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

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.