Quilts Using Strips
I need help with an Algebra 2 word problem?
A quilt consists of strips of material, a courtyard surrounded by rectangles to form larger squares successively. The inner square and all the rectangles have a width of 1 m. Write an expression using the notation of summation gives the total area of all bands of fabric used to make the quilt shown. Then evaluate the expression.
The square is a square 1 * 1. Now, for around what you need four rectangles. There are several ways to do so. I make four rectangles of equal size arranged in a cross "Bridget" type of scenario … I wish I could draw this. Each rectangle is a unit of a side of the square. It is aligned with the square of one side and is located on the other – in one unit. Another rectangle is marked on the top of it as Excel and so on … until he made his way around the place. What really have to draw. Therefore, each rectangle is a unit more than the side of the square where a new place that is 2 units longer than the original. Therefore (It can be proved by induction if you want, but there is no real need here) each square is 2 successive units more than the previous. Thus, the first side of the square is of length 1, the second is of length 3 … n is the length 2n – 1. Today, four rectangles added to each iteration. The length of a rectangle is one less than the length of the side of the square that represents, namely the length of a rectangle in the manufacture of the square is n 2n – 2 which is equal to your area because it is the unit width. Except for first place, which has only a 1 (not 0) However, there are four rectangles by iteration, all area 2n – 2, so the total is added per iteration is 8 (n – 1) Thus, the expression is: 1 (for the inner square) + Sigma (8 (n – 1)) If Sigma is supposed to be the plus sign. Now, Sigma (8 (n – 1) = () Sigma 8n – 
n = 8Sigma (- 1) = 8 * 1.2 * N (N – 1) … Capital N because it is we add the point n that is the dummy "variable" of the sum. = 4N (N – 1) It is after n iterations becomes: 1 + 4N (N – 1) The first few terms of the sequence are 1, 9, 25 … That's it! Note that the sequence is the same as the squares of numbers odd (2n – 1) ^ 2 Hope this helps, and I hope you get the ground because I can not draw it here!
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Country Quilts in a Day: Using Strip Quilting & Other Speed Techniques $14.95 An introduction to the sewing and cutting techniques of strip quilting which make it possible to make quilts in a day. The techniques are simple enough for beginners, yet precise enough for the more experienced. Patterns include the starburst, lover’s knot, Irish chain and more…. |
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Sizzle ‘n Pop: Six Strip-Pieced Quilt Patterns Using Bali Pops $19.99 Clerestory Window is for those of you who want to spend some time creating more of an art quilt. Simple techniques, with thought to choosing fabrics, values and sewing angles –result is a gorgeous heirloom quilt. Includes a tips page for ideas and techniques. Hollyhocks is for beginners and uses two versions of the same block. Even the setting triangles are easy! Great for a weekend project or fo… |
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Country Quilts in a Weekend Using Strip Quilting & Other Speed Techniques … |
