Question

How do you find the height of the arch??

A bridge is built in the shape of a semiplliptical arch. The bridge has a span of 80 feet and a mas height of 20 feet. Choose a suitable rectangular coordinate system and find the height of the arch at a distance of 30 feet from the center.
The height is about ______ feet
(round to two decimal places)

Answer 1

draw it out

Answer 2

you want x=0, y=20
y=0, x=80/2

then what is the value of that when x=20?

Answer 3

what do you mean x=20?

Answer 4

@amistre64

Answer 5

i meant x=30, just hit the wrong key on the keyboard.

Answer 6

\[\frac{x^2}{p^2}+\frac{y^2}{q^2}=1\]
\[\frac{y^2}{q^2}=1-\frac{x^2}{p^2}\]
\[y^2=q^2-\frac{(qx)^2}{p^2}\]

Answer 7

q=20, p=40, and x=30 if i se it right

Answer 8

so you are trying ot find for y? since 30 is x

Answer 9

yes

Answer 10

so what am I suppose to do with y? wait thats the height?

Answer 11

lol, yes. that will be the height at any value of x

Answer 12

y^2 = some #

y = sqrt(some #)

Answer 13

when x=p, we have q^2 = q^2 = 0 which is what we would expect at a distance of p from the center.

Answer 14

so would it be 18.97 for the height of the arch

Answer 15

maybe, let me check my calculator ....

Answer 16

i get something closer to 13

Answer 17

\[y=\sqrt{20^2-\frac{(20*30)^2}{40^2}}\]

Answer 18

okay thank you for the correcting me!