Results 1 to 4 of 4

Math Help - Dimensions of Kindle (Electronic pad with a screen)

  1. #1
    Junior Member
    Joined
    Dec 2009
    From
    U.S
    Posts
    60

    Dimensions of Kindle (Electronic pad with a screen)

    I created this problem and wanted to check my answers with the MathForum.

    x = length
    y = width

    Scenario:
    There are two Kindles.
    K(1) has the dimensions of 3.6 in by 4.8 in. with a surface area (SA) of 17.28in^2 and a diagonal that measures 6 in
    K(2) has the dimensions of 5.4 in by 7.9 in. with a surface area of 42.66in^2 and a diagonal that measures 9.56 in

    a. How much bigger is K(2)'s SA compared to K(1)'s SA?
    my answer: ~2.47 times

    b. Write an equation that represents the maximum and minimum value of
    x and y when the SA of K(3) is 42.66 in.
    my answer: Either x=42.66*y or y=42.66*x


    Note: For 'c' I want to know if it's possible to have a minimum and maximum value of the length and width when the diagonal is 6 in. My guess is that you can only have 1 combination of 'x' and 'y' that gives you a SA of 42.66 and a diagonal of 6 in.

    c. Write an equation/system of equations that represents the maximum and minimum value of x and y if the diagonal of K(3) is 6 inches.

    my answer: x^2 + y^2 = (6)^2 --> y = -X + 6 (If I simplified that right) and x=42.66*y or y=42.66*x; where the two lines intersect is the value of x and y when the diagonal is 6.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,693
    Thanks
    1466
    Quote Originally Posted by Masterthief1324 View Post
    I created this problem and wanted to check my answers with the MathForum.

    x = length
    y = width

    Scenario:
    There are two Kindles.
    K(1) has the dimensions of 3.6 in by 4.8 in. with a surface area (SA) of 17.28in^2 and a diagonal that measures 6 in
    K(2) has the dimensions of 5.4 in by 7.9 in. with a surface area of 42.66in^2 and a diagonal that measures 9.56 in

    a. How much bigger is K(2)'s SA compared to K(1)'s SA?
    my answer: ~2.47 times
    Yes, that is correct.


    b. Write an equation that represents the maximum and minimum value of
    x and y when the SA of K(3) is 42.66 in.
    my answer: Either x=42.66*y or y=42.66*x
    What? You said there were two kinds of "kindle", K(1) and K(2). Where did K(3) come from? Without any information about K(3) it is impossible to answer this. Did you leave something out?


    Note: For 'c' I want to know if it's possible to have a minimum and maximum value of the length and width when the diagonal is 6 in. My guess is that you can only have 1 combination of 'x' and 'y' that gives you a SA of 42.66 and a diagonal of 6 in.

    c. Write an equation/system of equations that represents the maximum and minimum value of x and y if the diagonal of K(3) is 6 inches.

    my answer: x^2 + y^2 = (6)^2 --> y = -X + 6 (If I simplified that right)
    No, you didn't. " x^2+ y^2= z^2" does NOT reduce to "x+ y= z". For example, 4^2+ 3^2= 16+ 9= 25= 5^2 but 4+ 3\ne 5.

    and x=42.66*y or y=42.66*x; where the two lines intersect is the value of x and y when the diagonal is 6.
    If x^2+ y^2= 36 and xy= 42.66, then y= 42.66/x so x^2+ \frac{1819.8756}{x^2}= 36. Multiplying both sides by x^2, x^4+ 1819.8756= 36x^2 or x^4- 36x^2+ 1819.8756= 0. If you let u= x^2, this becomes the quadratic equation u^2- 36u+ 1819.8756= 0. Solve that for u, then take the square root to find x.

    But are you sure you have interpreted the question correctly? The problem said "find maximum and minimum" values, not specific values.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Dec 2009
    From
    U.S
    Posts
    60
    Sorry, I did make that last problem confusing.
    I hope this clarifies it.

    K(3) is a hypothetical Kindle device with a surface area of 42.66in^2 and a diagonal of 6 in.

    c1. Can you have more than one dimensions that satisfy the SA & the diagonal length of 6in? Why or why not?
    my answer: Not if the diagonal is 6 inch -- there is only 1 value of x and y (length and width)

    c2. Can you represent c1. with and equation?
    my answer: Since the diagonal is 6, if I was to use the Pythagorean theorem, there is only 1 value of x and y that would fit the specifications.

    (specifications)
    You know indefinitely that the K(3) has a surface area of 42.66 and a diagonal of 6 in:

    my equation:
    x^2 + y^2 = 6 (is it 6 or 6^2?) --> y=√(z^2 - x^2)
    x*y = 42.66

    If I was to graph the two equations, will where they intersect be the dimensions that fit the specifications?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member billa's Avatar
    Joined
    Oct 2008
    Posts
    100
    b. Write an equation that represents the maximum and minimum value of
    x and y when the SA of K(3) is 42.66 in.
    my answer: Either or
    If K(3) has a surface area of 42.66, then you know that

    xy=42.66

    since the diagonal is 6 inches, you know that

    x^2 + y^2 = 6^2 (draw a picture to understand why it is 6^2 and not 6)

    You have two equations, you can try to solve them both for y and graph them to approximate a solution

    y=42.66/x
    y=sqrt(36-x^2)

    Once you look at this graph you will realize that there is no solution to your problem

    K(3) is physically impossible

    ---------------------------------------
    To understand this, think of the kindle with diagonal 6 that has the largest surface area, this kindle would be square. It would have x = y = sqrt (18), so its largest surface area would be xy=18

    I created this problem and wanted to check my answers with the MathForum.
    To fix your problem, you must either increase the size of the diagonal or reduce the surface area of K(3) to make the two curves intersect
    Last edited by billa; January 6th 2010 at 04:57 AM. Reason: Fixed syntax and added bottom part
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Electronic bank teller question
    Posted in the Algebra Forum
    Replies: 3
    Last Post: February 1st 2011, 03:06 PM
  2. Dimensions of a TV screen problem.
    Posted in the Geometry Forum
    Replies: 1
    Last Post: January 16th 2010, 08:06 AM
  3. Question about Secure Electronic transaction?
    Posted in the Advanced Applied Math Forum
    Replies: 0
    Last Post: December 2nd 2009, 08:20 PM
  4. electronic amplification
    Posted in the Advanced Applied Math Forum
    Replies: 1
    Last Post: November 15th 2007, 11:24 AM

Search Tags


/mathhelpforum @mathhelpforum