CalleighMay

My professor wants me to PROVE the statement: "If b divides c, then (a,b) <= (a,c)." by completing a proof. I can't just give a set of numbers that show it's true, i actually need to have a "proof" with variables that would make the statement work. Does this make sense?

triclino, is that in correct "proof" format? I can't really follow it... Is there a way to answer this problem as a "proof" rather than with an example? We're not supposed to use an example, we're supposed to prove it with all those variables and everything, that shows one thing equals something and what not... Here's an example of a proof in the fashion he wants us to write them: "if c divides a and c divides b, then [a,b] <= ab" Assuming this is true, the proof would look like: We need to show that ab/c is a multiple of "a" and "b". a = ck b = cj ...(for ints k and j) (ck x b) / c = bk.... so ab/c is a multiple of b (a x cj) / c = aj..... so ab/c is a multiple of a Therefore ab/c is a common multiple of "a" and "b". So it's either the lowest multiple, or a larger. aka.... ab/c = LCM .... or.... ab/c < LCM This shows that [a,b] <= ab/c Is there a way to write my original problem in this manner using only variables etc?

Hey everyone, I'm taking this course called "Number Theory" and am having a lot of difficulty with it. We're currently on "proofs" and i am having some issues. Last week was my first weeks classes. The first day my professor jumped right into the material without giving much background. He's assigning problems left and right without giving any class examples, and the textbook seems like more of a novel than a math book. I'm stuck on one problem. I "think" it's asking for a proof, but the directions are very unclear. It asks: "Tell whether each statement is true and give counterexamples to those that are false. Assume a, b, and c are arbitrary nonzero integers." And the statement is: "If b divides c, then (a,b) <= (a,c)." So in english, if "c divided by b", then the GCD of "a" and "b" is less than or equal to the GCD of "a" and "c". The back of the book lists the answer as "TRUE" but doesn't give any reasoning or proof to go along with it. He gave us two proof examples in class using GCD and LCM etc, but i honestly don't understand them. Making up variables here and there, it doesn't look like any math i've seen before. Here are some random facts i picked up on: LCM = (a x b)/GCD LCM x GCD = a x b (a,b) stands for the GCD (greatest common divisor) [a,b] stands for the LCM (lowest common multiple) a divides b: b = a (k) with some int k b divides c: c = b (L) with some int L a divides c: c = a (k x L) with ints K and L Yeah, that's all i know... Can anyone help me out with this problem? I have honestly no idea where to begin. Thanks!

can you simply just "add m^2 to both sides in A4 ? I had a little help last night and came up with this method: Let n = 2k + 1 (since n is odd) plugging it into the m equation given, you get m = ( (2k+1)^2-1) )/2 1: so m = 2k^2 + 2k 2: so m+1 = 2k^2 + 2k + 1 3: so (m+1)^2 = 4k^4 + 8k^3 + 8k^2 + 4k + 1 4: and m^2 = 4k^4 +8k^3 + 4k^2 And using n = 2k + 1, 5: n^2 = 4k^2 + 4k +1 So we have that (4k^4 +8k^3 + 4k^2) + (4k^2 + 4k +1) = 4k^4 + 8k^3 + 8k^2 + 4k + 1 which is m^2 + n^2 = (m+1)^2

Hey guys, I'm in the class "Number Theory" at my college. It's WEEK 1 and we are already going over these weird proofs and i am COMPLETELY lost. The question asks: "Show that if n is any odd positive integer, and m = (n^2-1)/2, then m^2 + n^2 = (m+1)^2." My professor as awful and has given us absolutely NO background. He's given us two proof examples in class, but i don't understand either of them, so they don't help much. From what i can gather, odd numbers are "2k+1" and even numbers are "2k". I guess this makes sense, but i don't understand how to use it. So for the problem on hand, i understand i need to show how you get from point A to point B- but the question is how. We can assume that n is odd. So n=2k+1. We can also assume that m= (n^2-1)/2 And we need to get these two equations to look like: m^2 + n^2 = (m+1)^2 in the end Working backwards: m^2 + n^2 = (m+1)^2 .............= m^2 + 2m + 1 (expanding) m^2 + n^2 = m^2 + 2m + 1 ........n^2 = ........2m + 1 (subtraction) so n^2 = 2m+1 Working from the given that m = (n^2 - 1) / 2 m = (n^2 - 1) / 2 2m = n^2 - 1 (multiplication) 2m + 1 = n^2 (addition) n^2 = 2m + 1 (switch things around) So this gets the "n^2 = 2m + 1" in the final step. But how do i get the "+ m^2" ?? My biggest problem is that i don't know how this proof should "look". I understand the concept, but i am having difficulty getting it into proof form. So it should look like: A: Assume n is positive and odd, and assume m = (n^2 - 1) / 2 A1: A2: A3: A4: A5: A6: A7: A8: A9: B: Show that m^2 + n^2 = (m+1)^2 Then we have to write it in paragraph form.... Can anyone help me out with this problem? I just don't get it... This problem is from the text "Elementary Number Theory" 2/e by Charles Vanden Eynden. It's Chapter 0 page 9 number 11. Thanks for any help!!

Hey guys! I have been on the forum for about a week or so and have compiled a lot of information and techniques to help me understand calculus, so i really appreciate everyone's help! I am a soon-to-be freshman in college and am taking a summer class, calculus II (took calc I in HS). This is our last week of class after our final exam so my professor is taking this time to give us a preview of what we will be learning in the fall semester in Calc III (since this is the same professor). Every Tuesday class our professor gives us a few problems from future sections and asks us to "see what we can come up with" and to work together to find solutions. The following Tuesday he asks us to discuss the problems as a class, seeing which ones of us know our stuff =P Basically, i want to ask you guys what you think about these problems as i do them along before i have my discussion. I really want to make a lasting impression on my professor by "knowing my stuff" -to show him i can do it! All's i need is a little help! Would you guys mind giving me some help? We are using the textbook Calculus 8th edition by Larson, Hostetler and Edwards and the problems come from the book. The problem is on pg 1133 in chapter 15.8 in the text, number 14. It reads: Use Stoke's theorem to evaluate Integral (with C at bottom) of F (with a dot) dr It states that in each case, C is oriented counterclockwise as viewed from above. For this specific problem is gives, F(x,y,z)=4xzi + yj + 4xyk and S: z= 9-x^2-y^2 and z>=0 Again, i literally haven't a clue where to go with these =/ I looked at the soln's to the other problems in this set but still haven't a clue where to go! =/ Any help at all would be greatly appreciated. Thanks guys

Hey guys! I have been on the forum for about a week or so and have compiled a lot of information and techniques to help me understand calculus, so i really appreciate everyone's help! I am a soon-to-be freshman in college and am taking a summer class, calculus II (took calc I in HS). This is our last week of class after our final exam so my professor is taking this time to give us a preview of what we will be learning in the fall semester in Calc III (since this is the same professor). Every Tuesday class our professor gives us a few problems from future sections and asks us to "see what we can come up with" and to work together to find solutions. The following Tuesday he asks us to discuss the problems as a class, seeing which ones of us know our stuff =P Basically, i want to ask you guys what you think about these problems as i do them along before i have my discussion. I really want to make a lasting impression on my professor by "knowing my stuff" -to show him i can do it! All's i need is a little help! Would you guys mind giving me some help? We are using the textbook Calculus 8th edition by Larson, Hostetler and Edwards and the problems come from the book. The problem is on pg 1118 in chapter 15.6 in the text, number 24. It reads: Find the flux of F through S It gives: Integral (with S at bottom) of the integral of F (with a dot) N dS where N is the upward normal vector to S then it gives for this specific problem, F(x,y,x)=xi+yj and S: 2x+3y+z=6, first octant I'll be honest and say that i have no idea what's going on here. I looked at the other problems in this problem set and still have no idea what to do... Any help would be greatly appreciated. Thanks guys

Hey guys! I have been on the forum for about a week or so and have compiled a lot of information and techniques to help me understand calculus, so i really appreciate everyone's help! I am a soon-to-be freshman in college and am taking a summer class, calculus II (took calc I in HS). This is our last week of class after our final exam so my professor is taking this time to give us a preview of what we will be learning in the fall semester in Calc III (since this is the same professor). Every Tuesday class our professor gives us a few problems from future sections and asks us to "see what we can come up with" and to work together to find solutions. The following Tuesday he asks us to discuss the problems as a class, seeing which ones of us know our stuff =P Basically, i want to ask you guys what you think about these problems as i do them along before i have my discussion. I really want to make a lasting impression on my professor by "knowing my stuff" -to show him i can do it! All's i need is a little help! Would you guys mind giving me some help? We are using the textbook Calculus 8th edition by Larson, Hostetler and Edwards and the problems come from the book. The problem is on pg 1096 in chapter 15.4 in the text, number 24. It reads: Use green's theorem to calculate the work done by the force F on a particle that is moving counterclockwise around the closed path C It gives: F(x,y)=(3x^2+y)i + 4xy^2j and gives: C: boundary of the region lying between the graphs of y=(sqrt x) and y=0, and x=9 I looked at similar problems in the same section and came up with the following for this one: work= integral (with C at bottom) of 3x^2+y dx + 4xy^2 dy =Integral (with R at bottom) of the integral of ? ..this is where i get lost, kind of confused as to what the C is and how to integrate with it. Also, what's R? This doesn't seem that bad of a problem, i just think i'm missing something since it seems too easy? Any further help would be greatly appreciated. Thanks guys!! =/

Hey guys! I have been on the forum for about a week or so and have compiled a lot of information and techniques to help me understand calculus, so i really appreciate everyone's help! I am a soon-to-be freshman in college and am taking a summer class, calculus II (took calc I in HS). This is our last week of class after our final exam so my professor is taking this time to give us a preview of what we will be learning in the fall semester in Calc III (since this is the same professor). Every Tuesday class our professor gives us a few problems from future sections and asks us to "see what we can come up with" and to work together to find solutions. The following Tuesday he asks us to discuss the problems as a class, seeing which ones of us know our stuff =P Basically, i want to ask you guys what you think about these problems as i do them along before i have my discussion. I really want to make a lasting impression on my professor by "knowing my stuff" -to show him i can do it! All's i need is a little help! Would you guys mind giving me some help? We are using the textbook Calculus 8th edition by Larson, Hostetler and Edwards and the problems come from the book. The problem is on pg 1087 in chapter 15.3 in the text, number 16a and 16b ONLY. It reads: Find the value of the line integral integral (with a C at the bottom) of F (with a dot) dr. Then it gives integral (with c at bottom) of (2x-3y+1)dx -(3x+y-5)dy For a) it gives a graph with the vertices's: (0,0), (4,1) and (2,3) and there is a label (c1) in the graph on the line from (0,0) to (2,3) For b) it gives another graph with the vertices's: (0,1), (0,-1) and it gives a half-circle with an equation x=sqrt(1-y^2) and a label (C2) in the graph. There are graphs C and D but he told us to only try a and b... If you have a copy of the book calculus 8th edition you can see the problem for yourself... if you think it's confusing here, you can only imagine how confusing it is to me lol =( I did look at the solutions to the other odd (i cannot find answers to even ones) problems in this problem set but it's no use, i'm totally lost. He said this will eventually be important so i want to learn it now! lol Can you guys help me? Thank you!!!!!

Hey guys! I have been on the forum for about a week or so and have compiled a lot of information and techniques to help me understand calculus, so i really appreciate everyone's help! I am a soon-to-be freshman in college and am taking a summer class, calculus II (took calc I in HS). This is our last week of class after our final exam so my professor is taking this time to give us a preview of what we will be learning in the fall semester in Calc III (since this is the same professor). Every Tuesday class our professor gives us a few problems from future sections and asks us to "see what we can come up with" and to work together to find solutions. The following Tuesday he asks us to discuss the problems as a class, seeing which ones of us know our stuff =P Basically, i want to ask you guys what you think about these problems as i do them along before i have my discussion. I really want to make a lasting impression on my professor by "knowing my stuff" -to show him i can do it! All's i need is a little help! Would you guys mind giving me some help? We are using the textbook Calculus 8th edition by Larson, Hostetler and Edwards and the problems come from the book. The problem is on pg 1075 in chapter 15.2 in the text, number 26. It reads: Find the total mass of the wire with density p. And it gives: r(t)=2 cos ti + 2 sin tj + 3tk and p(x,y,z)=k+z (the p is a different looking p, most likely represents something else, something that sounds like roe maybe? lol. and k is really k below) and: (k>0), 0<=t<=2pi I looked at similar problems in the same section and came up with the following for this one: r'(t)=2 cos ti =2 sin tj but when finding II r'(t) II how do i do this with sin and cos? I know it's sqrt of each term squared, so would it be: sqrt( 2cos^2t - 2sin^2t ) ? Then at this point, even if the above was correct, it's telling me to do: integral from C to ? of p(x,y,x) dx and integral from C to ? of kz ds Yeah i'm lost!!! Any further help would be greatly appreciated. Thanks guys! =/

Hey guys! I have been on the forum for about a week or so and have compiled a lot of information and techniques to help me understand calculus, so i really appreciate everyone's help! I am a soon-to-be freshman in college and am taking a summer class, calculus II (took calc I in HS). This is our last week of class after our final exam so my professor is taking this time to give us a preview of what we will be learning in the fall semester in Calc III (since this is the same professor). Every Tuesday class our professor gives us a few problems from future sections and asks us to "see what we can come up with" and to work together to find solutions. The following Tuesday he asks us to discuss the problems as a class, seeing which ones of us know our stuff =P Basically, i want to ask you guys what you think about these problems as i do them along before i have my discussion. I really want to make a lasting impression on my professor by "knowing my stuff" -to show him i can do it! All's i need is a little help! Would you guys mind giving me some help? We are using the textbook Calculus 8th edition by Larson, Hostetler and Edwards and the problems come from the book. The problem is on pg 1033 in chapter 14.6 in the text, number 44. It reads: Find the centroid of the solid region bounded by the graphs of the equations or described by the figure. Assume uniform density. And it gives: y=sqrt(4-x^2), z=y, and z=0 The question also asks to find the tripple integrals but he said that's WAY over our heads lol and i looked at every other problem in this problem set and i don't understand a word of it. I looked at other worked out examples and they too make no sense to me I would attempt this one myself but i am literally stumped on this one 100% Can anyone help me with this one? Thanks guys

Hey guys! I have been on the forum for about a week or so and have compiled a lot of information and techniques to help me understand calculus, so i really appreciate everyone's help! I am a soon-to-be freshman in college and am taking a summer class, calculus II (took calc I in HS). This is our last week of class after our final exam so my professor is taking this time to give us a preview of what we will be learning in the fall semester in Calc III (since this is the same professor). Every Tuesday class our professor gives us a few problems from future sections and asks us to "see what we can come up with" and to work together to find solutions. The following Tuesday he asks us to discuss the problems as a class, seeing which ones of us know our stuff =P Basically, i want to ask you guys what you think about these problems as i do them along before i have my discussion. I really want to make a lasting impression on my professor by "knowing my stuff" -to show him i can do it! All's i need is a little help! Would you guys mind giving me some help? We are using the textbook Calculus 8th edition by Larson, Hostetler and Edwards and the problems come from the book. The problem is on pg 1015 in chapter 14.4 in the text, number 14. It reads: Find the mass and center of mass of the lamina bounded by the graphs of the equations for the given density or densities (Hint: some of the integrals are similar in polar coordinates). And it gives: y=x^3, y=0, x=2, p=kx (the p looks a little different, most likely represents something else, and the k really is a k, not to be confused with that wavelength symbol lol) I looked at similar problems in the same section and came up with the following for this one: I first graphed the equations on the same coordinates. I think im supposed to take the integral from (0 to 2) of the integral from (0 to x^3) kxdxdy? or kxdydx? (something about horix simple or vert simple??) And then i'm confused as to what to do next, even if i was sure what i have so far is correct. Any further help would be greatly appreciated. Thanks guys

Hey guys! I have been on the forum for about a week or so and have compiled a lot of information and techniques to help me understand calculus, so i really appreciate everyone's help! I am a soon-to-be freshman in college and am taking a summer class, calculus II (took calc I in HS). This is our last week of class after our final exam so my professor is taking this time to give us a preview of what we will be learning in the fall semester in Calc III (since this is the same professor). Every Tuesday class our professor gives us a few problems from future sections and asks us to "see what we can come up with" and to work together to find solutions. The following Tuesday he asks us to discuss the problems as a class, seeing which ones of us know our stuff =P Basically, i want to ask you guys what you think about these problems as i do them along before i have my discussion. I really want to make a lasting impression on my professor by "knowing my stuff" -to show him i can do it! All's i need is a little help! Would you guys mind giving me some help? We are using the textbook Calculus 8th edition by Larson, Hostetler and Edwards and the problems come from the book. The problem is on pg 998 in chapter 14.2 in the text, number 26. It reads: Use a double integral to find the volume of the indicated solid: And it gives a picture of a solid with the vertices's: (0,0,0), 2,0,0), (0,2,0) and (0,0,2). The solid is given the equation: x+y+z=2 I looked at similar problems in the same section and came up with a few ideas as to how to get started. This is what i came up with. Making a sketch of the side on the xy-plane, i have the line: y=-x+2 Then the integral from 0 to 2 of the integral of 0 to (-x+2) of (this is where i get confused) I get confused from here... Any help would be greatly appreciated. Thanks guys

Hey guys! I have been on the forum for about a week or so and have compiled a lot of information and techniques to help me understand calculus, so i really appreciate everyone's help! I am a soon-to-be freshman in college and am taking a summer class, calculus II (took calc I in HS). This is our last week of class after our final exam so my professor is taking this time to give us a preview of what we will be learning in the fall semester in Calc III (since this is the same professor). Every Tuesday class our professor gives us a few problems from future sections and asks us to "see what we can come up with" and to work together to find solutions. The following Tuesday he asks us to discuss the problems as a class, seeing which ones of us know our stuff =P Basically, i want to ask you guys what you think about these problems as i do them along before i have my discussion. I really want to make a lasting impression on my professor by "knowing my stuff" -to show him i can do it! All's i need is a little help! Would you guys mind giving me some help? We are using the textbook Calculus 8th edition by Larson, Hostetler and Edwards and the problems come from the book. The problem is on pg 974 in chapter 13.10 in the text, number 10. It reads: Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. And it gives: minimize: f(x,y)= sqrt(x^2+y^2) with the constraint: 2x+4y-15=0 I looked at similar problems in the same section but they're little help. I did the best i could so far and this is what i came up with. subject to the constraint: 2x+4y=15 let g(x,y)=2x+4y=15 since tri f(x,y)=x/sqrt(x^2+y^2) I got this step, then in the next step i'm supposed to use some symbol that looks like, well i remember it as wavelength in physics, kinda looks like a k?? and tri g(x,y)=2(wavelength symbol)i+4(wavelength symbol)j but to attain a system of linear equations, how do i do that with x/sqrt(x^2+y^2)?? Any help would be greatly appreciated. Thanks guys

so does that come out to .24 as well? Is that correct? lol