Results 1 to 9 of 9

Math Help - *HeLp* geometry & algebra question

  1. #1
    Junior Member
    Joined
    Sep 2007
    Posts
    56

    *HeLp* geometry & algebra question

    Hey guys I need help on one last problem well, actually two.

    1. A rectangular parcel of land is 70 feet longer then it is wide. Each diagonal between opposite corners is 130ft. What are the dimensions of the parcel?

    I know the L = 70 + W but other then that, no idea how to even start on this problem.

    2. For what values of x is the expression Sqroot of 6x-x^2 defined as a real number?

    this one I'm just at a pure loss.

    thanks once again
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member topher0805's Avatar
    Joined
    Jan 2008
    From
    Vancouver
    Posts
    336
    1) You know that L = W + 70, and you know that from corner to corner the length is 130 feet. You need to use pythagorean theory to solve this one. The hypotenuse is 130, and the other sides are W, and W + 70.

    This gives us:

    130^2 = W^2 + (W + 70)^2

    Now we simply have to solve for W. First multiply out the last term:

    130^2 = W^2 + (W^2 + 140W + 4,900)

    Note that 130^2 is equal to 16,900. Now, bring everything to one side:

    <br />
2W^2 + 140W - 12,000 = 0

    Now just use the quadratic equation to find W.

    2) The square root function is only defined for numbers greater than or equal to 0. Therefore:

    6x - x^2 >= 0

    Now just solve the inequality for x:

    6x >= x^2

    So:

    <br />
6 >= x

    We now have that x must be equal to or less than 6 for the function to be defined.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Sep 2007
    Posts
    56
    2) The square root function is only defined for numbers greater than or equal to 0. Therefore:

    6x - x^2 >= 0

    Now just solve the inequality for x:

    6x >= x^2

    So:

    <br />
6 >= x

    did you divide out the X?

    We now have that x must be equal to or less than 6 for the function to be defined.[/QUOTE]

    ok i'm having a hard time understanding how to get from this
    6x >= x^2 to this
    <br />
6 >= x

    if you can elaborate it would help alot thanks.
    did you divide out the X?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member topher0805's Avatar
    Joined
    Jan 2008
    From
    Vancouver
    Posts
    336
    I just divided both sides by x.

    Oh, and I forgot to mention that x must also be greater than 0.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Sep 2007
    Posts
    56
    Quote Originally Posted by topher0805 View Post
    I just divided both sides by x.

    Oh, and I forgot to mention that x must also be greater than 0.
    can you explain that a little bit. the X being greater than 0

    hey thanks for all the help seriously
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Senior Member topher0805's Avatar
    Joined
    Jan 2008
    From
    Vancouver
    Posts
    336
    When you divide both sides by x, there are actually two options. Either x is positive or x is negative.

    In an inequality, when you divide by a negative number, you must switch the sign. So, the two cases are:

    x \leq 6 when x is positive.

    and:

    x \geq 6 when x is negative.

    You then test both solutions by plugging in values both above and below 6. By doing this you will notice that values above 6 make the function undefined. Therefore, x can not be negative, and your final answer is:

    0 \leq x \leq 6
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Junior Member
    Joined
    Sep 2007
    Posts
    56
    Thanks for helping me so much. Hopefully I'll get the knack of this stuff soon enough, until then I'll be counting on your help thanks!!
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Senior Member topher0805's Avatar
    Joined
    Jan 2008
    From
    Vancouver
    Posts
    336
    No problem. I struggle with math myself so any help I can provide I always do. I know what it feels like to be frustrated with a problem for a long time.

    Just a reminder that there is a thanks button in the bottom right of posts to thank helpful posters. Just for future reference.
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Super Member angel.white's Avatar
    Joined
    Oct 2007
    Posts
    723
    Awards
    1
    Quote Originally Posted by Afterme View Post
    can you explain that a little bit. the X being greater than 0
    You have \sqrt{6x-x^2}

    Consider if the value of 6x-x^2 were negative, lets say x = 7, then we have
    \sqrt{6(7)-7^2} = \sqrt{42-49} = \sqrt{-7}

    Lets say the answer of \sqrt{-7} is equal to some value a.
    Then
    \sqrt{-7}=a
    -7=a^2

    What value can a have? It must be equal to -7 when multiplied by itself. But if a is positive, then a^2 is positive. And if a is negative, then a^2 is still positive (a negative number times a negative number is a positive number). So there is no real number which can be equal to a negative number when it is squared. This means that if \sqrt{6x-x^2} is a real number, then 6x-x^2 must not be negative, so it must be greater than or equal to zero.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. algebra geometry
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: August 17th 2009, 04:50 AM
  2. Algebra in Geometry
    Posted in the Algebra Forum
    Replies: 1
    Last Post: May 13th 2009, 12:00 PM
  3. Geometry and algebra
    Posted in the Calculus Forum
    Replies: 2
    Last Post: September 3rd 2008, 06:52 AM
  4. Algebra/Coordinate Geometry
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: July 30th 2007, 05:18 PM
  5. geometry algebra
    Posted in the Geometry Forum
    Replies: 9
    Last Post: January 6th 2006, 05:00 AM

Search Tags


/mathhelpforum @mathhelpforum