Ellipse Watch

Wish
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#1
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QuestionA racecar track is in the shape of an ellipse 80 ft long and 40 ft wide. What is the width 10 ft from the side?

ProblemI think the equation would be \frac{x^2}{40^2} + \frac{y^2}{80^2} = 1 but that doesn't answer the question.
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2^1/2
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(Original post by Wish)
I think the equation would be \frac{x^2}{40^2} + \frac{y^2}{80^2} = 1 but that doesn't answer the question.
your latex failed - check the end tag

Very confusing question, i'm not sure what it is asking
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Wish
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(Original post by 2^1/2)
your latex failed - check the end tag
Fixed.
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2^1/2
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where is the side? and from in which direction?
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Wish
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(Original post by 2^1/2)
where is the side?

I would have thought 10 ft from each axis. Hence, height would be 60ft and width would be 20ft?
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2^1/2
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yes, but it seems very simple.

my thought was it could be 10ft in the other direction, so height: 100ft and width: 60ft

EDIT: what level is this question
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Icy_Mikki
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(Original post by Wish)
QuestionA racecar track is in the shape of an ellipse 80 ft long and 40 ft wide. What is the width 10 ft from the side?

ProblemI think the equation would be \frac{x^2}{40^2} + \frac{y^2}{80^2} = 1 but that doesn't answer the question.
Well if the track is 80ft long (in the X axis) and 40ft wide (i.e. tall in the Y axis) the equation would be

\frac{x^2}{40^2} + \frac{y^2}{20^2} = 1

Since you'd have to half the 'width' and 'height' of the track (they've essentially given you the diameter and equations need radii, right?). This equation will give you a graph wider than it is taller (i.e. bigger in the X direction than in the Y direction) which I think is what they're asking for/the best way to do it.

Now, I'd interpret the width 10ft from the side of the graph to mean the 'height' of the track (i.e. double the Y co-ordinate) 10ft from the far right hand/left hand side of the graph, and since the right hand side of the graph is when X = 40, 10ft from this would be when X = 30.

When X = 30,

\frac{30^2}{40^2} + \frac{y^2}{20^2} = 1

Now you can solve that Y^2 = 175, or Y = 13.23- double this being 26.46ft.

That's how I'd do it anyway.
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2^1/2
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you just beat me to correcting the equation,

what you put makes sense, i just couldn't see what the question was asking.
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