Mathematical Modelling

While i was doing my daily routine of reading the blog, I've seen some homework that were posted by my peers. I should say that I'm quite impress by the quality of their work. I'm starting to really like this bunch of people. I can see that they are really enthusiastic to learn math. Now, i kinda want to go to the class and meet all of them, so i left their homework some comments.

First of all good job on the detailed answer. I really like how you put a lot of space so your solution will be easy to follow.After doing the whole question myself, I therefore conclude that Zeph's answer is the right one. There is something wrong with the algebra. There are many different ways to check this problem. One of them is to use your calculator. First of all, you need to plug in the function. Then press the 2ND button then TRACE then press 1.After that plug in your answer as the x value then press ENTER. You should see that the y value should be very close to 4. Thats the quick way of doing it.

-m@rk

Here's another comment from another homework.

Great work everyone! I really like that your solution is easy to follow because of the added space. After checking your solutions, I therefore conclude that it is perfect. Now, I just need to check two more questions from the other groups.

-m@rk

Critical Thinking

While I was surfing through the blog, I noticed that most of the post were talking about Mr. K's new gimmick of making his students think. His new gimmick is to tell one lie per day so that his students will critically analyze everything that he says. This method sorta reminds me of this blog post that i read on one of the blogs on my rss feeds. The post talks about another teacher that uses the same methodology to make his students pay more close attention to what he is saying.

Zeph,

I'm quite impress that you caught that lie. I didn't even caught that one when i was trying to redo the whole question by myself. It's quite nice to see that many of you guys are getting a lot from Mr. K's lies. I guess that his strategy makes all of you critical analyze what he is saying.Good job and keep up the good work!

-m@rk

Trigonometric Equations

While I was checking the blog for more questions to answer, I stumbled upon one of my classmates questions. This question is about trigonometric equations, so here was my response:

Benofschool,

Good job for trying to look for the answers. Your hard work only shows how dedicated you are to this class and how much effort you give into it.
Unfortunately, i don't think the answers are right.

Let's examine the first question first.

cos(2x)=1/2

Think of this as your regular algebra question. You can see that the only thing that is in your way is the cosine, so what you have to do is use arccos on both side to get rid of the cosine. That will leave you with this:

2x= 1.0472

Then with some more algebra you will get:

x= 0.5236 + kpi
AND the other other angle at quadrant 4 which is 2.6180 +kpi


Another way to solve this is to use the exact values of the unit circle.

cos2x= 1/2

We know that the cosine of 1/2 is pi/3, so that will leave you with this:

2x=pi/3

Now, again solving for x with some algebra we will get this:

x=pi/6+ kpi
AND
the other angle at quadrant 4 which is 5pi/6 +kpi

Im gonna let you finish up the next question. Hopefully that helps you in some way.

-m@rk

Tangent Function

Second post on my mentoring blog.While I was doing my regular routine of reading our blog the most common thing that i see people have problems with is the,tangent function. Anyways,what is the tangent function? It's time to put my thinking cap on and help my fellow classmates with this.


Zeph,

As for your other question. The graph of the tangent function can be viewed here: http://fooplot.com/index.php?q0=tan(x)

The tangent function has some cool properties. It has an amplitude of undefined, a period of pi and y intercept of zero.

I have so much more to say but i don`t want to spoil the fun.

-mark

Also, I've seen a similar question from Roxanne, so i decided to give her some insights about the tangent function. I gave her more details.


Roxanne,

If you want to see the graph of the tangent function, you can go right ahead and use fooplot.com. You will see that the shape of the tangent function is somewhat different from cosine and sine.

The graph of the tangent function has some distinct properties.It has a period of pi unlike both cosine and sine which has a period of 2pi.
Second, it has a y-intercept of zero. (There are so much more to say about this function but i wont go into them, because i don't want to spoil the fun).

Graphing the tangent function follows the same rule as graphing both cosine and sine functions. The general equation for the tangent function is f(x) = a*tan(bx+c)+d. You can see that it uses the same parameters.All the parameters work the same way as the one in the sine and cosine equations. It also follows the same algorithm DABC (but i prefer using BCDA).

I hope this helps you clarify things.

-m@rk

Function Notation

First post on my mentoring blog. Kind of weird trying to help my fellow classmates in their math studies based on my experiences and wisdom that I gained from taking this class last year.


Zeph,

Question #15 on exercise 2 is just simply using function notation. Since f (x) = 2x + 3 and you have to find k so that f(k+2) = k + f(k).
so we`ll work on the right side first, all you have to do is just substitute k+2 to x so you have:
2(k+2) + 3

On the other side since k is just a constant you just leave it and then again reading the function notation you need to substitute k to x so you have this:
k+ 2(K)+3

Therefore, you will end up with this kind of equation:
2(k+2) + 3 = k + 2k + 3

Then with the help of some algebra you will get this answer:
2k + 7 = 3k + 3
4 = k

-mark