A Problem Solving Approach to Mathematics for Elementary School Teachers (12th Edition)
12th Edition
ISBN: 9780321987297
Author: Rick Billstein, Shlomo Libeskind, Johnny Lott
Publisher: PEARSON
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Textbook Question
Chapter 6.4A, Problem 1A
Answer the following regarding the English alphabet.
a. Determine the ratio of vowels to consonants.
b. What is the ratio of consonants to vowels?
c. What is the ratio of consonants to letters?
d. Write a word that has a ratio of 2:3 of vowels to consonants.
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Q3: Define the linear functional J: H(2)
R by
1(v) = a(v. v) - L(v)
Let u be the unique weak solution to a(u,v) = L(v) in H() and suppose that
a(...) is a symmetric bilinear form on H(2) prove that
1- u is minimizer. 2- u is unique. 3- The minimizer J(u,) can be rewritten under
algebraic form
u Au-ub.
J(u)=u'Au-
Where A. b are repictively the stiffence matrix and the load vector
==
1. A separable differential equation can be written in the form hy) = g(a) where h(y) is a function of y
only, and g(x) is a function of r only.
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a general solution by integrating both sides. Determine whether the solutions you found are explicit
(functions) or implicit (curves but not functions)
(a) 1' = — 1/3
(b) y' =
=
---
Y
(c) y = x(1+ y²)
Chapter 6 Solutions
A Problem Solving Approach to Mathematics for Elementary School Teachers (12th Edition)
Ch. 6.1 - Mathematical Connections Explain why 25 cents is...Ch. 6.1 - Mathematical Connections In each of two different...Ch. 6.1 - Prob. 3MCCh. 6.1 - Prob. 4MCCh. 6.1 - Prob. 10MCCh. 6.1 - Prob. 11MCCh. 6.1 - MATHEMATICAL CONNECTIONS A students claims that...Ch. 6.1 - Prob. 13MCCh. 6.1 - MATHEMATICAL CONNECTIONS Ann claims that she...Ch. 6.1 - How would you respond to each of the following...
Ch. 6.1 - Prob. 16MCCh. 6.1 - Prob. 17MCCh. 6.1 - Prob. 18MCCh. 6.1 - What fraction of the figure is shaded?Ch. 6.1 - Prob. 2NAEPCh. 6.1 - Prob. 3NAEPCh. 6.1 - NATIONAL ASSESSMENT OF EDUCATIONAL PROGRESS NAEP...Ch. 6.1A - Write a sentence that illustrates the use of 78 in...Ch. 6.1A - For each of the following, write a fraction to...Ch. 6.1A - If the entire rectangle is a whole, what fraction...Ch. 6.1A - Prob. 4ACh. 6.1A - Prob. 5ACh. 6.1A - In each case, subdivide the whole shown on the...Ch. 6.1A - Referring to the figure, represent each of the...Ch. 6.1A - Prob. 8ACh. 6.1A - For each of the following fractions, write three...Ch. 6.1A - Find the simplest form for each of the following...Ch. 6.1A - For each of the following fractions, choose the...Ch. 6.1A - Find the simplest form for each of the following...Ch. 6.1A - Determine whether the following pairs are equal....Ch. 6.1A - Determine whether the following pairs are equal by...Ch. 6.1A - Draw an area model to show that 34=68.Ch. 6.1A - If a fraction equals 34 and the sum of the...Ch. 6.1A - Mr. Gomez filled his cars 16 gal gas tank. He took...Ch. 6.1A - Solve for x in each of the following. a. 23=x16 b....Ch. 6.1A - For each of the following pair of fractions,...Ch. 6.1A - Arrange each of the following in descending...Ch. 6.1A - For each of the following, find two rational...Ch. 6.1A - a. 6 oz is what part of a pound? A ton? b. A dime...Ch. 6.1A - Determine whether the following is true: If a, b,...Ch. 6.1A - Based on your visual observation write a fraction...Ch. 6.1A - Fill in missing numbers for x, y, z, and w to...Ch. 6.1A - Mathematical Connections Explain why in...Ch. 6.1A - Prove that any integer n can be written as a...Ch. 6.1A - Prob. 28ACh. 6.1A - Ten bulbs were in a chandelier. One-fifth of the...Ch. 6.1A - At a party, there were 35 guests. Two-fifths of...Ch. 6.1B - Write a sentence that illustrate the use of 710 in...Ch. 6.1B - For each of the following write the fraction to...Ch. 6.1B - If the entire rectangle is a whole, what fraction...Ch. 6.1B - Complete each of the following figures so that it...Ch. 6.1B - Prob. 5ACh. 6.1B - In each of the following models represents the...Ch. 6.1B - Referring the figure represent the each of the...Ch. 6.1B - Prob. 8ACh. 6.1B - For each of the following write three equal...Ch. 6.1B - Find the simplest form for each of the following...Ch. 6.1B - Prob. 11ACh. 6.1B - Find the simplest form for each of the following...Ch. 6.1B - Determine whether the following pairs are equal....Ch. 6.1B - Determine whether the following pairs are equal by...Ch. 6.1B - Prob. 15ACh. 6.1B - Prob. 16ACh. 6.1B - The following two parking meters are next to each...Ch. 6.1B - Solve for x in each of the following. a.23=x18...Ch. 6.1B - For each of the following pairs of fractions,...Ch. 6.1B - Prob. 20ACh. 6.1B - a. 12oz is what part of a pound. b A nickel is...Ch. 6.1B - Prob. 22ACh. 6.1B - Fill in missing numbers for x, y, z, and w to...Ch. 6.1B - Use the Fundamental Law of Fractions Theorem 6-1...Ch. 6.1B - Prob. 25ACh. 6.1B - Prob. 26ACh. 6.1B - Ten light bulbs were in a chandelier. Three-fifths...Ch. 6.1B - At a party, there were 40 guests. One-fifth of the...Ch. 6.2 - Suppose a large pizza is divided into 3 equal...Ch. 6.2 - Prob. 2MCCh. 6.2 - Prob. 3MCCh. 6.2 - Kara spent 12 of her allowance on Saturday and 13...Ch. 6.2 - Compute 334+513 in two different ways and leave...Ch. 6.2 - Prob. 6MCCh. 6.2 - Write a story problem for 2314.Ch. 6.2 - Prob. 8MCCh. 6.2 - a. With the exception of 23, the Egyptians used...Ch. 6.2 - Kendra showed that 13+34=47 by using the following...Ch. 6.2 - Prob. 12MCCh. 6.2 - Prob. 13MCCh. 6.2 - Explain the error pattern on Jons test. a....Ch. 6.2 - Prob. 15MCCh. 6.2 - Prob. 16MCCh. 6.2 - Prob. 17MCCh. 6.2 - Prob. 18MCCh. 6.2 - Prob. 19MCCh. 6.2 - Prob. 20MCCh. 6.2 - Prob. 1NAEPCh. 6.2 - Prob. 2NAEPCh. 6.2A - Perform the following additions or subtractions....Ch. 6.2A - Change each of the following fractions to a mixed...Ch. 6.2A - Change each of the following mixed numbers to a...Ch. 6.2A - Approximate each of the following situations with...Ch. 6.2A - Use the information in the table to answer each of...Ch. 6.2A - Sort the following fraction cards into the ovals...Ch. 6.2A - Approximate each of the following fractions by...Ch. 6.2A - Prob. 8ACh. 6.2A - The following ruler has region marked M, A, T, H....Ch. 6.2A - Use clustering to estimate the following sum....Ch. 6.2A - A class consists of 25 freshmen, 14 sophomores,...Ch. 6.2A - A clerk sold three pieces of one type ribbon of...Ch. 6.2A - Martine bought 834yd of fabric. She wants to make...Ch. 6.2A - Give an example illustrating each of the following...Ch. 6.2A - Insert five fractions between the numbers 1 and 2...Ch. 6.2A - Prob. 17ACh. 6.2A - Prob. 18ACh. 6.2A - Prob. 19ACh. 6.2A - One recipe calls for 134 cups of milk and a second...Ch. 6.2A - Prob. 21ACh. 6.2A - Prob. 22ACh. 6.2A - Prob. 23ACh. 6.2A - The energy sources for the US in 2012 included...Ch. 6.2B - Perform the following additions or subtractions....Ch. 6.2B - Change each of the following fractions to a mixed...Ch. 6.2B - Prob. 3ACh. 6.2B - Place the numbers 2,5,6, and 8 in the following...Ch. 6.2B - Use the information in the table to answer each of...Ch. 6.2B - Sort the following fraction cards into the ovals...Ch. 6.2B - Prob. 7ACh. 6.2B - Prob. 8ACh. 6.2B - Compute each of the following mentally. a. 678 b....Ch. 6.2B - The following ruler has regions marked M, A, T, H....Ch. 6.2B - A class consists of 14 freshmen, 15 sophomores,...Ch. 6.2B - The Naturals Company sells its products in many...Ch. 6.2B - A recipe requires 312 cups of milk. Ran put in 134...Ch. 6.2B - A 1534in. board is cut in a single cut from a...Ch. 6.2B - Students from Rattlesnake School formed four teams...Ch. 6.2B - Insert four fractions between the numbers 1 and 3...Ch. 6.2B - Solve for x in each of the following. a. x56=23 b....Ch. 6.2B - Joe has 34 cup of paint in a container. He uses 13...Ch. 6.2B - a. Find 12+14. b. Find 12+14+18. c. Find...Ch. 6.2B - Prob. 21ACh. 6.2B - Prob. 22ACh. 6.2B - The energy sources for the US in 2012 included...Ch. 6.3 - Suppose you divide a natural number n by a...Ch. 6.3 - If the fractions represented by points C and D on...Ch. 6.3 - If the product of two numbers is 1 and one of the...Ch. 6.3 - Write a story or model for 13412.Ch. 6.3 - Bente says to do the problem 1214334 you just find...Ch. 6.3 - Amy says that dividing a number by 12 is the same...Ch. 6.3 - Dani says that if we have 3425, we could just...Ch. 6.3 - Noah says that dividing a number by 2 is the same...Ch. 6.3 - Jim is not sure when to use multiplication by a...Ch. 6.3 - A student claims that division always makes things...Ch. 6.3 - A student simplified the fraction m+np+n to mp....Ch. 6.3 - Jillian says she learned that 17 divided by 5 can...Ch. 6.3 - Perform each of the following computations. Leave...Ch. 6.3 - Each student at Sussex Elementary School takes one...Ch. 6.3 - Prob. 20MCCh. 6.3 - Determine which of the following is always...Ch. 6.3 - Both figures below show the same scale. The marks...Ch. 6.3 - Jim has 34 of a yard of string which he wishes to...Ch. 6.3 - Nick has a whole pizza. Nick says he will eat 12...Ch. 6.3A - In the following figures, a unit rectangle is used...Ch. 6.3A - Use a rectangular region to illustrate each of the...Ch. 6.3A - Find each of the following products. Write your...Ch. 6.3A - Prob. 4ACh. 6.3A - Find the multiplicative inverse of each of the...Ch. 6.3A - Solve for x. a. 23x=76 b. 34x=12 c. 56+23x=34 d....Ch. 6.3A - Show that the following properties do not hold for...Ch. 6.3A - Compute the following mentally. 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Amal can finish a job in 12 of a day working by...Ch. 6.4 - Prob. 1NAEPCh. 6.4 - Prob. 2NAEPCh. 6.4A - Answer the following regarding the English...Ch. 6.4A - Solve for x each of the following proportions. a....Ch. 6.4A - a. If the ratio of boys to girls in a class is...Ch. 6.4A - There are approximately 2lb of muscle for every...Ch. 6.4A - Prob. 5ACh. 6.4A - Prob. 6ACh. 6.4A - Prob. 7ACh. 6.4A - Two numbers are in the ratio 3:4. Find the numbers...Ch. 6.4A - Gary, Bill, and Carmella invested in a corporation...Ch. 6.4A - Sheila and Dora worked 312hr and 412hr...Ch. 6.4A - Vonna scored 75 goals in her soccer kicking...Ch. 6.4A - Express each of the following ratios in the form...Ch. 6.4A - Prob. 13ACh. 6.4A - The rise and span for a house roof are identified...Ch. 6.4A - Gear ratios are used in industry. A gear ratio is...Ch. 6.4A - A Boeing 747 jet is approximately 230 ft long and...Ch. 6.4A - Prob. 17ACh. 6.4A - The electrical resistance of a wire, measured in...Ch. 6.4A - In a photograph of a father and his daughter, the...Ch. 6.4A - The amount of gold in jewelry and other products...Ch. 6.4A - If Amber is paid 8 per hour for typing, the table...Ch. 6.4A - a. In Room A, there are 1 man and 2 women; in Room...Ch. 6.4A - Prob. 23ACh. 6.4A - A car travels about 26 miles on 1 gallon of gas,...Ch. 6.4A - Susan bikes 20 miles in 2 hours, while Nick bikes...Ch. 6.4A - There are 40 students in a classroom, and the...Ch. 6.4A - The ratio of oblong tables to round tables at a...Ch. 6.4A - A recipe uses 112 c flour to make 2 dozen cookies....Ch. 6.4B - Answer the following regarding the letters in the...Ch. 6.4B - Solve for x in each of the following proportions....Ch. 6.4B - There are 5 adult drivers to each teenage driver...Ch. 6.4B - A candle is 30 in. long. After burning for 12 min,...Ch. 6.4B - A rectangular yard has a width-to-length ratio of...Ch. 6.4B - A grasshopper can jump 20 times its length. If...Ch. 6.4B - Juan found out that after working for 9 months he...Ch. 6.4B - Prob. 8ACh. 6.4B - At a particular time, the ratio of the height of...Ch. 6.4B - The following table shows several possible widths...Ch. 6.4B - Find three sets of x- and y-values for the...Ch. 6.4B - If rent is 850 for each 2 weeks, how much is the...Ch. 6.4B - Leonardo da Vinci in his drawing Vitruvian man...Ch. 6.4B - On a city map, a rectangular park has a length of...Ch. 6.4B - Jims car will travel 240 mi on 15 gal of gas. How...Ch. 6.4B - Some model railroads use an 0 scale in replicas of...Ch. 6.4B - a. On an American flag, what is the ratio of stars...Ch. 6.4B - On an American flag, the ratio of the length of...Ch. 6.4B - If xy=ab,a0,x0 is true, what other proportion do...Ch. 6.4B - If a certain recipe takes 112c flour and 4 c milk,...Ch. 6.4B - Prob. 21ACh. 6.4B - Prob. 22ACh. 6.4B - Prob. 23ACh. 6.4B - Prob. 24ACh. 6.4B - The ratio of oblong tables to round tables at a...Ch. 6.4B - Prob. 26ACh. 6.4B - Prob. 27ACh. 6.CR - CHAPTER 6 REVIEW For each of the following, draw a...Ch. 6.CR - Write three rational numbers equal to 56.Ch. 6.CR - Write each of the following rational numbers in...Ch. 6.CR - Prob. 4CRCh. 6.CR - CHAPTER 6 REVIEW Find the additive and...Ch. 6.CR - Prob. 6CRCh. 6.CR - Prob. 7CRCh. 6.CR - Prob. 8CRCh. 6.CR - CHAPTER 6 REVIEW John has 5414 yd of material. a....Ch. 6.CR - Prob. 10CRCh. 6.CR - Prob. 11CRCh. 6.CR - CHAPTER 6 REVIEW. 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