Your Daily Math Problem

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Incongruent

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Despite what the title implies, this isn't going to be a recurring thing, unless someone else has their own math problems share. Assumed figures are made up.




You are digging a tunnel through a mountain. The path is 310 km in length and in the form of an equilateral equiangular quadrilateral prism having only sides perpendicular or parallel to the downward vector of earth's gravity with a bisected sphere cross section prism on top.

Assuming that the light outside is 2000 lux, the intensity of the light decreases by 21.7% every 9 meters, and your eye can only detect light above 0.0259 lux, how far in must you be, in meters, before you can see light at the end of the tunnel? (Ignore light that enters from the entrance of the tunnel.)

Round your answer to the nearest thousandth.


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Nytrunner

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Are you auditioning for full-time forum troll, or professor that always puts superfluous info on tests?
 

Incongruent

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Can you use my act for both?

Neither. I was wondering how many people would get the right answer.
It's actually a simple problem once you sort through the info.
 

Incongruent

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6.9 that number is ruined by the period!
How did you get that 6.9 and what do you mean by ruined?

As far as I know none of the digits divide into 6.9 or into single decimal figures but I haven't added and divided or done multi step processes and I don't plan on wasting time doing so.
 

Woody's Workshop

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Before I can solve that problem, you have to explain what all those big words mean.
Tunnel boring machines only make round holes, assuming you are using the most efficient tech available today.
 

Incongruent

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The big words only exist to add confusion. I'll explain the words anyways, even the ones as think you know.

Equiangular mans all the angles are equal and equilateral means all the sides are equal. Quadrilateral prism is a prism which has a four sided base, and since the base is also of equal angles and sides, it's a square.

Parallel means going in the same direction (or the opposite, if you have a ray) and perpendicular means at a 90° angle to.

The cross section of a sphere is a circle, and a prism with circular bases is a cylinder. With half circles as bases, it's half a cylinder.

Lux is lumens/square meter.

Yea, I know about the tunnel boring machines creating circular holes, but it's a math problem! They're almost as unrealistic as science problems!
 

rms

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Doesn't matter, I'm not going into that tunnel!
 

Tonimus

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No problem. I didn't see it as harsh. This is how I read the question: You're digging a hole through a mountain. Ignoring the light coming in from the hole you just made, how far do you need to go to see the light at the other end? Exactly the length of said hole to the other side.
 

cerving

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What if you're digging at night?
 

Cabernut

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I got to "just over 414 meters" before I lost interest.

Can you tell me why you cannot have one infinity larger than another despite otherwise intelligent mathematicians on YouTube telling you that you can?
 

Lowpuller

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IN COMING!!!!!!!!!


mountain gone......

Problem solved.
 

blackbrandt

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How did you get that 6.9 and what do you mean by ruined?

As far as I know none of the digits divide into 6.9 or into single decimal figures but I haven't added and divided or done multi step processes and I don't plan on wasting time doing so.
I'm holding my tongue on this one....
 

Incongruent

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No problem. I didn't see it as harsh. This is how I read the question: You're digging a hole through a mountain. Ignoring the light coming in from the hole you just made, how far do you need to go to see the light at the other end? Exactly the length of said hole to the other side.
The answer is to be given in meters. Otherwise you got it correct.
 

jderimig

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0.000 meters. What do i win?
 
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adrian

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0.000 meters. What do i win?
You win what is left of the mountain.

The path is a square. It is 310km long. Therefore it is also 310km wide, giving it an area of 96100km^2. To put that into perspective, the entire state of South Carolina has an area of 82931km^2. So at least one side of this path is going to be outside the mountain and you are able to see light from the other side before tunnelling has even begun. By the time tunnelling is completed, there won't be much left of the mountain, or for that matter the state in which it is located.
 

Incongruent

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You win what is left of the mountain.

The path is a square. It is 310km long. Therefore it is also 310km wide, giving it an area of 96100km^2. To put that into perspective, the entire state of South Carolina has an area of 82931km^2. So at least one side of this path is going to be outside the mountain and you are able to see light from the other side before tunnelling has even begun. By the time tunnelling is completed, there won't be much left of the mountain, or for that matter the state in which it is located.
The path is a square prism.
 

Nytrunner

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The big words only exist to add confusion......
....but it's a math problem!....
Nope. Its a troll question.
By the way, did no one stop to consider that 310km is about as wide as California? Unless you were digging straight through Bhutan, you'd find daylight way faster...

What if you're digging at night?
An African or European tunnel?
These are the only replies that really matter here.
Trolling the troll is the only right answer
 

adrian

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The path is a square prism.
An equilateral square prism, according to the original question. Or, in plain English, a cube. One side is already defined to be 310km, therefore so are all the others, which means it's also at least 310km high. Mount Everest is less than 9km high. Olympus Mons is about 22km. Wherever this tunnel is being dug, it's not on Earth and probably not in this solar system. The question is not whether it's African or European, but whether it's Klingon or Narn. :dark:
 

TRFfan

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35546536q76r54y thgf7y45nh7b6bt5 nb65ruyu 66n6r chf65658 (in meters).

EDIT: 1000th post
 

TRFfan

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q, r, y,t,h,g,f,y,n,h,b,t,n,r,u,y,c,h, and f are variables.
 

Incongruent

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An equilateral square prism, according to the original question. Or, in plain English, a cube. One side is already defined to be 310km, therefore so are all the others, which means it's also at least 310km high. Mount Everest is less than 9km high. Olympus Mons is about 22km. Wherever this tunnel is being dug, it's not on Earth and probably not in this solar system. The question is not whether it's African or European, but whether it's Klingon or Narn. :dark:
I see your point. I intended it to mean a square base, but the phrasing is poor.
 
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