Math Problem
-
I have a math test tommorrow on hyperbolas. On it there will probably be a word problem like this: "Points a and b are 1000m apart and it is determined from the sound of an explosion heard at these points at different times that the location of the explosion is 600 m closer to A than B. Show the location of the explosion is restrcted to a particular curve, and find an equaiton for it" In the example I know c = 500. I guess a = 300, thats what my teacher said, but I dont understand why. (I dont need help finding the third variable). If anyone knows why a = 300, please help me out. -KMaz
-
I have a math test tommorrow on hyperbolas. On it there will probably be a word problem like this: "Points a and b are 1000m apart and it is determined from the sound of an explosion heard at these points at different times that the location of the explosion is 600 m closer to A than B. Show the location of the explosion is restrcted to a particular curve, and find an equaiton for it" In the example I know c = 500. I guess a = 300, thats what my teacher said, but I dont understand why. (I dont need help finding the third variable). If anyone knows why a = 300, please help me out. -KMaz
I have a math test tommorrow on hyperbolas. On it there will probably be a word problem like this: "Points a and b are 1000m apart and it is determined from the sound of an explosion heard at these points at different times that the location of the explosion is 600 m closer to A than B. Show the location of the explosion is restrcted to a particular curve, and find an equaiton for it" In the example I know c = 500. I guess a = 300, thats what my teacher said, but I dont understand why. (I dont need help finding the third variable). If anyone knows why a = 300, please help me out. First you talk about points a and b, and then you talk about "a = 300" and "c = 500", which makes me think that "a" and "c" are distances. You might be confusing yourself with that. (BTW, you never explained what "c" is. Is "c" the location of the explosion?) Assuming "c" is the location of the explosion: In the trivial case, where the explosion occurs between points a and b, the distance "ac" is 200m and the distance "bc" is 800m. I'm not sure what you mean by "c = 500" and "a = 300". ------------------------------------------ Law of Nazi Analogies: As an online discussion grows longer, the probability of a comparison involving Nazis or Hitler approaches one. In any debate, Hitler's opinion on the subject is automatically the evil one, so it had better be contrary to the side you're arguing.
-
I have a math test tommorrow on hyperbolas. On it there will probably be a word problem like this: "Points a and b are 1000m apart and it is determined from the sound of an explosion heard at these points at different times that the location of the explosion is 600 m closer to A than B. Show the location of the explosion is restrcted to a particular curve, and find an equaiton for it" In the example I know c = 500. I guess a = 300, thats what my teacher said, but I dont understand why. (I dont need help finding the third variable). If anyone knows why a = 300, please help me out. First you talk about points a and b, and then you talk about "a = 300" and "c = 500", which makes me think that "a" and "c" are distances. You might be confusing yourself with that. (BTW, you never explained what "c" is. Is "c" the location of the explosion?) Assuming "c" is the location of the explosion: In the trivial case, where the explosion occurs between points a and b, the distance "ac" is 200m and the distance "bc" is 800m. I'm not sure what you mean by "c = 500" and "a = 300". ------------------------------------------ Law of Nazi Analogies: As an online discussion grows longer, the probability of a comparison involving Nazis or Hitler approaches one. In any debate, Hitler's opinion on the subject is automatically the evil one, so it had better be contrary to the side you're arguing.
Thanks for the response. In as standard usage a = length from center to vertex. b = length of the conjugate axis. c = focus of axis.
-
Thanks for the response. In as standard usage a = length from center to vertex. b = length of the conjugate axis. c = focus of axis.
Hmmm. I'm not quite familiar with those terms. Maybe I should let someone else answer that question. My best guess at what you are talking about is shown in the figure below. In this case, "a" is 300m off the center of the line between points a and b.
o o 200m o 300m 500m \\ o | |point a-> (a)--o---x------(b) <- point b
o ^ ^
o | |
o | center point (halfway between point a and point b)
o a (distance from center to "o")If that's the case, then finding "a" is easy. Go back to the concrete example where the hypotenuse crosses the line between a and b, we know that the distance from point a to the hypotenuse is 200m and the distance from point b to the hypotenuse is 800m. We know this because if the explosion is 600m closer to point a than point b, and the distance from a to b is 1000m, then: distance from point a to point b ("ab") is 1000m "ab" = 1000 distance from point a to explosion ("ae") is 600m closer than point b to explosion ("be") "ae" + 600 = "be" If we assume "e" occurs on line "ab", then we can say that "ae" + "be" = "ab" Using some substitution, start with "ae" + 600 = "be" then convert "ae" to "ab" - "be" to get: "ab" - "be" + 600 = "be" add "be" to both sides: "ab" + 600 = 2 * "be" substitute 1000 for "ae": 1000 + 600 = 2 * "be" "be" = 800 Since the center is at 500m, we know that the distance from the center to the intersection is 300m away. BTW, if that doesn't answer the question, it's probably because I don't understand the terms. Someone else might need to answer this. ------------------------------------------ Law of Nazi Analogies: As an online discussion grows longer, the probability of a comparison involving Nazis or Hitler approaches one. In any debate, Hitler's opinion on the subject is automatically the evil one, so it had better be contrary to the side you're arguing.
-
Hmmm. I'm not quite familiar with those terms. Maybe I should let someone else answer that question. My best guess at what you are talking about is shown in the figure below. In this case, "a" is 300m off the center of the line between points a and b.
o o 200m o 300m 500m \\ o | |point a-> (a)--o---x------(b) <- point b
o ^ ^
o | |
o | center point (halfway between point a and point b)
o a (distance from center to "o")If that's the case, then finding "a" is easy. Go back to the concrete example where the hypotenuse crosses the line between a and b, we know that the distance from point a to the hypotenuse is 200m and the distance from point b to the hypotenuse is 800m. We know this because if the explosion is 600m closer to point a than point b, and the distance from a to b is 1000m, then: distance from point a to point b ("ab") is 1000m "ab" = 1000 distance from point a to explosion ("ae") is 600m closer than point b to explosion ("be") "ae" + 600 = "be" If we assume "e" occurs on line "ab", then we can say that "ae" + "be" = "ab" Using some substitution, start with "ae" + 600 = "be" then convert "ae" to "ab" - "be" to get: "ab" - "be" + 600 = "be" add "be" to both sides: "ab" + 600 = 2 * "be" substitute 1000 for "ae": 1000 + 600 = 2 * "be" "be" = 800 Since the center is at 500m, we know that the distance from the center to the intersection is 300m away. BTW, if that doesn't answer the question, it's probably because I don't understand the terms. Someone else might need to answer this. ------------------------------------------ Law of Nazi Analogies: As an online discussion grows longer, the probability of a comparison involving Nazis or Hitler approaches one. In any debate, Hitler's opinion on the subject is automatically the evil one, so it had better be contrary to the side you're arguing.
Brit wrote: I'm not quite familiar with those terms. You and me both !! Your diagram is pretty though, however I think your curve needs to be the other way around. Regardz Colin J Davies
*** WARNING *
This could be addictive
**The minion's version of "Catch :bob: "It's a real shame that people as stupid as you can work out how to use a computer. said by Christian Graus in the Soapbox
-
Brit wrote: I'm not quite familiar with those terms. You and me both !! Your diagram is pretty though, however I think your curve needs to be the other way around. Regardz Colin J Davies
*** WARNING *
This could be addictive
**The minion's version of "Catch :bob: "It's a real shame that people as stupid as you can work out how to use a computer. said by Christian Graus in the Soapbox
ColinDavies wrote: Your diagram is pretty though, however I think your curve needs to be the other way around. Yeah, that's what I thought at first. Then I started thinking maybe it curved the other direction. But now I'm thinking you're right - I had it right the first time. [Edit] Maybe I drew the curve right afterall. It looks like I correctly understood the terms "a" and "c", too: http://mathworld.wolfram.com/Hyperbola.html[^] [\Edit] ------------------------------------------ Law of Nazi Analogies: As an online discussion grows longer, the probability of a comparison involving Nazis or Hitler approaches one. In any debate, Hitler's opinion on the subject is automatically the evil one, so it had better be contrary to the side you're arguing.
-
ColinDavies wrote: Your diagram is pretty though, however I think your curve needs to be the other way around. Yeah, that's what I thought at first. Then I started thinking maybe it curved the other direction. But now I'm thinking you're right - I had it right the first time. [Edit] Maybe I drew the curve right afterall. It looks like I correctly understood the terms "a" and "c", too: http://mathworld.wolfram.com/Hyperbola.html[^] [\Edit] ------------------------------------------ Law of Nazi Analogies: As an online discussion grows longer, the probability of a comparison involving Nazis or Hitler approaches one. In any debate, Hitler's opinion on the subject is automatically the evil one, so it had better be contrary to the side you're arguing.
Brit wrote: [Edit] Maybe I drew the curve right afterall. It looks like I correctly understood the terms "a" and "c", too: http://mathworld.wolfram.com/Hyperbola.html\[^\] [\Edit] I disagree. :-) You only drew one curve for the positive a and c terms, if you draw it for the negative terms you would be correct. :-) Regardz Colin J Davies
*** WARNING *
This could be addictive
**The minion's version of "Catch :bob: "It's a real shame that people as stupid as you can work out how to use a computer. said by Christian Graus in the Soapbox
-
I have a math test tommorrow on hyperbolas. On it there will probably be a word problem like this: "Points a and b are 1000m apart and it is determined from the sound of an explosion heard at these points at different times that the location of the explosion is 600 m closer to A than B. Show the location of the explosion is restrcted to a particular curve, and find an equaiton for it" In the example I know c = 500. I guess a = 300, thats what my teacher said, but I dont understand why. (I dont need help finding the third variable). If anyone knows why a = 300, please help me out. -KMaz
at a guess from the info in your other post b = 1000 - 600 and c = 500 as you said so a= sqr( c^2 - b^2) a= 300 It's best to graph this stuff to understand it better. so o b o o o -c o-a x a o c o o o -b o The distance to c will always be the largest number, as the xy axis is square the line axis_a combined with axis_b would give axis_c. If you morph the graph a bit in your head you can see how a Pythagorus type hypotenuse is similar. So your teachers example appears to be just a big convorted 3,4,5 triangle. If I'm wrong, sue me. :-) Regardz Colin J Davies
*** WARNING *
This could be addictive
**The minion's version of "Catch :bob: "It's a real shame that people as stupid as you can work out how to use a computer. said by Christian Graus in the Soapbox
-
Hmmm. I'm not quite familiar with those terms. Maybe I should let someone else answer that question. My best guess at what you are talking about is shown in the figure below. In this case, "a" is 300m off the center of the line between points a and b.
o o 200m o 300m 500m \\ o | |point a-> (a)--o---x------(b) <- point b
o ^ ^
o | |
o | center point (halfway between point a and point b)
o a (distance from center to "o")If that's the case, then finding "a" is easy. Go back to the concrete example where the hypotenuse crosses the line between a and b, we know that the distance from point a to the hypotenuse is 200m and the distance from point b to the hypotenuse is 800m. We know this because if the explosion is 600m closer to point a than point b, and the distance from a to b is 1000m, then: distance from point a to point b ("ab") is 1000m "ab" = 1000 distance from point a to explosion ("ae") is 600m closer than point b to explosion ("be") "ae" + 600 = "be" If we assume "e" occurs on line "ab", then we can say that "ae" + "be" = "ab" Using some substitution, start with "ae" + 600 = "be" then convert "ae" to "ab" - "be" to get: "ab" - "be" + 600 = "be" add "be" to both sides: "ab" + 600 = 2 * "be" substitute 1000 for "ae": 1000 + 600 = 2 * "be" "be" = 800 Since the center is at 500m, we know that the distance from the center to the intersection is 300m away. BTW, if that doesn't answer the question, it's probably because I don't understand the terms. Someone else might need to answer this. ------------------------------------------ Law of Nazi Analogies: As an online discussion grows longer, the probability of a comparison involving Nazis or Hitler approaches one. In any debate, Hitler's opinion on the subject is automatically the evil one, so it had better be contrary to the side you're arguing.
Thanks a bunch. a whole lot of help. -KMaz