{"id":26,"date":"2018-01-05T00:08:25","date_gmt":"2018-01-05T00:08:25","guid":{"rendered":"http:\/\/salguod.net\/blog\/?p=26"},"modified":"2021-05-29T03:43:34","modified_gmt":"2021-05-29T03:43:34","slug":"algebra","status":"publish","type":"post","link":"https:\/\/salguod.net\/blog\/2018\/01\/algebra.shtml","title":{"rendered":"Algebra"},"content":{"rendered":"

\"\"<\/a>The other day I got to use algebra to show my youngest how we could determine the shelf spacing on an Ikea shelf by only knowing it’s height and the height of another in the same family.<\/p>\n

She was looking at this Mulig shelf unit<\/a> for her new turntable and wanted to know if the shelves were tall enough for the records.\u00a0 All we knew was that it was 35.375″ tall.\u00a0 However, they have other units in the same family and this one<\/a> is the same width and is 5 shelves instead of 3 and it’s 63.75″ tall.\u00a0 With a couple of rational assumptions and some algebra we determined that it would work.<\/p>\n

First the assumptions:<\/p>\n

    \n
  1. They are made from the same components.<\/li>\n
  2. The shelf spacing is the same between the two units.<\/li>\n
  3. The space above the top shelf and the space below the bottom shelf is equal.<\/li>\n<\/ol>\n

    Given that, once can write the following with X being the center to center spacing of the shelves and Y the space at the top and bottom:<\/p>\n

    4x+2y=63.75<\/p>\n

    2x+2y=35.375<\/p><\/blockquote>\n

    Solving one for 2y we get:<\/p>\n

    2y=35.375-2x<\/p><\/blockquote>\n

    Which we can then substitute in the first equation and solve for X:<\/p>\n

    4x+(35.375-2x)=63.75<\/p>\n

    2x+35.375=63.75<\/p>\n

    2x=28.375<\/p>\n

    x=14.1875<\/p><\/blockquote>\n

    That then lets us solve for Y:<\/p>\n

    2y=35.375-2x<\/p>\n

    2y=35.375-2*14.1875<\/p>\n

    2y=35.375-28.375<\/p>\n

    2y=7<\/p>\n

    y=3.5<\/p><\/blockquote>\n

    So, the shelf to shelf dim should be about 14.1875″ and the shelf center to floor dim should be about 3.5″.\u00a0 Assuming a shelf thickness of about 1″, reasonable looking at the images, I estimated the open space to be 13.1875″. Plenty of space for 12″ records, so we ordered one.<\/p>\n

    After picking it up and putting it together I measured the space and found it was exactly what the algebra told us it would be – 13.1875″.<\/p>\n

    Gotta love math.<\/p>\n

    <\/div>\n
    <\/div>\n","protected":false},"excerpt":{"rendered":"

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He advocates a rather high level of study for those who want to read adn study the Bible in the original Greek, and for good reason: It is simply not realistic that a Greek scholar will be produced through\u2026","rel":"","context":"In "God and Church"","block_context":{"text":"God and Church","link":"https:\/\/salguod.net\/blog\/god-and-church"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":190,"url":"https:\/\/salguod.net\/blog\/2004\/08\/more_politics_y.shtml","url_meta":{"origin":26,"position":1},"title":"More politics (Yeah, I know I said I wouldn’t)","author":"Doug Schaefer","date":"August 31, 2004","format":false,"excerpt":"Well, it's an election year and the Big Day is only about two months away. Absolutely everything on radio and TV is election related. So I've succumbed to Election Fever. I've actually watched some of a convention. I managed to avoid the Democratic convention, but we were watching the Amazing\u2026","rel":"","context":"In "News & Current Events"","block_context":{"text":"News & Current Events","link":"https:\/\/salguod.net\/blog\/news-current-events"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":533,"url":"https:\/\/salguod.net\/blog\/2006\/07\/my_example.shtml","url_meta":{"origin":26,"position":2},"title":"My Example","author":"Doug Schaefer","date":"July 31, 2006","format":false,"excerpt":"Yes, it's another Patrick Mead link. Hey, It's been a few weeks, you're due for another. Go read this and see if you can act the same around your kids again. I hope I can't.","rel":"","context":"In "Family and Friends"","block_context":{"text":"Family and Friends","link":"https:\/\/salguod.net\/blog\/family-and-friends"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":92,"url":"https:\/\/salguod.net\/blog\/2004\/03\/california_cont.shtml","url_meta":{"origin":26,"position":3},"title":"California Contraceptive Ruling","author":"Doug Schaefer","date":"March 2, 2004","format":false,"excerpt":"VirusDoc has a post today on the California supreme court decision that catholic charities must include birth control in the health insurance coverage for employees. There are a couple of things that bother me about this story. The first is the Catholic Charities stance of not allowing birth control prescriptions\u2026","rel":"","context":"In "God and Church"","block_context":{"text":"God and Church","link":"https:\/\/salguod.net\/blog\/god-and-church"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":892,"url":"https:\/\/salguod.net\/blog\/2009\/01\/two_weeks.shtml","url_meta":{"origin":26,"position":4},"title":"Two Weeks","author":"Doug Schaefer","date":"January 5, 2009","format":false,"excerpt":"Wow, has it really been two weeks since I posted? It's been a busy holiday season, sorry for the absence. 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Not this year though: This year, though, the merry menagerie stayed indoors.\u2026","rel":"","context":"In "News & Current Events"","block_context":{"text":"News & Current Events","link":"https:\/\/salguod.net\/blog\/news-current-events"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]}],"_links":{"self":[{"href":"https:\/\/salguod.net\/blog\/wp-json\/wp\/v2\/posts\/26"}],"collection":[{"href":"https:\/\/salguod.net\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/salguod.net\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/salguod.net\/blog\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/salguod.net\/blog\/wp-json\/wp\/v2\/comments?post=26"}],"version-history":[{"count":6,"href":"https:\/\/salguod.net\/blog\/wp-json\/wp\/v2\/posts\/26\/revisions"}],"predecessor-version":[{"id":2230,"href":"https:\/\/salguod.net\/blog\/wp-json\/wp\/v2\/posts\/26\/revisions\/2230"}],"wp:attachment":[{"href":"https:\/\/salguod.net\/blog\/wp-json\/wp\/v2\/media?parent=26"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/salguod.net\/blog\/wp-json\/wp\/v2\/categories?post=26"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/salguod.net\/blog\/wp-json\/wp\/v2\/tags?post=26"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}