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Math Help - Variable rates of change problems

  1. #1
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    Variable rates of change problems

    Okay, nevermind, I solved that one too (for being the "Urgent Homework Help" forum, ya'll are kinda slow on the draw). Here's one thet's really giving me some trouble.

    A hot air balloon rising vertically is tracked by an observer located 5 miles from the lift-off point. At a certain moment, the between the observer's line-of-sight and the horizontal is [π/6] , and it is changing at a rate of 0.1 rad/min. How fast is the balloon rising at this moment?
    Last edited by G-Rex; September 30th 2007 at 03:23 PM. Reason: Solved the first problem
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by G-Rex View Post
    Could anyone give me a hand with these? I'm stuck on quite a few of them (more to come).

    1)The altitude of a triangle is increasing at a rate of 2 cm/min, while the area of the triangle is increasing at a rate of 2 cm^2/min. At what rate is the base of the triangle changing when the altitude is 10 cm and the area is 80 cm^2?

    The formula I'm coming up with to solve is a'=.5(b')(h) + .5(h')(b). Then, plugging in the values given me, I get 2=.5(b')(10) + .5(2)(16), solving for b by solving a=.5(a)(b), in this case being 80=.5(10)(b). However, when I solve for b', I get -14/5, which is incorrect. What am I doing wrong here?
    why do you say that's incorrect? that's what i got
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    It's webwork. It instantly tells me whether I got the answer right or wrong.
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by G-Rex View Post
    It's webwork. It instantly tells me whether I got the answer right or wrong.
    maybe the way you inputed the answer was wrong. maybe it wanted -2.8 or something as opposed to -14/5
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    is up to his old tricks again! Jhevon's Avatar
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    Do not delete a question after it has been answered. it may help someone else
    Quote Originally Posted by G-Rex View Post
    Okay, nevermind, I solved that one too (for being the "Urgent Homework Help" forum, ya'll are kinda slow on the draw).
    My apologies Master G-Rex that your servants were so slow in answering your question, especially since you've paid us to help you


    Here's one thet's really giving me some trouble.

    A hot air balloon rising vertically is tracked by an observer located 5 miles from the lift-off point. At a certain moment, the between the observer's line-of-sight and the horizontal is [π/6] , and it is changing at a rate of 0.1 rad/min. How fast is the balloon rising at this moment?
    here's a diagram of the situation. what relationship can you think of to link the unknowns?
    Attached Thumbnails Attached Thumbnails Variable rates of change problems-balloon.jpg  
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    [quote=Jhevon;73596]My apologies Master G-Rex that your servants were so slow in answering your question, especially since you've paid us to help you [quote]

    Jeesh, chill out, man. No need to take offense. I think a comment on the relative slowness of assistance around here is justified when it takes half an hour to get a reply on a problem posted in a forum specifically labeled "urgent", don't you? I'm not demanding that you pick up the pace. I'm just saying, the name is sorta misleading. And if you'd like me to leave up the previous problems, I will.
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    is up to his old tricks again! Jhevon's Avatar
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    [quote=G-Rex;73601][quote=Jhevon;73596]My apologies Master G-Rex that your servants were so slow in answering your question, especially since you've paid us to help you

    Jeesh, chill out, man. No need to take offense. I think a comment on the relative slowness of assistance around here is justified when it takes half an hour to get a reply on a problem posted in a forum specifically labeled "urgent", don't you? I'm not demanding that you pick up the pace. I'm just saying, the name is sorta misleading. And if you'd like me to leave up the previous problems, I will.
    not really. when you consider what type of forum this is, i would understand that. we have people from all around the world, that is, different time zones, helping (sometimes several people at once) for free, while sometimes doing their own homework. i don't think half an hour is that long when considering that. but maybe i reacted too harshly. my apologies (for real this time ), i've been off lately.

    anyway, what do you think for the second problem?
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    Sorry about the long reply time. I stepped out for a bite to eat, and then my internet connection went out. Anyways, I had already considered the information you posted earlier, and had decided to relate the two using tangent. However, this did not work for me before, and so I figured I had done something wrong. It was only after I reworked the problem that I discovered my error was simply multiplying by .01 instead of .1. My work is rife with such mistakes.
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by G-Rex View Post
    Sorry about the long reply time. I stepped out for a bite to eat, and then my internet connection went out. Anyways, I had already considered the information you posted earlier, and had decided to relate the two using tangent. However, this did not work for me before, and so I figured I had done something wrong. It was only after I reworked the problem that I discovered my error was simply multiplying by .01 instead of .1. My work is rife with such mistakes.
    yes, that was the relationship i was thinking of as well. good job
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