Normal Human Body Temperature

[harpazo]

Section R.2
Algebra Essentials
Michael Sullivan
Textbook: College Algebra Edition 9

Normal human body temperature is 98.6 degrees F. A temperature x differs from normal by at least 1.5 degrees F is considered unhealthy. A formula that describes this is

|x - 98.6| ≤ 1.5

A. Show that a temperature of 97 degrees F is unhealthy.

Solution:

|x - 98.6| ≤ 1.5

Let x = 97

|97 - 98.6| ≤ 1.5

| -1.6 | ≤ 1.5

1.6 ≤ 1.5...This is an untrue statement. I conclude that a 97 degrees F is an unhealthy temperature.

B. Show that a temperature of 100 degrees F is not unhealthy.

Solution:

|x - 98.6| ≤ 1.5

Let x = 100

|100 - 98.6| ≤ 1.5

| 1.4 | ≤ 1.5

1.4 ≤ 1.5...This is a true statement. I conclude that a temperature of 100 degrees F is NOT unhealthy.

I'm almost sure to be right for A and B.

 

[lev888]

Are there answers in the textbook?

 

[harpazo]

Are there answers in the textbook?

The textbook by Sullivan, like most textbooks, only has the answers to odd number questions. I only post even number questions.

 

[Dr.Peterson]

If I were studying on my own, I would only do the odd-numbered questions. You lose nothing by not doing the evens, which are going to be essentially the same as the odds -- they are there only so a teacher can assign them and find out whether you can do them without seeing the answers. They don't teach or test anything not already present in the odds (most of the time).

That's how I use them: I tell students to do the odd problems to learn, and a few of the even problems to show me (and themselves) that they have really learned. Since you have no one but yourself to show, you don't need to do that.

 

[harpazo]

If I were studying on my own, I would only do the odd-numbered questions. You lose nothing by not doing the evens, which are going to be essentially the same as the odds -- they are there only so a teacher can assign them and find out whether you can do them without seeing the answers. They don't teach or test anything not already present in the odds (most of the time).

That's how I use them: I tell students to do the odd problems to learn, and a few of the even problems to show me (and themselves) that they have really learned. Since you have no one but yourself to show, you don't need to do that.

The odd number questions only have the answers in the back of the book. Step by step solutions are not provided. What good is it to know the answer to a question and not know how to get there?

 

[Dr.Peterson]

The odd number questions only have the answers in the back of the book. Step by step solutions are not provided. What good is it to know the answer to a question and not know how to get there?

This, of course, is an entirely separate issue. The issue at present is that you don't need to ask people about even-numbered questions, as you have been doing a lot, because you don't need to do them at all in order to learn. If you keep doing that, you'll eventually frustrate people ...

But it is a valid question: what good is it to know the answer? Mostly just so you can know you're right, and move on, or can know you're wrong, and try again. It's not a good idea to try to work backward from the answer; students who do that too often invent a wrong way to get that answer!

Now, what do you do if you try a problem, and check in the back, and find that you are wrong, and still can't get the right answer after a couple tries? Then, of course, you can feel free to show your work and ask us for help! (If you had a teacher, you would ask them for help.) That's why we're here, and why there are teachers. As much as an author may imagine otherwise, a book alone will rarely be enough.

For many textbooks, it is possible to get a "student solutions manual" that gives complete work for all odd problems. These are probably harder to get as a matching set if you aren't buying new, of course. And they don't fix everything -- they may show a method that doesn't match what the author of the main text taught, or that doesn't match your own way of thinking, or that skips a step you need help with; or they may be wrong (because humans like you and me write them). I've had many questions from students who were frustrated by these books. But that's the publisher's answer to your complaint here: They do provide full solutions (for a price).

If you are wise, there is another reason for your comment: Even when you get a correct answer, you can't be sure that your work is all it should be. That, of course, is why we ask you to show your work when you have a question, so we can see if you got the right answer in a valid way. (I don't say "in the right way", because there may be many, and what's best for you may not be what I'd do.)

So there's my recommendation for using this site effectively: Do the odd problems to learn, and ask for help on them when you need it, following the guidelines out of respect for the helpers. Don't just send in questions to fill a daily quota, whether you need help or not.

 

[harpazo]

This, of course, is an entirely separate issue. The issue at present is that you don't need to ask people about even-numbered questions, as you have been doing a lot, because you don't need to do them at all in order to learn. If you keep doing that, you'll eventually frustrate people ...

But it is a valid question: what good is it to know the answer? Mostly just so you can know you're right, and move on, or can know you're wrong, and try again. It's not a good idea to try to work backward from the answer; students who do that too often invent a wrong way to get that answer!

Now, what do you do if you try a problem, and check in the back, and find that you are wrong, and still can't get the right answer after a couple tries? Then, of course, you can feel free to show your work and ask us for help! (If you had a teacher, you would ask them for help.) That's why we're here, and why there are teachers. As much as an author may imagine otherwise, a book alone will rarely be enough.

For many textbooks, it is possible to get a "student solutions manual" that gives complete work for all odd problems. These are probably harder to get as a matching set if you aren't buying new, of course. And they don't fix everything -- they may show a method that doesn't match what the author of the main text taught, or that doesn't match your own way of thinking, or that skips a step you need help with; or they may be wrong (because humans like you and me write them). I've had many questions from students who were frustrated by these books. But that's the publisher's answer to your complaint here: They do provide full solutions (for a price).

If you are wise, there is another reason for your comment: Even when you get a correct answer, you can't be sure that your work is all it should be. That, of course, is why we ask you to show your work when you have a question, so we can see if you got the right answer in a valid way. (I don't say "in the right way", because there may be many, and what's best for you may not be what I'd do.)

So there's my recommendation for using this site effectively: Do the odd problems to learn, and ask for help on them when you need it, following the guidelines out of respect for the helpers. Don't just send in questions to fill a daily quota, whether you need help or not.

I will post only odd number questions from now on. You need to understand one thing. I said this many times through the years in several forums. I do NOT RANDOMLY SELECT QUESTIONS from sections without trying at least three times to find the answer on my own.

My goal is not to bombard the forums with hundreds of questions just for fun or to drive people bunkers here. Trust me, this is not my intention. What do you mean work backward from the answer? Do you mean solving questions that the book does not provide answers to? I often find that even number questions are detailed (with several parts) and more interesting (the topic is less dull).

Again, I never, and I do mean never, post a single question without first trying several times on my own. It is super frustrating, however, learning how to solve questions in the early sections of the textbook to find out several chapters later, that I have already forgotten the early chapters.

 

[Dr.Peterson]

What do you mean work backward from the answer? Do you mean solving questions that the book does not provide answers to? I often find that even number questions are detailed (with several parts) and more interesting (the topic is less dull).

Some students look at the answer in the back, see that it is, say, 10, and then ask themselves, "How could I get a 10 from the data in the problem?" That's what I mean by "working backward from the answer". (How could I have been referring to problems that have no answer given??) This doesn't teach you to apply the methods or concepts you are learning, even if you find the right method. (I'm not suggesting that you have done that, only that this is what some students think is "what good it is to know the answer".)

Yes, occasionally an even problem will look interesting and seem worth doing; and other times I find that there is no odd analogue to an even problem, just because the author apparently didn't notice that it has an interesting special feature. I don't think anyone will object if you ask about such an interesting question. (I said "most of the time" in post #4 with this in mind!)

I'm trying to nicely suggest to you ways to avoid the animosity you seem to provoke (and which I try not to join in). I hope you can take it in that spirit. I didn't accuse you of anything. It just seems that sometimes you submit things you didn't need to submit, and these are some ways to avoid appearing to just write for the sake of writing.

 

[harpazo]

Some students look at the answer in the back, see that it is, say, 10, and then ask themselves, "How could I get a 10 from the data in the problem?" That's what I mean by "working backward from the answer". (How could I have been referring to problems that have no answer given??) This doesn't teach you to apply the methods or concepts you are learning, even if you find the right method. (I'm not suggesting that you have done that, only that this is what some students think is "what good it is to know the answer".)

Yes, occasionally an even problem will look interesting and seem worth doing; and other times I find that there is no odd analogue to an even problem, just because the author apparently didn't notice that it has an interesting special feature. I don't think anyone will object if you ask about such an interesting question. (I said "most of the time" in post #4 with this in mind!)

I'm trying to nicely suggest to you ways to avoid the animosity you seem to provoke (and which I try not to join in). I hope you can take it in that spirit. I didn't accuse you of anything. It just seems that sometimes you submit things you didn't need to submit, and these are some ways to avoid appearing to just write for the sake of writing.

I totally understand what you are saying and agree. Maybe I do provoke anger and dispute in the forums. This stops today. I thank you, Dr. Peterson, for your tips and reply.

Questions for you.

1. When did you know that math is a natural talent for you?

2. How long have you been teaching?

3. Have you taught graduate level courses like abstract algebra, algebraic topology, differential geometry, axiomatic geometry, etc?

4. I love math but dislike statistics. What math course do you dislike, if there is one for you? If so, why do you dislike the course?

5. Lastly for tonight, why do you like math? Why do you find the subject interestingly enough to become a math professor?

Thank you.