Honors Algebra II

1.

The bridges  supports are porabolas on the two outside ones and the one in the middle if you look at the reflextion, it is a circle.

2.Scribeing i thought was a really good idea. I liked it alot. The ability to get on and read and see it infront of you is alot easier then going through the book reading the words that half the time doesnt make sense and trying to put it all togather in your head and understand it. Scribe posting should carry on forever .

3  My two favorite posts are http://mrhiggins.net/algebra2/?p=205#respond because of the massive color use and how when you  read it you can figure it out and understand it . Also my other favorite is

http://mrhiggins.net/algebra2/?p=55#comments because of how much info is there.  Any one can go to it and learn that section.

This is the Moon. During its full moon phase, it appears as a circle in the sky. If a dot is placed in the center of this circle, the edge of the moon at any point is equidistant from the center point.

My two favorite posts were RHarp’s first post and KFrerik’s first post. In fact, both of RHarp’s posts went above and beyond what was asked for in a Scribe Post. It also really showed his personality. KFrerik’s post, written all in pink, really stood out to me. It was easy to tell who exactly posted it, and it showed her personality.

The only thing I didn’t like about the scribe posrts is that we cannot view more that about one half of a post at once because of the size of the viewing area.

Cartman’s head is an ellipse. The equation is (x - h)² / a² + (y - k)² / b² = 1. This ellipse is a contributor to the devolution of the human race. Rivaling it could only be the parabolas fixed in Peter’s chin. While I could give a large speech derailing the topic completely, I don’t feel like it. Cartman’s head is an ellipse, nuff said.

Favorite posts are from Bogen on Logarithms, and Bright on base numbers. Nicks was in depth, and I can’t say no to rainbows. Bogen had nice tips for remembering the way to do logs.

http://mrhiggins.net/algebra2/?p=200

http://mrhiggins.net/algebra2/?p=87

Wordpress was fine, although there were browser related issues. The layout was simple, even if people can’t left click the right category, or read. I felt we really didn’t do enough on this blog, perhaps a student focus per month, or something of the sort. Only needing to go on this site once every 45 days or so didn’t help build enthusiam for the site. Of course the fact I was looking forward to going onto a teacher monitored blog shows a lot about my social life. I digress with shame.

This is Qualacomm Field which is the staduim of the Sandiego Chargers. Now how this applies to conics is that   the shape of this staduim  is  an ellipse which is one of the crosssection for aconic. The formula for an ellipse  is:    ( (x-h)2/A2 ) +  ( (y+2)2 /B2)=  1. This equation was most likely  used in the constuction of thestadium.  Most all sports arenas are made in an elliptical shape in order to seat as many people as possible  around a rectangular field. Some stadiums aren’t made with an elliptical shape like the Horseshoe  (which is basically  just a parabola), but most are elliptical.

 Regarding scribe posting I really liked this and I wish i had this for some of my other classes. Word  Press as a program works pretty well the only complaint I have is that the text box starts so small but  you can change it so its not a big deal. I thought posting was easy and have no other complaints.

My first favorite scribe posts was our very first post done by RHarp about  Exponential Growth the  reason I like this post was because he went above and beyond what he need to and also explained  it in a different way which helped me understand it. The link is:  http://mrhiggins.net/algebra2/?p=55  The other post i liked was the intro to conics section  done by CSweet. The reason i like was because I think that the post described the section really well and also presented excellent images to back up what she was saying The  Link is http://mrhiggins.net/algebra2/?p=210

Now since i mentioned the San Diego Chargers here is a random picture of Ladainain Tomlinson, who is one of the N.F.L.’s leading rushers for the last couple years. Thats all I have peace.

This is a perfect example of two parabolas side by side. Each parabolas has four parts to it. The axis which runs right down the middle of each arch. The vertex which is the farthest most point or the point at the very top of the arch. The focus which is below the arch. and the Directrix which is the same distance from the arch as the focus except its above the arch. This can all be figured out with the equation of (x-h)²=4p(y-k) or (y-k)²=4p(x-H).

This idea was a very good one and wordpress worked fine. The only problem was that I had trouble finding things sometimes. And once it wouldn’t let me put any foplot graphs on it.

one of my favorite post was 0cassela’s post on base numbers and color coding http://mrhiggins.net/algebra2/?p=205

Another of my favorite post was 0lewarnv’s post on graphing. It must have taken awhile to do all of those graphs which were done very well. http://mrhiggins.net/Algebra2/index.php?paged=3.

1.This hourglass demonstrates the characteristics of (you guessed it!) a hyperbola. This device used to tell time dates back to the 14th century. Though they technically are not connected like this one, it shows other properties of hyperbolas. For instance, there would be an imaginary line through the glass called the transverse axis. On this line there would be the center and both foci. The equation for this would be (y-k)²/a²-(x-h)²/b²=1, since the hyperbola is vertical.

2.As long as I can remember how to log in, make a new post, comment, etc., using Wordpress is relatively easy. Since I don’t use it every day, I forget what to do when it comes time for me to be the scribe. One thing that would make using this site easier would be creating a more consistent way of titling posts. Correctly categorizing posts would also make it easier for the reader to benefit from the information. Also, starting sooner next year would give everybody the opportunity to post multiple times. However, I really liked creating and using this blog. It is a handy reference.

3. I really like this post (http://mrhiggins.net/algebra2/?p=102). This was a difficult topic for me and reading this was very helpful. I also like this post (http://mrhiggins.net/algebra2/?p=234). The pictures and diagrams made this very easy to understand (I’m a visual learner).

These buttons are perfect examples of a Conic Cirlce.
The equation for a concic cirlce is (x-h)+(y-k)=r².
Plus, and more importantly, there pretty freakin sweet !

Doing the posts was a really good idea. Number one, it gave us a chance to learn some new computer skills, wich is deffinatly important in this day in age. Number two, if you were absent the day before, or just needed a little refresher of the notes, they were right there handy at your computer. Number three, and probably the best reason, NO HOMEWORK :] If you were the scribe for the day you didnt have to worry about doing your homework, you just had to go home and get on the computer which 90% of us do everyday anyway.

 My favorite post that some one did was probably the one that Ryan just did about Micky Mouse. Just because it’s such a “Ryan” thing to do. haha I didnt even have to look to see who’s post it was. It was a really good idea for this student post too. Way to go Ryan :] (& plus, i <3 Ryan’s dad. hahaha) Click the link to check it out (http://mrhiggins.net/algebra2/?p=262)
I also really liked Charles post, because she had really nice pictures to go with it. Take a look (http://mrhiggins.net/algebra2/?p=210)

This picture of gears is a good example of the circle conic.  The equation for a conic circle is (x-h)+(y-k)=r².  What more is there to say? The gears intersect in order to keep spinning. 

I think that the scribe posts were a good idea because they helped students if they missed a day.  The posts gave all the needed information to catch up with class.  The only problem with the posts is when you are the scribe, it takes almost triple the time it would take to do the normal homework.

One of the posts that i really liked was 0brightn’s post on base numbers.  It made base numbers easy to understand and it was very simple to understand.[http://mrhiggins.net/algebra2/?p=200]

Another good post was was 0cooperr’s post on compound interest.  It was also very easy to understand the color changes help to keep my short attention span.[http://mrhiggins.net/algebra2/index.php?paged=3]

Most people know what a slinky is. They are those fun little toys from the 1940s that could “walk” down steps. Here’s the catch though. They don’t even run on batteries! Isn’t that a revolution? Anyways, this particular one happens to be rainbow-colored and made out of plastic. Personally, I think the metal ones worked a whole lot better, but oh well. Moving on to the assignment…

 1. The slinky is a perfect example of one of the conic sections; the parabola, and a good example of another; the circle. Since it can be picked up and moved, the slinky can represent all the directions that the parabola can take. This means that the slinky represents the equations (x-h)²=4p(y-k), (x-h)²=-4p(y-k), (y-k)²=4p(x-h), and (y-k)²=-4p(x-h). In addition, the slinky can somewhat represent the fact that parabolas can go on forever on a grid by being stretched out. Meanwhile, the slinky’s rings can somewhat represent the circle. Although the rings never connect, the fact that the rings repeat make it look like it’s made out of a bunch of circles. All I can really say now is that the circle formula is (x-h)+(y-k)=r².

2. Overall, I didn’t really mind our scribe process. The only thing that could be improved is composing with Wordpress. I have found it to be somewhat wonky while typing in the past with things such as the subscript and superscripts and even with the colors. I do like the fact that there are so many colors and options to choose from. It makes customizing one’s own post to be rather interesting. Meanwhile, the only thing that I have found to dislike is having to upload pictures from my own hard drive. It’s slightly inconvienent to have to download a picture in order to post it. Other than that, it has been fairly easy posting with Wordpress.

3. Out of all of the posts that have been made this year, it is actually somewhat difficult to choose just two. However, if I must choose just two, than I shall. In particular, 0brightn’s post on base numbers is astounding. I can tell that he put a lot of work into it. I like how it goes really in depth and even tells a little about the history of some of the other bases. In addition, his use of coloring is good, as well as his format. If everyone’s post was like his, then it would be extremely easy for absent students to catch up. You can find his post here: http://mrhiggins.net/algebra2/?p=200. My second favorite post would have to be 0bogens’s post on section 8.4: Introduction to Logarithms. I believe she did a good job with the format and with her use of pictures. Although the post is short, I believe that this somewhat helps it. There is something comendable in being to the point. Her use of hidden answers to practice problems was also good. The post can be found here: http://mrhiggins.net/algebra2/?p=87.

1. Hmm…. wonder who this is. Yes, it’s Mickey Mouse! Mickey’s ears are circles which are conic sections. The equation is (x-h)+(y-k)=r² for a circle. What’s interesting is that Mickey’s ears are always circles no matter where the camera is. Weird huh?

2. Using the scribe post was helpful if you weren’t in class the day before. Usually, the student that wrote it did a very good job and you could understand it after reading it once or twice. I thought that on some days, a scribe post wasn’t needed, like if we only learned one or two small things. This should have just been added onto the next scribe post the following day. All in all, the scribe post was very helpful.

3. One of my favorite posts was by 0becketh because she made it interesting and fun and added in pictures to make it more exciting. Also, I liked the random fact for the day. (http://mrhiggins.net/algebra2/?p=226). I also liked 0sweetc’s post on conics because she added in neat pictures and colorful text that made the post more fun to read. She did an overall good job on the post. (http://mrhiggins.net/algebra2/?p=210).

2

1)  The smile of the “smiley face” is in the shape of a parabola.

  The smiley face was designed in 1964 in Worcester, Massachusettes by Harvey Ball, and has become a crazy-huge symbol all over the world.  

   The equation for a parabola is: (x-h)^2=4p(y-k)             (h,k)=vertex    p=distance from vertex to focus

 2)  The good thing about doing these scribe posts is that they give us an opportunity to work with computers and see how things like blogs and such really work.  It was a fairly good experience all around.

       The bad thing was that it was soooo time consuming and sometimes very frustrating because we had an older computer taht wouldn’t cooperate with the website. 

3)  One of the best scribe posts, recently, was Haley’s on ellipses and eccentricity.  The picture showing the orbits in the solar system really describes best how ellipses work.  Also, it was well set up and understandable.   http://mrhiggins.net/algebra2/?p=226

    Another scribe post that I found quite informative was the scribe post over base numbers.  I think it was done by Justin.  That can be a hard thing to explain, especially online, but I think that he did a fine job of it, and kept it neat, simple and to the point.   http://mrhiggins.net/algebra2/?p=200

Here’s an application of a parabola that most of us use every single day, especially since we’re all new drivers or at least soon-to-be new drivers.

Using a parabolic mirror, you can point a light at a certain point, or focus, of the mirror and all the light particles will start to go in different directions. But, reflecting off the mirror, they will all shine in one area, allowing the light to move great distances. This technology is used in car headlights.

The formula for a parabola is (x-h)²=4p(y-k).

I really didn’t mind doing the scribe posts, especially because we didn’t have to do the homework. That was nice; it kind of gave you a break to do something different. I know I almost forgot to do the story on the moodle, though. I agree with SBenson that the moodle shouldn’t effect our grade because it’s pretty easy to forget. I can also see how some people didn’t enjoy this assignment because not everyone is very experienced with computers. Personally, I thought it was a good way to get people a chance to experiment with technology. I also agree that the layout was complicated sometimes; even for this post I have to use Firefox because that sidebar didn’t show up again on Internet Explorer. Maybe if the layout was a little more clear it’d be a bit more enjoyable and less frustrating.

One post that I thought was well done was NBright’s post about base numbers. Here’s the link: http://www.mrhiggins.net/algebra2/?p=200. I liked it because it seems as though he put a lot of effort into it. I know that, even when you only have a little bit to write about, it takes a lot longer than you would expect. It takes even longer to put all the little details like colors in, and NBright’s post is extremely organized and colorful.

Another post that was good was CSweet’s post about conic sections. I know it’s kind of repetitive (at least two other people have named NBright and Csweet), but it’s true. She found some very nice pictures of conics that definitely illustrate the point where some people may not have chosen to search for pictures. It’s also very colorful and clear about the topic. Like NBright’s post, it’s easy to read and informative. Here’s the link: http://www.mrhiggins.net/algebra2/?p=210.

**Any cylinder sliced on an angle will reveal an ellipse in cross-section

 1. This is a picture of Tycho Brahe Planetarium in Copenhagen.  This cylindrical building was designed bye the Danish architect Knud Munk.  This Planetarium is on of the largest of its kind in Europe.  It was opened in 1989.  The theater screen in 75 ft and the theater seasts 275 people.  There is even a gift shop and restaurant inside of it. 

The equation for this ellipse would be (x-h)²/a²+ (y-k)²/b²=1

SOURCES USED:

 http://www.planetware.com/copenhagen/tycho-brahe-planetarium-dk-z-coptp.htm

http://britton.disted.camosun.bc.ca/jbconics.htm

2. I think the scribe post has been an interesting part of algebra 2.  It is fun to create the post.  Some of the difficulties were at first it was confusing to learn how to upload pictures and graphs, but now I understand it.  I think you should continue to do the scribings and post.  Wordpress is also easy to use and organizes the information very well.  Overall I really don’t have any negative imput about the scribe posts.

3. I like CSweet’s scribe 10.3 Introduction to conics because it has very clear pictures of all the conics and she explained the section very well.  She also did a good job with her examples and organizational skills.

http://mrhiggins.net/algebra2/?p=210

I also like NBright’s on Base Number’s because he explained it very well and gave a good background on why we have base numbers and what they are used for.  His examples were very good and easy to understand

http://mrhiggins.net/algebra2/?p=200

While an actual clock is a cylinder, it face is a circle. It is very obvious, since the minute hand is the radius, the point is in the very center that connects the hand to the clock, and the lines around the clock are it’s locus, which forms a circle.

I really don’t mind making post, but some times I found it hard to post a picture. My first scribe post had a lot of graphs on it and it was easy to make them on fooplot.com.  But I was on a laptop and it wouldn’t let me post the graphs no matter what I did.

My favorite recent post are Kayla K’s 10.5 and 9jonesb’s 10.4. I loved how they broke it up in to sections and gave basic directions to do problems. It made it easier to understand because it was so organized.

1. Hyperbolic and parabolic mirrors and lenses are used in systems of telescopes. R-C telescopes use two hyperbolic mirrors as the primary and secondary mirror, which correct for coma, which also results in a smaller spot size on and off axis; Cassegrain telescopes have a primary parabolic mirrors focusing its rays onto a convex hyperbolic secondary mirror, which yields correction over moderate fields both for visual and photographic astronomy. Like ellipsoidal mirrors and parabolic mirrors, hyperbolic mirror also can be on-axis or off-axis and can be supplied in a variety of materials, including BK7 glass, copper, fused silica, UV grade fused silica, nickel, and other optical glasses. Common coatings include none (uncoated), enhanced aluminum, protected aluminum, dielectric, protected gold, and silver. 

2. This scribe process has been fun. Although, at times, the website can be confusing such as, using the different passwords, and trying to find that little login button. It did give me some trouble  However, it has been a good learning experience and it was fun doing the story and seeing other student’s posts. It is definitely something to keep up. Oh, and I have no clue what WordPress is, so I’m not too sure what to say about it.

As you can see the St. Louis Arch is an example of a parabola IN REAL LIFE! This parabola would be a negative parabola because it is facing down. Parabolas are used very often but people don’t tend to notice. Another example would be the McDonald’s golden arches. Yum Yum! The equation to graph this conic would be: (x-h)²=4p(y-k)

I didn’t like doing the scribe post because I am not very good with computers. I often got confused and for some reason my computer made it even harder to do. That’s why I am at hbeckett’s house doing it right now. One thing I would change is to not do the story. I do find the story amusing but it shouldn’t be mandatory.

My favorite scribe post was also 10.3 Intro to Conics by Csweet. It was very descriptive and also colorful and had helpful picture http://www.mrhiggins.net/algerbra2/?p=210. My other favorite was Nbright’s Base Numbers. It was very helpful and colorful. It also looked like he put a ton of work into it http://www.mrhiggins.net/algebra2/?p=200.

This is obviously a satilite dish. These are examples of parabolas beacuse of their shape. Engineers use the parabola formula (x-h)²=4p(y-k), to design and build satilite dishes. One can also use the formula to figure out the dimensions of a dish.

I like the fact that we did scribe post. It helps mostly when a person misses a day and needs the notes/homework from the previous day or days. It was also somtimes easier than doing the homework. The only thing i would change is to make it easier to get into the system to be able to make the post. I think this is a good idea and wished we would have started it earlier in the year.

My two other favorite post other than the ones I did were made by 0bensons and 0kiedrok. Obensons (http://mrhiggins.net/algebra2/?p=225) was one of my favorites casue it was on a day i did not understand much. After reading the post I pretty well understood everything i did not from class. 0kiedrok’s (http://mrhiggins.net/algebra2/?p=225) is also one of my favorites. This is becasue the post was made on a day i missed. So this post was very helpful at getting the notes I needed and understanding what I missed that day in class.

Doesn’t this look good?  This is a pepperoni pizza, obviously.  In class, we learned about the conic section the circle, and this picture is a perfect example of one in real life.  Also, the pepperonis themselves are circles.  The equation to graph this pizza or any circle would be (x-h)+(y-k)=r² 

^{I think that the scribe posts are a good idea, and they’re alot easier than the homework sometimes.  However, I’m still not completely sure how to get to it every time, so it would be nice if it was a little easier to find.  It is usually pretty easy to do once I find it, but sometimes it’s also hard to upload a picture I might need.}

I liked Charlie’s 10.3 Intro to Conics, http://mrhiggins.net/algebra2/?p=210, because it was really easy to understand, and the pictures really helped.  It looked like she put a lot of work into it and I liked the color.

I also liked the post with the picture of the Eiffel Tower.  I don’t think there’s a link to it, other than going to the scribe post to see it, because it doesn’t even say who made it.  I liked it anyway because the picture really gives you perspective on how big the thing is, and I really want to go see it someday. 

Right Triangle Trigonometry!!!

-Given a right triangle, there are six trig. ratios which use side lengths and an angle.

(***think back to SOHCAHTOA***)

SIX TRIG. RATIOS:  1. sine, 2. cosine, 3. tangent, 4. secant, 5. cosecant, 6. cotangent

sin ?=opp/hyp —> csc=?hyp/opp    cos ?=adj/hyp —> sec ?=hyp/adj   tan ?=opp/adj —> cot ?=adj/opp             ** <A=?

The opposites are:   sin and csc ,  cos and sec,   tan and cot

 FIND ALL SIX TRIG. FUNCTIONS: 

Example 1:

   b=9, a=12, c=15, <A=?

sin ?=12/15=4/5      cos ?=9/15=3/5      tan ?=12/9=4/3

Solving A Triangle:

-Solving a triangle means finding all side lengths and angle measures.

EX 2:        WHEN: <B=63°,  a=15

(**act like 63° is ?**)       ***make sure your calculator is switched to degree (under mode) in order to solve these problems!!!

1)tan 63°=b/15 –>*15—> 29.440=b

2)180°-90°-63°=<A –>27°=<A                                    3) (a^2) + (b^2)= (c^2)–> (15^2)+(29.440^2)= c^2 –> 33.040=c      

***use common sense knowledge you already know about triangles (1. sohcahtoa ,  2. angles=180° ,  3. (a^2)+(b^2)=(c^2))

<A=27°, <B=63°, <C=90°,  a=15,  b=29.440,  c=33.040

     -Every right triangle with an angle of 45° has the same ratio of sides.

      -Both legs are x and the hypotenuse is x?2

EX 3:  if the legs are 5, than the hypotenuse= 5?2               EX 4:  if the legs are 7?2, than the hypotenuse is 14    

 EX 5: if the hyp. is ?11, than the legs are ?11/?2

2. 30°-60°-90° Right Triangles

     -Every right triangle with the angles 30-60-90 has the same ratio of sides.

     *hyp=2x  ,  opp 60°=x?3  ,   opp 30°=x

EX 1:  if the hyp. is 10, than 10/2=5 (opp. 30° angle), 5?3 (opp 60°angle)

EX 2:  if the side opp. the 30° angle=8, than the hyp. = 16 (8*2)  and the side opp. the 60° degree angle is 8?3

EX 3:  if the side opp. the 60° angle= 12, than the side opp. the 30° angle= 12/?3   and the hyp.= 24/?3

*Be able to apply these things to “real life” situations (story problems).

**This looks confusing, but is not that hard…

             *HOMEWORK!!!–> pg.772 #5, 6, 8, 9, 15, 16, 22-28, 45, 48, 50

This student focus to be completed into three different pieces.

1. Find a picture of one of the conic sections in a real life situation. Describe anything specific about the conic section. I have provided an example at the bottom of this post.
2. Provide some constructive criticism to our scribe process. Is there anything that needs to change? What did you like? What did you not like? How difficult/easy was it to post using Wordpress?
3. State your favorite two scribe posts other than any of your own. Remember, at the very bottom of the blog, you go to older entries. We have many many entries at this point. Please provide a link to the posts and describe why you like the posts. Remember, “It was cool” is not a description.

Obviously, the movement of the planets has to do with the fact that the orbit is elliptical. In class, we discussed the concept of eccentricity (measure of the ovalness), which can be used to measure how skewed the orbit is from being circular.