The equation for the design of the larger bridge is [tex]\frac{x^2}{3600} + \frac{y^2}{1296} = 1[/tex]
The equation of the small bridge is given as:
[tex]\frac{x^2}{225} + \frac{y^2}{144} = 1[/tex]
Express 225 and 144 as 15^2 and 12^2, respectively.
[tex]\frac{x^2}{15^2} + \frac{y^2}{12^2} = 1[/tex]
This means that the smaller bridge is 15 feet by 12 feet.
From the question, we have the dimension of the larger bridge to be:
Width = 4 * Smaller = 4 * 15 = 60
Length = 3 * Smaller = 3 * 12 = 36
Hence, the dimension of the larger bridge is 60 feet by 36 feet
In (a), we have:
Width = 60
Length = 36
The equation is represented as:
[tex]\frac{x^2}{Width^2} + \frac{y^2}{Length^2} = 1[/tex]
So, we have:
[tex]\frac{x^2}{60^2} + \frac{y^2}{36^2} = 1[/tex]
Evaluate the exponent
[tex]\frac{x^2}{3600} + \frac{y^2}{1296} = 1[/tex]
Hence, the equation for the design of the larger bridge is [tex]\frac{x^2}{3600} + \frac{y^2}{1296} = 1[/tex]
Read more about ellipse equations at:
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