Results 1 to 4 of 4

Math Help - outline the following two amounts

  1. #1
    Senior Member
    Joined
    Sep 2012
    From
    Sweden
    Posts
    250
    Thanks
    6

    outline the following two amounts

    This is from My exam today and i did not know how to solve that kind of pproblem
    Its problem nr 1 and it says outline the following two amountsoutline the following two amounts-image.jpg
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    14,971
    Thanks
    1121

    Re: outline the following two amounts

    You do know that you posted it upside down, don't you? It's also in Swedish which I, at least, cannot read. Surely, it wouldn't have been that hard to just type in the problem yourself.

    I assume that you to describe, or write in a more simplified way, the sets
    a) \{x\in R: (x-1)(x-5)\le 0\}\cap\{x\in R: (x- 3)(x- 1)> 0\}\cap \{x\in R: (x- 2)(x- 6)\le 0\}
    b) \{z\in C: Re((z-1)(\overline{z}+ i)= 1/2\}
    The first is simply asking for all numbers that satisfy all three of the inequalities. Do you know how to find numbers satisfying the inequalities separately? For example (x- 1)(x-5)= 0 when x= 1 or x= 5. Since the product is a continuous function of x, only those numbers can separate "<" and ">". In particular, if x= 2 (between 1 and 5), (2- 1)(2- 5)= (1)(-3)= -3< 0 so does satisfy the first inequality. You can check a number less than 1, say 0, and a number larger than 5, say 6, to see that numbers less than 1 or larger than 5 do NOT satisfy it. That is, the first set is simply the interval 1\le x\le 5 of all number between 1 and 5, including the endpoints. Find the solution sets of the other two inequalities in the say way and see what numbers, if any, satisfy all three.

    (b) is harder. In fact, I am surprised you would have trouble with (a) if you are in a course where you are expected to be able to do (b). I would write z= x+ iy so that \overline{z}= x- iy. Then z- 1= (x- 1)+ iy and \overline{z}+i= x+ i(1- y) and then (z-1)(\overline{z}+i)= [(x- 1)+iy][x+ i(1- y)]= (x(x-1)- y(1- y))+ i(xy+ (x-1)(1- y))=  (x^2+ y^2- x- y)+ (x+ y- 1)i

    Find the real part of that and set it equal to 1/2. What is the graph of that in the complex plane?
    Last edited by HallsofIvy; December 8th 2012 at 04:33 AM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member
    Joined
    Sep 2012
    From
    Sweden
    Posts
    250
    Thanks
    6

    Re: outline the following two amounts

    No i did not know it was upside down because i did uppload through My phone:P ... I did translate in My text:S the thing is i did start same with a as u did but u dont have to say like that.. I did never read this in My book actually so... Im actually searching for this in My book but cant find.. Ima see what i can progress with
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Mar 2011
    From
    Tejas
    Posts
    3,150
    Thanks
    591

    Re: outline the following two amounts

    note that (x - 1/2)2 = x2 - x + 1/4. this may prove useful.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Ratios of the unknown amounts in a recipe
    Posted in the Math Topics Forum
    Replies: 0
    Last Post: September 10th 2011, 06:49 PM
  2. Help with some problems on Schaum Outline
    Posted in the Algebra Forum
    Replies: 9
    Last Post: August 4th 2009, 09:26 PM
  3. [SOLVED] Amounts made up using 3 of the 6 coins
    Posted in the Math Topics Forum
    Replies: 0
    Last Post: February 17th 2009, 03:25 AM
  4. Help regarding amounts!
    Posted in the Statistics Forum
    Replies: 1
    Last Post: September 10th 2006, 06:38 AM
  5. Amounts consumed
    Posted in the Pre-Calculus Forum
    Replies: 0
    Last Post: July 20th 2006, 07:45 AM

Search Tags


/mathhelpforum @mathhelpforum