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I am new to matrices (and just about everything else), so be gentle. LOL
Can the following problems be solved?
And the second one (multiplication):
Bobby,
You got ahead of me, I am still trying to figure out how to properly express (e). LOL!
Charlie
This class is getting ridiculous. We have managed to go from large prime numbers to permutations & combinations to logical reasoning (where I had to explain the error in Zeno's "Achilles and the Tortoise" Paradox) to quadratic equations. I am stumped yet again. I am quickly realizing that the accelerated classes are incredibly challenging when your instructor expects you to research on your own to learn the material on your own.
Anyway, below is the problem I have now. It consists of several parts. I will put what I have come up with as answers, but the later questions don't work with my answers. It's hard to explain, but, hopefully it'll become clear.
Problem:
A retailer spent $48 to purchase a number of special mugs. Two of them were broken in the store, but by selling each of the remaining mugs for $3 above the original cost per mug, she made a total profit of $22.
Construct an equation that will allow us to solve for the number of mugs, denoted by n, that were originally purchased.
(a) If the price for n mugs is $48, how can we express the cost per mug?
***** My answer is below*****
(b) We are told that the retailer, in order to make a specific profit, sells the remaining mugs for $3 more than the original cost per mug. Using this information, and your answer to step (a), how can we express the selling price per mug?
*****My answer is below*****
(c) Since two of the mugs were broken in the store, how can we represent the number of mugs available for sale?
*****My answer is below*****
(d) Use your answers from steps (b) and (c) to construct an expression for the amount of money made on the sale of the remailing mugs.
*****My answer is below*****
*****I think I have it right so far*****
(e) The profit on the mugs can be found by subtracting the cost of the mugs from the amount of money made on the sale of the mugs. Write an equation that states this relationship between the money made, the cost, and the profit. HINT: If written correctly, your equation will contain only one variable, n.
*****My answer would be below, if I could figure one out to put there.*****
Then, the following problem refers to the answer that I don't have. It is:
Rewrite the equation that you wrote in step (e) in the standard form of a quadratic equation:
My head feels like it is going to explode!! I know I have been asking for a lot of help lately, and you have no idea how much I appreciate your assistance. I really have learned more here than I have in class. If it gets to where I am wearing out my welcome, please let me know. I really don't want to have to ask for help all of the time, but I don't know where else to go. I am going to continue to try to figure it out while waiting. I have actually discovered some errors in my equations while typing them out (the corrected versions are in this post), so hopefully, I can figure it out. If I do manage to do so, I will post a follow up message.
Charlie
Now I feel like an idiot! I guess I'm trying to make this a lot more complicated than it has to be. Thanks again for your help.
Charlie
I keep wondering if I should have used the formula for possible permutations:
The answer would be smaller.
Charlie
Bobby,
Can you give me a hint that would lead me to where I made the mistake? I have checked and rechecked with my calculator and can't find it. Maybe I am just blind to it - LOL.
Charlie
Me again! I have the following problem and I have arrived at the following answer. I have some doubts about my answer, but I can't seem to put my finger on what is wrong. The answer just seems to be too high. Hopefully, someone here can take a look and see if it is just my self-doubt or if there is an error I can't see.
Problem:
"A computer with an old processor locks up if more than 4 applications are running simultaneously. If the owner has 20 applications stored in his program file, how many different sets of 4 can he run, so that his computer does not lock up?"
Here is what I have so far:
Using the formula for calculating combinations
n = Total number of programs = 20
r = Possible combinations = 4
Does this sound right? I am fairly sure that my math is right. But that seems like an incredible large number of possible combinations of 4 from a set of 20.
Charlie
Ironically, enough, I spoke with the instructor today regarding this problem and I asked how we are expected to calculate the two prime numbers. I told her that I had researched it online and that I have the answer, but I couldn't figure out how to get the answer without accepting that the numbers I found online were accurate. She said "That's the answer". Apparently, we are supposed to simply look it up online and give the results of our research with a citation. Hell, I've been killing myself trying to figure out how to calculate it.
Charlie
Bobby,
The questions are all different topics. Some cover prime numbers, others velocity, others density, etc. I can get them all posted if you'd like, but I can probably figure out most of them. The book is called "Strageties for Problem Solving". It is the text for one of my classes at ITT Tech.
And thanks for the website links, I will study them and get back with you if I have any problems.
Incidentally, the last post I made (about the unsolvable equations) helped me get a full grasp on the concept. I have taught it to my wife and had two other students come to the house so I could help them out. I have been giving you guys all the credit, though. I really appreciate all of your help.
Charlie
Bobby,
That is part of what makes this class rather difficult. For a "final project" we are supposed to solve several problems that are found in chapters of our text that we will not cover in class. I basically have to learn how to solve them on my own. The instructor is pretty much useless. She refuses to help you understand the underlying principles.
I keep thinking that, since this is a college class, it may be assumed that I know how to solve them based on knowledge obtained during high school. But, I dropped out of high school in the 10th grade back in 1984, So, not only did I not learn the material (if it was even taught back then), it has been over two decades since I cracked a math book. I have a pretty good grasp of how things work, but I never learned it in the past. Now, I am somewhat behind the curve on understanding it.
I would love to understand the underlying principles and formulas involved. If for no other reason than to prove to the instructor that I can learn the material outside of class.
As a side not, I have spoken with both the department head and the dean of the school regarding this instructor. They agree that she should be doing a better job as an instructor, but I haven't seen any significant changes in her instructional manner.
Charlie
Just a couple of points I'd like to clarify. I am sure your answer is correct, but I'd like to understand the process. Please reference my questions below as indicated by the asteriks:
bobbym wrote:Hi Charlie;
Bob has raised good points:
You can use my two numbers and here is the proof that they are in the required range.
First some prerequisites:
10^399 is the smallest 400 digit number. 10^400 is the smallest 401 digit number.
Start with the inequality.
Expand
****** How did you get the exponent of 400 in the center number above? ******
Divide through by 10^399.
****** Here, I see what happened on the left side of the equation, but what happened to the exponent on the right side (the 400)?******
The inequality holds so it is a 400 digit number. You can give your teacher the numbers I gave you in post #5 and you are safe.
******Also,where did you manage to find the two prime number you started with?
and******************EDITTED AGAIN IN FOLLOW UP POST BELOW*******************
Just a couple of points I'd like to clarify. I am sure your answer is correct, but I'd like to understand the process. Please reference my questions below as indicated by the asteriks:
Hi Charlie;
Bob has raised good points:
You can use my two numbers and here is the proof that they are in the required range.
First some prerequisites:
10^399 is the smallest 400 digit number. 10^400 is the smallest 401 digit number.
Start with the inequality.
Expand
****** How did you get the exponent of 400 in the center number above? ******
Divide through by 10^399.
****** Here, I see what happened on the left side of the equation, but what happened to the exponent on the right side (the 400)?******
The inequality holds so it is a 400 digit number. You can give your teacher the numbers I gave you in post #5 and you are safe.
Incidentally, this is the same instructor who, when asked for a more detailed explanation of a different problem, told the student to "Google it". That's why I come here. You folks are much better instructors.
Charlie
To be honest, I have no idea what the purpose of this problem is. I am supposed to list the two numbers and "explain your strategy". That's it. I think I will just put the answer I found here and explain my strategy as "researched the problem on the internet". It is for a Problem Solving class that I am taking. Since there really isn't a simple way to solve the problem (my TI calc won't do it), I don't see how anyone can figure it out without looking online at lists of Mersenne primes.
Charlie
Just realized I had it wrong. The solution should read as:
The answer isn't important, provided it has 400 digits
Thanks,
Charlie
First off, I need to apologize for the missleading subject line. The problem has nothing to do with square roots.
Second, I think I may have had a brainstorm (or maybe a light shower, anyway).
Any number that is a multiple of 100 is a prime number if you add the number 1 to it, right? like, 101, 201, 100000001, 2000000001, 1000000000001, 2000000000001, etc....
Therefore, I think I can sufficiently solve the problem as follows:
Does this make any sense? Or am I just confusing myself? After re-reading the question, I discovered that the 400 digit number does not have to be a prime.
Thanks,
Charlie
I was given the following problem to work out:
"Find two prime numbers that, if multiplied, would generate a 400-digit number."
I have no idea where to begin looking for how to figure this.
I DO NOT WANT THE ANSWER ! I just want to know how to find the answer.
Thanks,
Charlie
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The original problem was sated incorrectly - the subtraction symbol should have been dividing. I corrected it in a later post.
Charlie
The instructions for the problems are (quote)"In exercises 89-96, solve each equation."(end quote). Unfortunately, there are no answers in the book. I ought to write your answer just to mess with the instructor's mind. But, then she would think that I have a far better understanding of algebra than I actually possess. I guess I'll just leave it as is, with the 0x=-251 answer and see what she says. Thanks for all of your time and help.
Charlie
I have never heard of the quadratic equation. LOL. I quit school while in the 10th grade back in 1982 and haven't thought about algebra until now. I have been working in the construction field, so I have actually utilized some basic geometry (finding areas, volumes, etc) but I learned those in the field, in a hands on approach.
Charlie
I did enter the equation into an equation calculator online to check my answer. The final answer it gave me was 1=1?!?!?! Which left me even more confused.
Charlie
***EDIT***
The calculator probably choked on the 0x=-251 answer. Sort of like an error on a calculator.
That is exactly what I thought. 0x=-251 is an impossible statement.
Charlie
Is it possible that the question is, in fact:
?
Incidentally, how would I go about solving the problem the way you have it written? I haven't learned that yet.
Charlie
The problems are written exactly as they are in the book. I don't know why I keep getting the strange answers. It really would have been nice if the instructor had explained the brackets to the class. It is my understanding that you perform the operations contained within the brackets first (similar to the parenthesis).
Charlie
When I arrived at the strange answer, I double and triple checked. As I said, the following problem is similar: