Question

the arch of an underpass is a semi ellipse 60 feet wide and 20 feet high, find the clearance at the edge of a lane if the edge is 20 ft at the middle? my answer was 25ft. am i right??

Answer 1

How did you get that answer?

Answer 2

getting the c..

Answer 3

i don't know.. i dont understand the clearance at the edge of a lane..

Answer 4

First, we need to get the axis.

Answer 5

The minor axis is \(20\) and the semi-major axis is \(60/2=30\)

Answer 6

Our equation is: \[
\frac{x^2}{30^2}+\frac{y^2}{20^2}=1
\]

Answer 7

"the edge is 20 ft at the middle"

This means \(x=20\)

Answer 8

So solve for \(y\): \[
\frac{20^2}{30^2}+\frac{y^2}{20^2}=1
\]

Answer 9

\[
\frac{y^2}{400}=1-\frac 49
\]

Answer 10

\[
y^2=400\cdot \frac 59
\]

Answer 11

15ft

Answer 12

tsk

Answer 13

\[
y=\pm \frac{20}{3}\sqrt{5}
\]

Answer 14

aaaaaaaah so heartbreaking..

Answer 15

We can disregard the \(-\) since we know it is positive.

Answer 16

thank you thank you

Answer 17

The answer is \(\approx 15\) if you don't mind rounding.

Answer 18

The exact answer is: \[
\frac{20\sqrt 5}{3}
\]

Answer 19

so? does that makes sense?

Answer 20

Yeah.