A bridge is built in the shape of a parabolic arch. The bridge has a span of feet and a maximum height of feet. Choose a suitable rectangular coordinate system and find the height of the arch at distances of​ 10, 30, and 50 feet from the center.

Height of the arch at distances of​ 10, 30, and 50 feet from the center is as follow:

Put x = 10 we get

the value of y = 0.695

Put x = 30

the vale of y = 6.26

Put x = 50

the value of y = 17.37

Step-by-step explanation:

The prabolic arch for bridge has span of 120 feet and height f 25 feet. The rectangular corordinate system is

such as

height = h = 25

Distance = x

(x-h) = -4a(y-k)

x² = -4ay

60 = -4a(-25) and

where the value of a =36

therefor the parabolic arch is

x = -144y

For distance of 10 , 20 and 30 let take the feet from center then we have

put x = 10 we get

10² = -144 y

100 / 144 = y

the value of y = 0.695

Put x = 30

30² = -144y

30/144 = y

the vale of y = 6.26

Put x = 50

50² = -144 y

50/144 = y

the value of y = 17.37

536

step-by-step explanation: