math

In Unit 4, there are three main topics, variation, inequalities, and linear equations. You will be exposed to all three topics by either formulating a response or commenting on a classmate’s response to each one. In your original response, you will choose

 

one type of problem to solve and post a complete solution. Then, in your responses to two classmates, you will comment on posts which involve the other two types of problems.
Original Response

1. The problems intended for use in this Discussion Board have been shared with you via Google Drive.  You should have received an email from your instructor that includes a link to the Excel document in your Google Drive listing the problems.  You can also access this Excel doc by clicking on “Drive” up on the top navigation bar of your gmail account.  Once you enter this document, select a variation, inequality or linear equation from the list and claim it by entering your name next to it.  This is a shared document so the only change you should make is to add your name to the problem that you choose.
2. Begin your response by typing the problem so that your classmates will know what problem you are solving.
3. Write a complete solution, showing all steps used in solving the problem. Explain each step as if you were the expert explaining it to a novice.

Responses to Classmates

4. Find the posts of two classmates who solved problems other than the type that you solved. In other words, if you solved a variation problem, you need to respond to a classmate’s formula problem and a classmate’s linear equation. Make sure that your responses to your classmates are substantive and advance the Discussion. You can check the classmate’s solution, show a different way to solve a problem, or help a classmate who has a question. The possibilities are endless.

LETTER FROM THE PROF.

Unit 4: Variation, Inequalities, and Graphing

 

Hi Great Class!
There are two concepts that are very important in this week’s learning objectives: slope and intercepts. Intercepts are where the solution line crosses the axes of the graph. Where x = 0, the solution line will cross the y-axis at some point, and that point is called the y-intercept. Where y = 0, the solution line will cross the x-axis at some point and is called the x-intercept.

 

In ski areas, they really understand the term of slope: when the ski slope is steep or when it is easy. We intuitively understand slope. However, to calculate the slope mathematically, we calculate the change in height (the change in the y-value) as the distance changes (the change in the x-value). If the hill slopes down 3 feet for every 10 feet of horizontal distance, that’s a negative slope of -3/10.  If we are going up in the ski lift and we go up 5 feet for every 10 feet of horizontal distance, that’s a positive slope of 5/10 or 1/2.

 

When we discuss slope in algebra, we use the letter-m. (Don’t ask me why we use the letter-m, I haven’t the foggiest idea. However it has been suggested that it is because it is the first letter of the French word “monter”, meaning to ascend or climb.)

Here’s the LINK …

The problems intended for use in this Discussion Board have been shared with you via Google Drive.  You should have received an email that includes a link to the Excel document in your Google Drive listing the problems.  You can also access this Excel doc by clicking on “Drive” up on the top navigation bar of your gmail account.

Tech support can help you find this, if needed.

Once you enter this document, select a variation, formula or linear equation from the list and claim it by entering your name next to it.  This is a shared document so the only change you should make is to add your name to the problem that you choose.

Here’s the link …

https://docs.google.com/spreadsheet/ccc?key=0Atyn_4TsRvl5dEdmTHgxOUlVUG1LaWlxOVd2M2EzYXc&usp=sharing

BTW — if there are no problems left by the time you access this document, then you may simply select a problem from our text in the readings for this week.

STUDENT 1

Problem: T varies directly as S.  If T = 12 when S = 40, determine T when S = 10.

If the variable T varies directly to variable S, and K is the constant, then the equation is as follows:

T = KS

We need to solve for the constant K first to determine the variable T. We use the variable amounts provided to determine K. T=12, S=40, and K.

T = KS

12 = K(40)

12/40 =K(40)/40

3/10 = K

Now we can input the constant K= 3/10, into the equation to find the variable T as it varies to S=10.

T = KS

T = 3

/10(10)

T = 30/10

T = 3

Check the answer by verifying the constant K when T=12 varies to S=40.

T = KS

12 = 3/10(40)

12 = 12

0/10

12 = 12

This verifies the constant K=3/10 is correct.

Therefore T=3 varies directly when S=10.

STUDENT 2

The volume, V, of a gas varies inversely as the pressure, P, on it. If the volume is 180 cm3 under pressure of 40 kg/cm2, what pressure has to be applied to have
a volume of 360 cm3 ?

V = k/P, where k is constant

thus k = V*P and

P = k/V

If V = 180 cm3 then P = 40 kg/cm2 and we can find k

k = 180 * 40

If V = 360 cm3 we need to find P

P = k/V

P = 180*40/360

P = 30 kg/cm2

We have to apply pressure of 30 kg/cm2 to have a volume of 360 cm3.