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anonymous
 one year ago
A railroad tunnel is shaped like a semiellipse as shown below.
The height of the tunnel at the center is 58 ft and the vertical clearance must be 29 ft at a point 21 ft from the center. Find an equation for the ellipse.
anonymous
 one year ago
A railroad tunnel is shaped like a semiellipse as shown below. The height of the tunnel at the center is 58 ft and the vertical clearance must be 29 ft at a point 21 ft from the center. Find an equation for the ellipse.

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Diagram: http://prntscr.com/7mjbvf

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1not sure, but let me think

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1is there anything about the ellipse not mentioned? I feel like there's some missing info

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0vertex is 0,58 and there are two points on the ellipse at +21,29

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1if the ellipse is taller than it is wide, then a = 58 and this pairs up with the y^2 term

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1and if (21,29) is on the ellipse, then (x,y) = (21,29) > x = 21 and y = 29

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1assume the center is (h,k) = (0,0)

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1\[\Large \frac{(xh)^2}{b^2}+\frac{(yk)^2}{a^2} = 1\] \[\Large \frac{(210)^2}{b^2}+\frac{(290)^2}{58^2} = 1\] solve for b

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1actually you don't have to solve for b you can stop at b^2

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1since b^2 is in the denominator under the x^2 term

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'm getting a "Max Iterations Error" on my calculator

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1what kind of calculator do you have?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1I'm not familiar with that type

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1but you should get b^2 = 588

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0It has a number solve function where I can type in 2 sides of an equation and It'll solve for a variable in the equation. That's what I was using and it gave that error. When I solved for b^2 it works

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok so we found b^2 and b, so now what?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1replace b^2 with 588 and a^2 with whatever 58^2 is

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1(h,k) = (0,0)

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1x and y are left alone in the equation

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so \[\large \frac{ x^2 }{ 588 }+\frac{ y^2 }{ 3364 } =1\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0then we need to add the values

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0is that the equation or is there something left?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1the last thing you posted is the equation they want

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1I guess you could solve for y to get some expression in the form y = ... that will get you the top half of the ellipse, which is the tunnel

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1hmm now I'm not sure if they want the full ellipse or just the upper half ellipse

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So do I just solve for y=?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So I'm stuck at \[\frac{ y^2 }{ 3364 }=1\frac{ x^2 }{ 588 }\]

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1multiply both sides by 3364 then take the square root of both sides you focus on the positive square root because you want the upper half

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0how I multiply x^2/588 by 3364 and what would that come out to

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1\[\Large \frac{ y^2 }{ 3364 }=1\frac{ x^2 }{ 588 }\] \[\Large 3364*\frac{ y^2 }{ 3364 }=3364*(1\frac{ x^2 }{ 588 })\] \[\Large y^2=3364*(1\frac{ x^2 }{ 588 })\] \[\Large y^2=3364*13364*\frac{ x^2 }{ 588 }\] \[\Large y^2=3364\frac{3364x^2 }{ 588 }\] \[\Large y^2=3364\frac{841x^2 }{ 147 }\] \[\Large y=???\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0It was that last part I was confused about.\[y=58\frac{ 29x }{ 7\sqrt{3} }\]

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1you can't take the square root like that

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1\[\Large y^2=3364\frac{841x^2 }{ 147 }\] \[\Large \sqrt{y^2}=\sqrt{3364\frac{841x^2 }{ 147 }}\] \[\Large y=\sqrt{3364\frac{841x^2 }{ 147 }}\]

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1you apply the square root to the entire side

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0then what? Is that all we can do

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1yeah that's as far as you can go

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1\[\Large \sqrt{x + y} \ne \sqrt{x} + \sqrt{y}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0It's been a long day of math for me. Finally off to bed. Thanks for all the help, dude!
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