This is quite graphic...  TOPIC_SOLVED

Simplificatation, evaluation, linear equations, linear graphs, linear inequalities, basic word problems, etc.

This is quite graphic...

Postby diaste on Wed Jan 28, 2009 1:51 am

:wink:

I don't know why I'm having so much trouble with this, obviously I'm missing something.
SO here goes.
I have a tent that's going to be staked out on a polar ice cap and as you can imagine it's cold and windy out here. My partner is the meticulous type and wants to know how high the tent is so he can put the stakes just where the instructions say. I think that's a bit overboard as I'm cold and I want to make some tea but I relent and tell him I can figure it out for him. The only info I get from the instructions is that the tent lies on the graph of: and the tent ropes are supposed to lie on the graph of: From the first equation I quickly assess the height of the tent to be 10' and the base to be ten feet with the slope of thrown in for good measure. This impresses my partner but it's the cold that's motivating me. However, now we're in trouble because I told him the tent stakes should go 18' from the edge of the tent and we don't have that much rope.

Seriously, this equation is baffling me. The vertex is (5,6) and the slope is but I keep coming up with x intercepts at -23 and 23. This is what I did:




Of course that's wrong because the graph demands a slope of -1 to 3 and that means I should have 18 and -18 as an answer. Which, from the vertex would put the stakes at 13' from the edge of the tent.

I thought of just eliminating the absolute value and dividing 6 by because that would work. Is that the way I should treat a negative slope that's greater than 1? The first equation worked out just fine with intercepts at ( 0,0) and (10,0) and the vertex at (5,10) I assume there has to be a set of rules to follow I just can't seem to find what they are. I'm going to try one more idea I just thought of and then come back and look for a reply.

One thing I would request is that you remember I'm a mere math mortal and a pretty green one at that. :) You two are way advanced! :wink:

Thanks for your patience and please hurry, it's winter in the arctic regions ya know! :D
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  TOPIC_SOLVED

Postby stapel_eliz on Wed Jan 28, 2009 11:41 am

diaste wrote:Seriously, this equation is baffling me. The vertex is (5,6) and the slope is but I keep coming up with x intercepts at -23 and 23. This is what I did:



Absolute-value bars are not the same as parentheses. You have to deal with cases, accounting for the possible sign of the argument. For absolute-value equations, that means taking the bars off twice: one way positive and the other way negative:

. . . . .-(1/3)|x - 5| + 6 = 0

. . . . .-(1/3)|x - 5| = -6

. . . . .(1/3)|x - 5| = 6

. . . . .(1/3)(x - 5) = 6 or (1/3)(x - 5) = -6

. . . . .x - 5 = 18 or x - 5 = -18

...and so forth.

It should be noted that the stakes' rope is measured from the ends of the tent, not from the center.

Eliz.
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Re: This is quite graphic...

Postby diaste on Wed Jan 28, 2009 6:34 pm

Thanks for the reply Elizabeth,

I went over the examples about 10 times last night and finally figured it out. Everything you're saying I know. I guess I didn't have the confidence in my work that I should have. The answer to the problem is indeed -13 and 23. if the tent is 10' wide then coming from (0,0) with the vertex at x=5, 13 to the left and 23 to the right is indeed 13' from the edge of the tent. I was focused on the vertex and not on (0,0) which is where it all begins. So let that be a lesson to me!! :oops:

Thanks again Elizabeth :)
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