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princiebebe57
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How do you find the total width of the ellipse given by the equation 7x^2 + 7(y-6)^2 = 6.
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SUMMARY
The total width of the ellipse defined by the equation 7x² + 7(y-6)² = 6 can be determined by first simplifying the equation to the standard form of an ellipse. Dividing through by 7 yields x² + (y-6)² = 6/7, indicating that the semi-major axis (a) is √(6/7). The total width of the ellipse, which is twice the semi-major axis, is therefore 2√(6/7).
PREREQUISITES- Understanding of conic sections, specifically ellipses
- Familiarity with algebraic manipulation of equations
- Knowledge of the standard form of an ellipse equation
- Basic geometry concepts related to axes and dimensions
- Study the properties of ellipses, including foci and directrices
- Learn how to convert general conic equations to standard form
- Explore the applications of ellipses in physics and engineering
- Practice solving problems involving the dimensions of ellipses
Mathematics students, educators, and anyone interested in geometry or conic sections will benefit from this discussion.
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