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An arch in the shape of the upper half of an ellipse is used to support a bridge that is to span a river 60 meters wide. The middle of the arch is 10 meters above the center of the river. Start by writing an equation for the ellipse if the x-axis coincides with the water level and the y-axis passes through the center of the arch. How high above the river is the arch at a distance of 8 meters from the center?

The arch is ____ meters above the river at a distance of 8 meters from the center. Do not round until the end. Round to the nearest tenth of a meter.

An arch in the shape of the upper half of an ellipse is used to support a bridge that is to span a river 60 meters wide The middle of the arch is 10 meters abov class=

Respuesta :

irspow

Answer:

Step-by-step explanation:

(y/10)^2+(x/30)^2=1

y^2/100+x^2/900=1

9y^2+x^2=900

9y^2=900-x^2

y^2=(900-x^2)/9, when x=8 we have

y^2=(900-8^2)/9

y^2=(900-64)/9

y^2=836/9

y=9.6 meters

The arch is 9.6 meters above the river at a distance of 8 meters from the center.

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