the observer's eye refet. ror at a height y above the table. Find y in terms of the height of the flower, h. PICTURE THE PROBLEM The physical situation is shown in the diagram, along with a ray from the top of the flower to the eye of the observer. The point where the ray hits the mirror is a height y above the table. The flower is a distance d to the left of the mirror and its image is a distance d to the right of the mirror. Finally, the observer's eye is a distance 2d to the left of the mirror STRATEGY To find y, we must use the fact that the angle of reflection is equal to the angle follows, then, that tan 0 obtained from the small yellow triangle must be equal tan 0 equal to one another yields a relation that can be solved for y. of incidence. In the diagram we indicate these two angles by the symbol 6. It to tan 0 obtained from the larger green triangle. Setting these expressions for
  26-2 FORMING IMAGES WITH A PLANE MIRROR 911 SOLUTION 1 Wit an expression for tan e tusing the yelow triangle h- y Now, write a similar expression for tan θ using the green triangle 2 3. Set the two expressions for tan 6 equal to one another: L Rearrange the preceding equation and solve for y: 2d d 2d h-y- INSIGHT Netethat the observer will see the entire image of the flower in a section of mirror that is only two-thirds the height of the flower. RACTICE PROBLEM l the observer moves farther from the base nd ocation? As a check on your answer, calculate the point of reflection for th r from the base of the flower, does the point of reflection move upward, downward, or stay at the e case where the distance between the observer the base of the flower is 2d. (Answer The point of reflection moves upward. In this case, we find y- on nlaled homework problems Problen 5,Problem 7
  
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  ##### How do you find the vertex and intercepts for  y^2+6y+12x+33=0?
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explanation: The text extract provided is a question from a physics problem set or textbook, specifically about the derivation of a height in a mirror reflection problem. The user is asking for an explanation of how the height \( y \) is determined to be \( \frac{2}{3}h \) in the context of the problem. The extract does not contain an answer to the question, only the question itself.
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: # How did they come to the conclusion of 2/3h? Thanks! How did they come to the...
  
  ###### Question:
  
  How did they come to the conclusion of 2/3h? Thanks!
  
  How did they come to the conclusion of 2/3h? Can someone show me exactly how they got to this number?
  EXAMPLE 26-1 REFLECTING ON A FLOWER to the leit ofa An observer is at table level, a distance d to the left of a flower of height h. The flower itself is a distance d to as shown in the sketch. Note that a ray of light propagating from the top of the flower to the observer's eye refet. ror at a height y above the table. Find y in terms of the height of the flower, h. PICTURE THE PROBLEM The physical situation is shown in the diagram, along with a ray from the top of the flower to the eye of the observer. The point where the ray hits the mirror is a height y above the table. The flower is a distance d to the left of the mirror and its image is a distance d to the right of the mirror. Finally, the observer's eye is a distance 2d to the left of the mirror STRATEGY To find y, we must use the fact that the angle of reflection is equal to the angle follows, then, that tan 0 obtained from the small yellow triangle must be equal tan 0 equal to one another yields a relation that can be solved for y. of incidence. In the diagram we indicate these two angles by the symbol 6. It to tan 0 obtained from the larger green triangle. Setting these expressions for
  26-2 FORMING IMAGES WITH A PLANE MIRROR 911 SOLUTION 1 Wit an expression for tan e tusing the yelow triangle h- y Now, write a similar expression for tan θ using the green triangle 2 3. Set the two expressions for tan 6 equal to one another: L Rearrange the preceding equation and solve for y: 2d d 2d h-y- INSIGHT Netethat the observer will see the entire image of the flower in a section of mirror that is only two-thirds the height of the flower. RACTICE PROBLEM l the observer moves farther from the base nd ocation? As a check on your answer, calculate the point of reflection for th r from the base of the flower, does the point of reflection move upward, downward, or stay at the e case where the distance between the observer the base of the flower is 2d. (Answer The point of reflection moves upward. In this case, we find y- on nlaled homework problems Problen 5,Problem 7
  
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  ##### How do you find the vertex and intercepts for  y^2+6y+12x+33=0?
  How do you find the vertex and intercepts for  y^2+6y+12x+33=0?...
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The text extract provided is a question from a physics problem set or textbook, specifically about the derivation of a height in a mirror reflection problem. The user is asking for an explanation of how the height \( y \) is determined to be \( \frac{2}{3}h \) in the context of the problem. The extract does not contain an answer to the question, only the question itself.
  
  Label: question