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Answer :
Final answer:
To find the height of the arc at the point 1.5m from one end of the semi-ellipse, substitute x = 1.5m into the ellipse's equation to solve for y, which represents the height at that point.
Explanation:
The semi-ellipse mentioned in the question is defined by two measurements: width (8m) and height (2m) at the center. To find the height of the arc at a point 1.5m from one end of the semi-ellipse, we can use the equation of an ellipse in standard form. An ellipse with a major axis of 8m and a minor axis of 2m has the equation ( x^2/16 ) + ( y^2/4 ) = 1, where x-values represent the horizontal distances from the center, and y-values represent the vertical distances.
By substituting x = 1.5m into this equation, we can solve for y, which will give us the height at that point: 1.5^2/16 + y^2/4 = 1 => y^2 = 4(1 - (1.5^2/16)) => y = ±2 • √{1 - (1.5^2/16)}. Only the positive value of y is considered, as we are interested in the height above the x-axis.
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