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Parks a lake in a park is elliptically-shaped. if the
length of the lake is 2500 meters and the width is
1500 meters, find the eccentricity of the lake.

Answer :

The eccentricity of the elliptical lake will be equal to e=0.4.

What is an ellipse?

An ellipse is an oval shape geometry having two focuses and the curve is equidistant from the focus.

Given that:-

length of the lake is 2500 meters and the width is 1500 meters

So the eccentricity of the lake will be calculated as:-

[tex]e=\dfrac{\sqrt{a^2-b^2}}{a}\\\\\\e=\dfrac{\sqrt{2500^2-1500^2}}{2500}\\\\\\e=0.4[/tex]

Therefore the eccentricity of the elliptical lake will be equal to e=0.4.

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Rewritten by : Barada

Final answer:

The eccentricity of an elliptically-shaped lake can be calculated using the formula e = c/a, where c is the distance from the center of the ellipse to one of the foci (calculated using the equation [tex]c = \sqrt{(a^2 - b^2))[/tex] and a is half the length of the lake. After finding the values of a, b and c, these can be substituted into the eccentricity formula.

Explanation:

The question is asking for the eccentricity of an elliptically-shaped lake. Eccentricity refers to the degree of elongation of an ellipse. It's a mathematical measure that provides information about the shape of the ellipse. If the eccentricity is closer to 0, the ellipse is more circular. If the eccentricity is closer to 1, the ellipse is more elongated or 'flat'.

In this case, the length of the lake, 2500 meters, represents the major axis length (2a), and the width of the lake, 1500 meters, represents the minor axis length (2b). The foci of the ellipse can be calculated using the equation [tex]c = \sqrt{(a^2 - b^2)[/tex], where c is the distance from the center of the ellipse to one of the foci. Therefore, the eccentricity, represented as e, can be calculated using the formula e = c/a.

So, we start by finding a and b, which are half the length and width, respectively: a = 2500m/2 = 1250m, b = 1500m/2 = 750m. Next, calculate c:[tex]c = \sqrt{(1250^2 - 750^2) = sqrt(625000)[/tex]. If we substitute these values into the formula for eccentricity, we have e = sqrt(625000)/1250.

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