Results 1 to 13 of 13

Math Help - different questions

  1. #1
    Junior Member
    Joined
    Jun 2007
    Posts
    42

    different questions

    I need help with these questions.....they're from grade 12 geometry and discrete math.

    1. Analyse the normal vectors of the following planes and describe the situation of each system. Include a geometric interpretation of each solution:

    7x-5y+4z-9=0

    -5x+4y+z-3=0

    x+2y-z+1=0


    2. Analyse the normal vectors of the following planes and describe the situation of each system. Include a geometric interpretation of each solution:

    7x-5y+4z-9=0

    -x+3y+5z-2=0

    5x+y+14z-20=0
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,804
    Thanks
    115
    Quote Originally Posted by Raiden_11 View Post
    I need help with these questions.....they're from grade 12 geometry and discrete math.

    1. Analyse the normal vectors of the following planes and describe the situation of each system. Include a geometric interpretation of each solution:

    p_1:7x-5y+4z-9=0
    p_2: -5x+4y+z-3=0
    p_3: x+2y-z+1=0

    ...
    Hello,

    the normal vectors of the planes are: \overrightarrow{n_1}=\left(\begin{array}{c}7\\-5\\4\end{array}  \right) , \overrightarrow{n_2}=\left(\begin{array}{c}-5\\4\\1\end{array}  \right) , \overrightarrow{n_3}=\left(\begin{array}{c}1\\2\\-1\end{array}  \right)
    These vectors are linear independent(?) and the planes have one common point  P\left( \frac{4}{13},  \frac{7}{13},  \frac{31}{13} \right)

    Quote Originally Posted by Raiden_11 View Post
    I need help with these questions.....they're from grade 12 geometry and discrete math.
    ...
    2. Analyse the normal vectors of the following planes and describe the situation of each system. Include a geometric interpretation of each solution:

    7x-5y+4z-9=0
    -x+3y+5z-2=0
    5x+y+14z-20=0
    the normal vectors of the planes are: \overrightarrow{n_1}=\left(\begin{array}{c}7\\-5\\4\end{array}  \right) , \overrightarrow{n_2}=\left(\begin{array}{c}-1\\3\\5\end{array}  \right) , \overrightarrow{n_3}=\left(\begin{array}{c}5\\1\\1  4\end{array}  \right)
    These vectors are linear dependent(?) because the following equation has a unique solution:

    r \cdot \left(\begin{array}{c}7\\-5\\4\end{array}  \right) + s \cdot \left(\begin{array}{c}-1\\3\\5\end{array}  \right) = \left(\begin{array}{c}5\\1\\14\end{array}  \right) . This equation is true for r = 1 and s = 2.

    First guess: The planes intersect in a common line.

    According to my calculations the three planes are not parallel and there doesn't exist a common line thus they intersect in three different parallel lines.

    EDIT: I've attached a diagram of the three planes.
    Attached Thumbnails Attached Thumbnails different questions-threeplanes.gif  
    Last edited by earboth; July 3rd 2007 at 07:09 AM. Reason: used the wrong expression
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Jun 2007
    Posts
    42

    Can u help me with these?

    1. On page 345 of the textbook, the diagonal pattern of Pascalís Triangle illustrates that C(7, 5) = C(4, 4) + C(5, 4) + C(6, 4). Prove this relationship using the following methods.

    a)numerically by using factorials
    b)by reasoning, using the meaning of combinations


    different questions-pascals-20triangle.jpg
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Jun 2007
    Posts
    42

    heres another one

    2. Observe the relationship between the elements of Diagonal 1 and Diagonal 2 in Pascalís Triangle, shown on the next page. The sum of the first two elements in Diagonal 1 is equal to the second element in Diagonal 2. Similarly, the sum of the first 5 elements of Diagonal 1 is equal to the 5th element of Diagonal 2. Suppose we wish to use Pascalís Triangle to find the sum of the first n natural numbers. Use combinatorial notation to express the sum of the n elements of Diagonal 1 in terms of the corresponding value in Diagonal 2.

    different questions-untitled.bmp
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Jun 2007
    Posts
    42

    heres the last one

    3. Using the method of mathematical induction, prove that the following statements are false.
    different questions-sigma.bmp
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Bar0n janvdl's Avatar
    Joined
    Apr 2007
    From
    South Africa
    Posts
    1,630
    Thanks
    6
    I cant see those last 2 pics.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Junior Member
    Joined
    Jun 2007
    Posts
    42

    Is this for #1

    Is this for #1 a) and b)
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Junior Member
    Joined
    Jun 2007
    Posts
    42

    Can u see #2 now?

    2. Observe the relationship between the elements of Diagonal 1 and Diagonal 2 in Pascalís Triangle, shown on the next page. The sum of the first two elements in Diagonal 1 is equal to the second element in Diagonal 2. Similarly, the sum of the first 5 elements of Diagonal 1 is equal to the 5th element of Diagonal 2. Suppose we wish to use Pascalís Triangle to find the sum of the first n natural numbers. Use combinatorial notation to express the sum of the n elements of Diagonal 1 in terms of the corresponding value in Diagonal 2.


    different questions-pascal.jpg
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Junior Member
    Joined
    Jun 2007
    Posts
    42

    Can u see #3 now?

    3. Using the method of mathematical induction, prove that the following statements are false.

    different questions-sigma.jpg
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Eater of Worlds
    galactus's Avatar
    Joined
    Jul 2006
    From
    Chaneysville, PA
    Posts
    3,001
    Thanks
    1
    Quote Originally Posted by Raiden_11 View Post
    Is this for #1 a) and b)
    Yes, but I couldn't see it very well and misread it. Done wrong problem.

    \sum_{i=1}^{n}2i=2n^{2}-2n+2

    2+4+6+8+....+2n=2n^{2}-2n+2

    Show P_{1} is true: 2(1)=2...true

    Assume P_{k} is true: 2+4+6+8+....+2k=2k^{2}-2k+2

    Show P_{k+1} is true:

    2+4+6+8+....+2k+2(k+1)=2k^{2}-2k+2+2(k+1)=2k^{2}+4=2(k^{2}+2)

    This shows P_{k} is not true and, therefore, P_{n} is not true.

    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~

    Actually, another case may be to prove what the sum of 2i equals and, therefore, show that the statement is false.

    \sum_{i=1}^{n}2i=n(n+1)

    I will skip ahead of the first two steps and go right to P_{k+1}

    2+4+6+8+....+2k+2(k+1)=k(k+1)+2(k+1)=(k+1)(k+2)

    This shows that P_{k+1} is true and, therefore, P+{n} is true and the above statement is false.
    Last edited by galactus; July 4th 2007 at 09:03 AM.
    Follow Math Help Forum on Facebook and Google+

  11. #11
    Junior Member
    Joined
    Jun 2007
    Posts
    42

    Which one is a) and Which one is b)?

    Which one is a) and which one is b), also can u help me with #2 and #3, i made them bigger for you to see.
    Follow Math Help Forum on Facebook and Google+

  12. #12
    Eater of Worlds
    galactus's Avatar
    Joined
    Jul 2006
    From
    Chaneysville, PA
    Posts
    3,001
    Thanks
    1
    That was 3a. The first induction you posted.
    Follow Math Help Forum on Facebook and Google+

  13. #13
    Junior Member
    Joined
    Jun 2007
    Posts
    42

    And..what???

    oh that was 3a............what about 1 a) and b).....what about 3b) oh man i'm confused!!!!!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. More log questions
    Posted in the Algebra Forum
    Replies: 1
    Last Post: March 31st 2010, 04:58 PM
  2. Please someone help me with just 2 questions?
    Posted in the Algebra Forum
    Replies: 3
    Last Post: May 4th 2009, 04:55 AM
  3. Some Questions !
    Posted in the Geometry Forum
    Replies: 1
    Last Post: May 3rd 2009, 03:09 AM
  4. Replies: 4
    Last Post: July 19th 2008, 07:18 PM
  5. Replies: 3
    Last Post: August 1st 2005, 01:53 AM

Search Tags


/mathhelpforum @mathhelpforum