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    Proportions math problem

    Homework Statement T or F? a pizza with 20cm diameter will require approximately half of the raw materials of pizza of diameter 40cm. explain your answer. Homework Equations The Attempt at a Solution my thinking is this, if we take the area of both pizzas, then we get 100(pi)...
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    Solving equations

    Homework Statement I am having trouble with question 4(c).... part i and ii.... Homework Equations The Attempt at a Solution would it be okay for her to write iff between each line? I do not see why not but I cannot find the proper reasoning.
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    Rewrote f(x) in vertex form

    Homework Statement Can someone assist me with number 3 please... Homework Equations The Attempt at a Solution I went ahead and rewrote f(x) in vertex form in terms of a,b, and c but i'm having a hard time writing down how f can be thought of as a transformation of g.
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    Analyzing student strategies

    Homework Statement Homework Equations The Attempt at a Solution can someone help me out on #3 please. I can't see the reasoning behind her work.
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    Addressing student errors

    Homework Statement Mindy solves the problem (x+4)(x-3)=8 by setting x+4=8 and x-3=8, thereby getting the solutin x=4 from both equations. she checks her answer by substituting x=4 into the original equation and finds that it works. She concludes that this quadratic equation has only one...
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    Abstract algebra

    1. Homework Statement [/b] The set of positive real numbers, R+, is a group under normal multiplication. The set of real numbers, R, is a group under normal addition. For the sake of clarity, we'll call these groups G and H respectively. Prove that G is isomorphic to H under the isomorphism...
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    Fermat's little theorem

    Homework Statement I'm suppose to prove that if (x,7)=1, then x to the 6th is congruent to 1 mod 7. Homework Equations The Attempt at a Solution Now, i have the proof by induction when (a,p)=1 but how do i apply this to prove it when a=x and p=7?
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    Primitive roots

    Homework Statement Let w be a primitive cube root of 1. show that 1, w,w^2 are the three cube roots of 1. Homework Equations The Attempt at a Solution I'm not quite sure how to even start this. any help will be greatly appreciated.
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    Complex numbers

    Homework Statement Let Z and W be complex numbers. If /Z/ and /W/ are rational and /W-Z/ is rational, then /(1/Z)-(1/W)/ is rational. Homework Equations The Attempt at a Solution How do I represent Z and W as rational complex numbers?
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    Viete's relations

    Homework Statement Homework Equations The Attempt at a Solution I'm having trouble with number three. I know Viete's relations are X1+X2+X3, X1X2+X1X3+X2X3, and x1x2x3 for a cubic equation.
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    Fourier series

    Homework Statement I was able to do number one but can someone help me with 1(b) and 1(c)? I'm not too sure what they're asking. Homework Equations The Attempt at a Solution
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    Inverse square law

    Homework Statement Can someone help me out with number two please? I'm not sure what exactly it's asking me to do. Homework Equations The Attempt at a Solution
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    Parametric equations

    Homework Statement Homework Equations The Attempt at a Solution Can someone help me get started on number one please????
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    Groups of order p^2

    Homework Statement If the order of G is p^2 and p is prime, then show that G is either cyclic or isomorphic to ZpXZp... Homework Equations The Attempt at a Solution Any hints here will help!
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    Groups of order p^2 where p is prime

    Homework Statement let p be a prime number and let G be a group with order p^2. the task is to show that G is either cyclic or isomorphic to Zp X Zp. a. let a, not equal to the identity,be an element in G and A=<a>. What's the order of A. b. consider the cosets of A: G/A={A,g2A,...gnA}...
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    Show there exist an element of order 2 in this group

    Homework Statement If G is a finite groups whose order is even, then there exists an element a in G whose order is 2. Homework Equations The Attempt at a Solution does this mean that a^2 is the identity? how can i prove this? Also, would't this make G cyclic?
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    How to do this permutation?

    Homework Statement (1 2) (1 4 5) (2 3 4) (2 5)= (1 4) (3 5) Homework Equations The Attempt at a Solution Can someone explain to me how to do this permutation? I know it's the easiest thing to do but i just went blank! how did my professor get (1 4) (3 5)?
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    Sylow's theorem

    Homework Statement LET G BE A FINITE GROUP WHOSE ORDER IS DIVISIBLE BY THE PRIME P. SUPPOSE P^M IS THE HIGHEST POWER OF P WHICH IS A FACTOR OF |G|AND SET K=(|G|/P^M), THEN THE GROUP G CONTAINS AT LEAST ONE SUBGROUP OF |P^M|. I have the proof but can someone explain it in simpler terms...
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    Number theory

    Homework Statement If M and N are positive integers >2, prove that ((2^m)-1) is not a divisor of ((2^n)+1) Homework Equations The Attempt at a Solution Is this correct? I use the well-ordering principle. Let T be the set of all M,N positive integers greater than 2 such...
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    Number Theory

    Homework Statement Prove that they are no integers a,b,n>1 such that (a^n - b^n) | (a^n + b^n). Homework Equations The Attempt at a Solution Do I solve this by contradiction? If so, how do I start it?
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    A group that's a collection of sets

    Homework Statement Let S be a set of things and let P be the set of subsets of S. For A,B in P, define A*B=[(S-A)intersection B] union [A intersection (S-B)] I'm suppose to show that (p,*) is commutative, find the identity, and given that A is a subset of S, find the inverse of A. How do i...
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    Group that is a collection of sets

    Homework Statement Let S be a set of thing and let P be the set of subsets of S. For A,B in P, define A*B=[(S-A)intersection B] union [A intersection (S-B)] Homework Equations Consider the set S={alice, bob, carol, don, erin, frank, gary, harriot}. Using the set operation * find the...
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    Groups whose elements have order 2

    Homework Statement suppose that G is a group in which every non-identity element has order two. show that G is commutative. Homework Equations The Attempt at a Solution IS THIS CORRECT?????? ab=a[(ab)^2]b=(a^2)(ba)(b^2)=ba
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    Cyclic group properties

    Homework Statement Zn={0,1,...,n-1}. show that an element k is a generator of Zn if and only if k and n are relatively prime. Homework Equations The Attempt at a Solution it makes sense but im having a hard time proving this.
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    A group that is a collection of sets

    Homework Statement Let S be a set of things and let P be the set of subsets of S. For A, B in P define A*B = ((S-A) intersect B) union (A intersect (S-B)). Need to show that (P,*) is commutative and the group identity. Homework Equations The Attempt at a Solution only...
  26. H

    Groups whose elements have order 2

    Homework Statement suppose that G is a group in which every non-identity element has order two. Show that G is commutative. Homework Equations The Attempt at a Solution Is my answer correct? Suppose that a,b and ab all have order two. we will show that a and b commute. By...
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    Groups whose elements have order 2

    Homework Statement Suppose that G is a group in which every non-identity element has order two. show that G is commutative. Homework Equations The Attempt at a Solution DOES THIS ANSWER THE QUESTION????: Notice first that x2 = 1 is equivalent to x = x−1. Since every element of...
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    Groups/cyclic groups

    I need help here: Suppose that G is a group in which every non-identity element has order two. Show that G is commutative. Also, Consider Zn = {0,1,....,n-1} a. show that an element k is a generator of Zn if and only if k and n are relatively prime. b. Is every...
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    Groups whose order have order two

    I need help here: Suppose that G is a group in which every non-identity element has order two. Show that G is commutative. Also, Consider Zn = {0,1,....,n-1} a. show that an element k is a generator of Zn if and only if k and n are relatively prime. b. Is every...
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    Umbilic points

    discuss how to find the umbilic points of an ellipsoid and their connection to lines of curvature.
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