Mathematics for Elementary Teachers with Activities, Loose-Leaf Version Plus MyLab Math -- Access Card Package (5th Edition)
5th Edition
ISBN: 9780134800196
Author: Sybilla Beckmann
Publisher: PEARSON
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Textbook Question
Chapter 9.3, Problem 3P
In your own words explain how to solve each of the next " one - step " equation by reasoning in at least two different ways . Explain the reasoning in enough detail so that someone who doesnt already know how to solve such equation can understand why the method works .
a.
b.
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An Arts group holds a raffle. Each raffle ticket costs $2 and the raffle consists of 2500 tickets. The prize is a vacation worth $3,000.
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Please show as much work as possible to clearly show the steps you used to find each solution. If you plan to use a calculator, please be sure to clearly indicate your strategy.
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(20 p) 1. Find a particular solution satisfying the given initial conditions for the third-order
homogeneous linear equation given below. (See Section 5.2 in your textbook if you need a
review of the subject.)
y(3)+2y"-y-2y = 0; y(0) = 1, y'(0) = 2, y"(0) = 0;
y₁ = e*, y2 = e¯x, y3 = e−2x
(20 p) 2. Find a particular solution satisfying the given initial conditions for the second-order
nonhomogeneous linear equation given below. (See Section 5.2 in your textbook if you need
a review of the subject.)
y"-2y-3y = 6; y(0) = 3, y'(0) = 11
yc = c₁ex + c2e³x; yp = −2
(60 p) 3. Find the general, and if possible, particular solutions of the linear systems of
differential equations given below using the eigenvalue-eigenvector method. (See Section
7.3 in your textbook if you need a review of the subject.)
=
a) x 4x1 + x2, x2 = 6x1-x2
b) x=6x17x2, x2 = x1-2x2
c) x = 9x1+5x2, x2 = −6x1-2x2; x1(0) = 1, x2(0)=0
Chapter 9 Solutions
Mathematics for Elementary Teachers with Activities, Loose-Leaf Version Plus MyLab Math -- Access Card Package (5th Edition)
Ch. 9.1 - Write an expression that uses addition and...Ch. 9.1 - Write at least three different expression for the...Ch. 9.1 - Write at least three different expressions for the...Ch. 9.1 - a.Draw a design made of small circles ( or another...Ch. 9.1 - a.Draw a design made of small circles ( or another...Ch. 9.1 - Write two different expressions for the total...Ch. 9.1 - Write two different expressions for the total...Ch. 9.1 - Write two different expressions for the total...Ch. 9.1 - Prob. 9PCh. 9.1 - An auditorium has 50 rows of seats . The 1st row...
Ch. 9.1 - Write at least two expression for the total number...Ch. 9.1 - Write an expression using multiplication and...Ch. 9.1 - Write an expression using multiplication and...Ch. 9.1 - Shade 23.25+12.15 Of rectangle in such a way that...Ch. 9.1 - Shade 3413.12 Of rectangle in such a way that you...Ch. 9.1 - Show how to make the expression 21131356+17361834...Ch. 9.1 - Show how to make the expression (3111)(15+111)...Ch. 9.1 - Write equation that use rules about operating with...Ch. 9.1 - Explain why it is not valid to evaluate 22+377...Ch. 9.1 - Write equation that uses rules about operating...Ch. 9.2 - Describe the structure of the expression 3S3+2S3Ch. 9.2 - Describe the structure of the expression...Ch. 9.2 - a. Students sometime mistakenly think that the...Ch. 9.2 - Prob. 4PCh. 9.2 - a.Write at least two expression for the area of...Ch. 9.2 - Write at least two expression for the total number...Ch. 9.2 - Write and explain two equivalent expressions that...Ch. 9.2 - Draw label and shade a rectangle so that it gives...Ch. 9.2 - Draw label and shade a square so that it gives...Ch. 9.2 - a. Write two equivalent expressions , each using...Ch. 9.2 - Tyrone has a marble collection that he wants to...Ch. 9.2 - Kenny has stickers to distribute among some goodie...Ch. 9.2 - Ted is saving for a toy. He has no money now, but...Ch. 9.2 - If you pay $7 for a night light that cost $ 0.50...Ch. 9.2 - Bonnie had B stickers . First , bonnie gave away...Ch. 9.2 - There are X quarts of liquid in a container ....Ch. 9.2 - Martin had M dollers initially . First , martin...Ch. 9.2 - There are F cups of flour in a bag . First , 38 of...Ch. 9.2 - Write a scenario for the expression (x+15)13(x+15)...Ch. 9.2 - a. Write a scenario for the expression 45x25...Ch. 9.2 - At a store , the price of an item is $ P ....Ch. 9.2 - a. Try this mathematical magic trick several...Ch. 9.3 - Explain how to solve the next equation by...Ch. 9.3 - Write an equation that can be solved by reasoning...Ch. 9.3 - In your own words explain how to solve each of the...Ch. 9.3 - Solve 4x+5=x+8 In two ways : with equation and...Ch. 9.3 - Solve 3x+2=x+8 In two ways : with equation and...Ch. 9.3 - You asked your students to solve the equations...Ch. 9.3 - Give your own example of the following equations ....Ch. 9.3 - What's wrong with the next reasoning that...Ch. 9.3 - You are walking to azkaban when you come to a fork...Ch. 9.4 - A candy bowl contains 723 candies. Some of the...Ch. 9.4 - Sarah spends 25 of her monthly income on rent....Ch. 9.4 - After Joey spent 38 of his money on an electronic...Ch. 9.4 - Katie made some chocolate truffles. She gave 14 of...Ch. 9.4 - a. Suppose you want to modify Problem 4 about...Ch. 9.4 - Write something similar to Problem 4 in which a...Ch. 9.4 - By washing cars, Beatrice and Hannah raised $2000...Ch. 9.4 - There are 1700 bottles of water arranged into 4...Ch. 9.4 - Write something simiiar to Problem 8 in which a...Ch. 9.4 - One day a coffee shop sold 360 cups of coffee,...Ch. 9.4 - A 1-pound-5-ounce piece of cheese is divided into...Ch. 9.4 - A hot dog stand sold 38 of its hot dogs before...Ch. 9.4 - Write something similar to Problem 12 in which the...Ch. 9.4 - Julie bought donuts for a party - 16 of the donuts...Ch. 9.4 - Shauntay caught twice as many fireflies as Robert....Ch. 9.4 - At a frog exhibit, 35 of the frogs are bullfrogs,...Ch. 9.4 - {See Problem 15 in Section 9.2) Bonnie had some...Ch. 9.4 - (See problem 18 in Section 9.2 ) there are some...Ch. 9.4 - Not every algebra word problem is naturally...Ch. 9.4 - Not every algebra word problem is naturally...Ch. 9.4 - In a group of ladybugs there were 10% more male...Ch. 9.4 - A farmer planted 65% of his farmland with onions,...Ch. 9.4 - Some exercise equipment is on sale for 20% off....Ch. 9.4 - Clevere makes 30% more money than Shane. If...Ch. 9.4 - Two stores had a combined total of 210 teddy...Ch. 9.4 - If 23 of a cup of juice gives you 120% of your...Ch. 9.4 - Erika is weaving a wool blanket. So far, she has...Ch. 9.4 - Jane had a bottle filled with juice. At first, she...Ch. 9.4 - A flock of geese on a pond was being observed...Ch. 9.5 - Assume that the pattern of a square followed by 2...Ch. 9.5 - Assume that the pattern of a circle followed by 3...Ch. 9.5 - Assume that the repeating pattern of 4 squares...Ch. 9.5 - What day of the week will it be 1000 days from...Ch. 9.5 - Figure 9.52 shows a sequence of figures made of...Ch. 9.5 - Consider the arithmetic sequence whose first few...Ch. 9.5 - Consider the arithmetic sequence whose first few...Ch. 9.5 - Draw the first 5 figures in a sequence of figures...Ch. 9.5 - a. Consider the arithmetic sequence 5, 7,9,11,13,...Ch. 9.5 - Consider an arithmetic sequence whose third entry...Ch. 9.5 - Consider an arithmetic sequence whose fourth entry...Ch. 9.5 - Consider an arithmetic sequence whose fifth entry...Ch. 9.5 - Consider the geometric sequence whose first few...Ch. 9.5 - Consider the geometric sequence whose first few...Ch. 9.5 - Consider the geometric sequence whose first few...Ch. 9.5 - Describe four different rules for determining the...Ch. 9.5 - Describe four different rules for determining the...Ch. 9.5 - Describe four different rules for determining the...Ch. 9.5 - Suppose you owe $500 on a credit card that charges...Ch. 9.5 - Suppose you put $1000 in an account whose value...Ch. 9.5 - The Widget Company sells boxes of widgets by mail...Ch. 9.5 - Suppose a scientist puts a colony of bacteria...Ch. 9.5 - a. Use a calculator to compute 2161 . Are you able...Ch. 9.6 - Describe your own real or realistic context in...Ch. 9.6 - For each of the following descriptions, draw a...Ch. 9.6 - Consider the followmg scenario: Over a penod of 5...Ch. 9.6 - A patient receives a drug. This situation gives...Ch. 9.6 - Sketch three different graphs that could fit with...Ch. 9.6 - Sketch three different graphs that could fit with...Ch. 9.6 - Solar panels produce electricity by collecting...Ch. 9.6 - For each of the three scenarios below, sketch...Ch. 9.6 - An object is dropped from the top of a building....Ch. 9.6 - A skydiver jumps out of a plane. At first, the...Ch. 9.6 - Water is being poured at a steady rate into a...Ch. 9.6 - Write a story or describe a scenario that gives...Ch. 9.6 - Draw two different graphs of two different...Ch. 9.6 - Consider the doubling plus one function: The...Ch. 9.6 - Prob. 15PCh. 9.6 - Explain why the next proposed function is not a...Ch. 9.6 - The levels of a certain toxin in a lake have been...Ch. 9.7 - A small-order coffee company charges $12 for each...Ch. 9.7 - A company prints T-shirts with original designs....Ch. 9.7 - A company sells mail order T-shirts. The company...Ch. 9.7 - Today a T-shirt company has 500 T-shirts in stock....Ch. 9.7 - in a problem about the weight of animal feed in a...Ch. 9.7 - Some students are washing cars for a fund-raiser....Ch. 9.7 - Initially, a vat is filled with 500 liters of...Ch. 9.7 - Max was asked to write an equation corresponding...Ch. 9.7 - To cook rice, you need to use 112 times as much...Ch. 9.7 - A company sells 314 times as many tissues as...Ch. 9.7 - Show how to use strip diagrams to help you...Ch. 9.7 - After a vine that was 18 inches long was planted,...Ch. 9.7 - A mail order coffee company charges $12 for each...Ch. 9.7 - Assuming that the following tables are for linear...Ch. 9.7 - Consider a function that has the following...Ch. 9.7 - Consider a function that has the following...Ch. 9.7 - At one stage in a factory’s candy production,...Ch. 9.7 - A school bought 100 rolls of wrapping paper for a...Ch. 9.7 - For the spring fling, a school bought 200 slices...Ch. 9.7 - The Gizmo store sells gizmos. You pay $3 for the...Ch. 9.7 - At a store that sells fences, if you buy 15 feet...Ch. 9.7 - Describe a real-world scenario in which two...Ch. 9.7 - Consider these two relationships: Relationship 1:...Ch. 9.7 - For each of the following, either define variables...Ch. 9.7 - Compare and contrast inversely proportional...Ch. 9.7 - For each of the following tables, determine what...Ch. 9.7 - For each of the following tables, determine what...Ch. 9.7 - Find two different equations for two different...Ch. 9.7 - Consider the function whose equation is y2=x22x...Ch. 9.7 - An object is thrown down from the top of a...Ch. 9.7 - An oil company has determined that its profit...Ch. 9.7 - During a 6-hour rainstorm, rain fell at a rate of...Ch. 9.7 - In the country of Taxo, each household pays taxes...Ch. 9.7 - A company that sells coffee has determined that if...Ch. 9.7 - A projectile is launched. After tseconds, the...
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