Homework 16: Assigned 04.27. Due 04.30
1. This focuses on the Trigonometric movement. If you get stuck there are places online to help you, but don't jump there first. They may be using radians as well, so it may help you less than you think.
You are get into a ferris wheel, and are the last person to enter. The ferris wheel is three feet above the ground, completes a circle every 40 seconds, and has a diameter of 30 feet.
create an equation. You may want to use the desmos thing I made to help you. Link is http://www.desmos.com/calculator/qr9kz9lf2r
For how long in each rotation are you above 45 feet?
The ferris wheel stops after 4 minutes. where am I on the ferris wheel?
Extra: How fast is the ferris wheel going?
2. Glastonbury Mountain is just off to the east from here. There used to be a lot of people who lived there, but now it is mostly abandoned and part of the Bennington Triangle. Teenagers go up there, hang out and generally try to scare each other. But things are changing--people are moving in. Three families, in fact. They know each other well and are willing to share in some basic needs.
There are three houses. Call them A, B, and C.
These houses each need water coming from the well (W).
These houses each need electricity from the generator (G)
These houses each need propane from the shared Propane Tank (P)
You have plenty of piping for all of these different needs (W, G, and P), but there are some issues:
because you are on rocky ground, you cannot bury the pipes
none of the pipes can overlap
each person needs their own pipes from each utility directly to their house
This means that there are three different pipes from the Well that cannot overlap. These pipes also cannot overlap the three separate pipes from Propane, or the generator.
This family is depending on YOU to design the system for their utility needs. Design it in the best fashion--you may place the six objects wherever you want and make the pipes as convoluted as needed.
If, for some reason, you are not capable of accomplishing this task, dig into the reasons why. Attempt to come up with a reason that you are unsuccessful. A good, rational, clear reason.
Homework 15: Assigned 04.23. Due 04.27
1. In class we saw two examples of "Geek Logik". While I discussed some reasons why I don't like the whole book, I think it's an interesting idea--trying to quantify a decision based upon the positives and minuses. Notice in the examples there was often weight to the problems. Your job is to create one of htese types of equations and bring it to class for us to use and discuss. Important note: be aware of what possible outcomes there are for your function (think max value and minimum value that can occur) in order to determine your range for your decisions.
2. Below are some trigonometry word problems either using the law of sines or the law of cosines. The .pdf is "trig.laws.pdf." Do problems:
p. 415: 30, 32, 33
p. 422: 38, 40
p. 423: 48
Homework 14 (yes, I know we skipped some. I'm going with classes here). Assigned 04.21. Due 04.23
1. In class we showed the max distance a person can throw the ball happens at 45 degrees. But here's an extension. Say I have 2 players, each who can throw the ball at 60 mph. I want the ball to travel 400 feet as quickly as possible. In baseball, they often use a cut off person to achieve this (see video here). This is because they can often throw it faster this way -- more velocity in the x direction. Given this information, at what angle should each of the players throw to make the process as fast as possible. (in easy mode, assume the person in the middle takes no time to throw the ball again. For a more difficult question, assume it takes half a second for the person int he middle to catch the ball and then throw it again).
2. Below is "Right Triangle Trig.pdf". Answers are on the sheet. Look up how to find angles if you aren't sure. Solve each of them.
Midterm Assignment: Assigned 04.10. Due 04.20.
The midterm assignment is below. It is called "mitdterm.entry.15". Answer all questions fully and completely.
They get harder as the midterm goes on. Give yourself plenty of time.
These are due Monday, April 20.
As usual, let me see your thinking and reasoning. I want to know not just the answer, but how you got there and why you did what you did. For some, there are multiple possible answers. The clearer you make how you got to yours, the better it is for me (and your grade).
Homework Eleven: Assigned 04.02. Due 04.06
1. Below is "due.04.06.pdf". As you are working on these ten problems, focus on two things:
the answer. (obviously)
HOW you are getting the answer. Are you modeling, graphing, guess and checking, setting up systems of equations, using old notes, talking to other people, surfing the internet in hopes that someone has done the exact same problem and you won't have to do any more work, divining the answer in a scrying pool, or something else?
Our next class will be focused A LOT on those ideas. Be able to explain the questions--or explain what process you used and how far you got.
Here are some of my favorite what ifs:
https://what-if.xkcd.com/28/ <-- Steak Drop
https://what-if.xkcd.com/30/ <-- Planes
https://what-if.xkcd.com/34/ <-- Allowable Tweets
And wait-but-why is a site I just recently found and am digging:
http://waitbutwhy.com/2015/03/7-3-billion-people-one-building.html
http://waitbutwhy.com/2014/03/combined-wealth-world.html
Class Questions (I took some liberties)
Homework Ten: Assigned 03.30. Due 04.02
1. Below is "parent.movement.pdf". Do problems 15 - 20
2. One person at Bennington came back from long weekend with a terrible cold. They share it with two people. Those people each share it with two other people. Each of these 'Shares' we will consider a generation.
At what generation will everyone have had the terrible cold?
How many generations until all of Vermont has had the cold?
How about the entire WORLD?
3. If we take an integer and square it, what are all possible results for the ones place? Can you convince me of that fact?
(for example, we square 11 ... 11^2 = 121 ... so the ones digit is 1)
(if we square 14 ... 14^2 = 196 ... so the ones digit is 6)
Homework Nine: Assigned 03.26. Due 03.30
1. Below is a .pdf "ThreeQuestions.pdf". Work through these. Remember, if you can't solve something, you should be working towards an answer. Talk to a friend, a person in the class, someone who likes problems like this. Try to figure out a pattern, a reasoning, a goal for what a model might do for you.
2. This is you: http://abstrusegoose.com/353
Homework Eight: Assigned 03.23. Due 03.26
1. Below is a .pdf "Quadratic Questions". Work through these. If you have questions, e-mail away. Don't wait 'til the last moment--it'll take a while.
2. Below is a .pdf "domain.range.pdf". The first page is what we did in class. The next two are practice. We will go over them in class.
Homework Seven. Assigned 03.19. Due 03.23
1. Below is a .pdf "Your_Functions". Do those.
2. Below is a .pdf "function_assumptions". Do those as well. This is a little more in depth, so consider what you need to do here. You should be able to talk about these functions to start class on Monday. Plan accordingly as to how you are going to attack. If you aren't sure where to start, e-mail me and I'll try to send you in the right direction.
Homework Six: Assigned 03.16. Due 03.19
1. Below is a .pdf of "Linear Programming". Do the first two (we did the first one in class).
2. Create a system of equations like the one we did in class (the cars) that helps you analyze a problem. I'd like to consider all constraints, all issues that might arise from you problem, and what might me a minimum and maximum solution. We will be discussing and sharing in class.
3. Send me a quick, free form e-mail --
how is the class going so far?
Is it too easy, too hard or just right?
Is it meeting your expectations?
What can I do to help--and what can you do to help yourself?
Are there things I can do to make assignments, e-mail, classes easier to find or access?
What would you prefer -- a cat that always wanted to be petted, or a cat that was always three feet away from you?
What part of the course has been hardest ... the 'old school math', our way of thinking, or something else?
What can we do to make this class the most useful to you?
Anything else?
Homework Five: Assigned 03.12. Due 03.16
1. A quick reading: http://v.cx/2010/04/feynman-brazil-education
2. Solve the systems of equations in the sheet "Six Systems of Equations". There are multiple ways to solve a system. You should be comfortable with all of them.
Assignment Number One. Assigned 03.09. Due 03.16.
1. Find the .pdf "Assignment One" below. This is due by midnight on Monday, March 16. Be sure to show work where indicated, as well as make it easy for me to follow work and where you are in the Assignment. Extra points for clarity and neatness--remember, I'm trying to walk with you on the mathematical journey, so make it easy on me.
Homework Four: assigned 03.09. due 03.12
1. Head to the website on the three forms of a line. Try the problems there. Note which form they use when, and test yourself with the problems. http://cs.selu.edu/~rbyrd/math/equations/
2. Below you will find "Graphing Different Forms". Graph these, and then check your answers with a graphing utility (www.desmos.com is my suggestion--it's also a pretty sweet free application). Also a few more abstract questions are on the end.
Homework Three: assigned 03.05. due 03.09
1. Two sheets downloadable below: "Practice_Solving_Literal_Equations" and "fractional_operations"
Homework Two: assigned 03.02. due 03.05
1. Two sheets downloadable below: "Due Class 3" and "Kitties".
Homework One: assigned 02.26. due 03.02.
1. fill out this quick survey.
2. work on the problems linked to above.
3. after this first assignment, I will be e-mailing everyone the assignments; I just need to make the class list, which will be ready for the next class.