What Is the Maximum Value of x for Points on a Plane and Sphere in 3D Geometry?

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Discussion Overview

The discussion revolves around finding the maximum value of x for points that lie on both a specified plane and a sphere in 3D geometry. The participants explore the intersection of these geometric shapes and seek to understand the underlying concepts and calculations involved.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Homework-related

Main Points Raised

  • Participants inquire about the nature of the intersection between the plane defined by x+2y+3z=78 and the sphere defined by x^2+y^2+z^2=468.
  • Some participants suggest that the intersection forms a circle and discuss the implications of this shape.
  • There are requests for complete solutions and step-by-step guidance to understand the concepts better.
  • One participant mentions a specific value for the radius of the circle, suggesting a potential calculation but expresses uncertainty about its correctness.
  • Different approaches to solving the problem are acknowledged, with participants indicating that multiple methods may exist.

Areas of Agreement / Disagreement

There is a general agreement that the intersection is a circle, but the discussion remains unresolved regarding the specific steps to find the maximum value of x and the radius of the circle.

Contextual Notes

Participants have not reached consensus on the exact calculations or methods to apply, and there are unresolved questions about the radius and the maximum value of x.

Who May Find This Useful

This discussion may be useful for students or individuals interested in 3D geometry, particularly those exploring the intersection of geometric shapes and seeking to understand related mathematical concepts.

jingu
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(x,y,z)∈R^3 are points that lie on the plane x+2y+3z=78, and lie on the sphere x^2+y^2+z^2=468. The maximum value of x has the form a/b, where a and b are coprime positive integers. What is the value of a+b?
 
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Here is a hint: How does the intersection of a plane and a sphere look like?
Once you know the maximum value of x, calculating a+b should be easy.
 
hello friend, i even don't know from which topic is this question,help?

mfb said:
Here is a hint: How does the intersection of a plane and a sphere look like?
Once you know the maximum value of x, calculating a+b should be easy.
i even don't know from which topic is this question,please help?
 
Last edited:
So can anyone give me its complete solution,?

so that I can understand the concept.
 
Can you first answer mfb's question? What does the intersection of a sphere and a plane look like? What kind of figure is that?

You can find the equation of that graph by solving the two equations, x+2y+3z=78, and x^2+y^2+z^2=468 simultaneously. Since that is two equations in three variables, you can solve for two, say x and y, in terms of the third.
 
Last edited by a moderator:
I think it would be a circle.Please check whether I am correct or not...
 
It is a circle, right.
 
then what to do, you guys just tell me the steps I will do all by my own,so what will be the next step?
 
mfb said:
It is a circle, right.
then i think we have to find the radius of this circle...am i correct...?
 
  • #10
That is possible. I used a different approach, but there are many ways to solve this.

Can you link the source of the question? If it is not a current question, I might give more hints.
 
  • #11
mfb said:
That is possible. I used a different approach, but there are many ways to solve this.

Can you link the source of the question? If it is not a current question, I might give more hints.

yes give me hints...
 
  • #12
I think the radius is 5.78, and that is not the answer...help!
 

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