An arch is in the shape of a parabola. it has a span of 100 feet and a maximum height of 25 ft.
find the equation of the parabola, and use that to determine the height of the arch 10 feet from the center. round to 2 decimal places.

the height of the arch 10 feet from the center is 24 feet

Step-by-step explanation:

An arch is in the shape of a parabola. It has a span of 100 feet, the vertex lies at the center 50 and the maximum height of 25 ft.

Vertex at (50,25)

vertex form of the equation is

, (h,k) is the center

the parabola starts at (0,0) that is (x,y)

subtract 25 from both sides

divide both sides by 2500

the height of the arch 10 feet from the center.

center is at 50, 10 feet from the center so x=40 and x=60

y=24

the height of the arch 10 feet from the center is 24 feet

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.

entering that problem on the tube might get you an answer