Chapter 6 Review
Jan 10th, 2011 by corricelli
Hello,
Use this section to post questions/ respond to questions while preparing for your Chapter 6 Test
Thanks,
Mrs. Corricelli
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hey guys
i hope you’re having a great weekend!
i got stuck on #75 on the review…it seems easy enough, but i can’t figure it out. i looked on calcchat, & what they did confused me even more because i don’t think we went about solving a problem like that in class…if someone understands it, could you explain it to me? thank you!
hey olivia, yeah I am trying to do that problem now too. I set up a triangle with sides 85, 50, and x. And I made the angle between the 85 and 50 sides 15 deg. Then i tried doing the law of cosines which i think is what they do on calcchat. But they used cos165 instead of cos15 and I don’t understand why that’s correct.
Olivia and Meg,
for #75….
so i set it up on a graph, where the vector with the force of 50 pounds was on the x-axis and then a 15 degree angle inbetween them, and then the vector with the 85 pound force..this was all in quadrant I.
so the vector is equal to (rcos(theta), rsin(theta)), so the vector for the 85 pounds would be (85cos(15degrees), 85sin(15degrees))
and the vector for the 50 pound force is on the x-axis so the vector would be (50,0)
to find the resultant force, you would add the 2 vectors.
so the resultant force would be equal to (85cos(15), 85sin(15)) + (50,0)
hopefully this is helpful…sorry its kinda long and confusing.
Also, I have a question on #113 on the review. when trying to find the angle, arctan(4/0) is undefined…so how do you know that the angle is equal to pi/2?
Hello everyone!
Good work, so far!
As far as 113 (Sarah and friends): think about where is arctan undefined – that is pi/2! (and other areas, but this is what makes sense here!)
Happy reviewing (and programming!)
Mrs. Corricelli
ok thanks…yeah when i continued to think about it, it made a lot more sense
hey everyone.on the review for question 17, i can do it the long way, but i remember there was a formula mrs. corricelli gave us to do it more easily…but i can’t seem to find that formula in my notes.can anyone give it to me? its the one that has to do with finding the side of a building when you are only given two angles of elevation and the distance between them
Hello Ryan,
If no one responds to you, I can help you to remember it. However, I would say that a better use of your time would be to use a known formula to derive it and/or program it… If it is not accessible and/or derivable, it probably will not help you to understand. However, if you program or derive it, you will – by just doing this – pulling it apart and putting it back together – understand it SO much more than you would by memorizing a formula.
Again, if you need help/guidance with the derivation, see me.
Take care,
Mrs. Corricelli
Ryan, I know what formula you are talking about. I found it in my chapter 4 notes, on December 1st…Idk how to explain the forumla because it depends on the problem, but in terms of problem number 17, the height of the building would be tan 31° [(50 tan 17°)/ (tan 31° - tan 17°)]
I wasn’t sure if we are supposed to blog about tonight’s article here…but I didn’t see any other place to write it.
After reading the article, I was surprised that the ancient math problem involved such huge numbers “that if their digits were written out by hand they would stretch to the moon and back.” It’s smart that the mathematicians invented a program to do these calculations, and their results seem valid since they used 2 different computers to minimize errors and to make their results more reliable. At first I didn’t really understand the problem they were trying to solve, until I read it again and again….now it kind of makes sense. However, one thing I am confused about is what’s the exact purpose behind finding these figures? In what ways will finding congruent numbers help others? Are there any real life applications to this?
After reading this article, I was really amazed and surprised at what mathematicians can do. Solving equations with numbers that could not even fit into the main memory of computers and finding congruent numbers all the way since the Persian mathematician al-Karaji are amazing investigations. Since c.953, mathematicians have been working to discover new ways to solve complex problems. Mawra, I see your point in questioning the purpose, but I think that these new discoveries are going to come in handy in the future. It’s amazing what these people can do and just to think what we could do in the future.