A Problem Solving Approach to Mathematics for Elementary School Teachers, Books a la Carte Edition plus NEW MyLab Math with Pearson eText - Access Card Package (12th Edition)
12th Edition
ISBN: 9780133865479
Author: Rick Billstein, Shlomo Libeskind, Johnny Lott
Publisher: PEARSON
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Textbook Question
Chapter 14.4, Problem 3MC
In the drawing below, cube B was cut from a larger cube of surface area
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10-2
Let A =
02-4
and b =
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Denote the columns of A by a₁, a2, a3, and let W = Span {a1, a2, a̸3}.
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a. Is b in {a1, a2, a3}? How many vectors are in {a₁, a₂, a3}?
b. Is b in W? How many vectors are in W?
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a. Is b in {a₁, a2, a3}? Select the correct choice below and, if necessary, fill in the answer box(es) to complete your
choice.
○ A. No, b is not in {a₁, a2, 3} since it cannot be generated by a linear combination of a₁, a2, and a3.
B. No, b is not in (a1, a2, a3}
since b is not equal to a₁, a2, or a3.
C. Yes, b is in (a1, a2, a3} since b = a
(Type a whole number.)
D. Yes, b is in (a1, a2, 3} since, although b is not equal to a₁, a2, or a3, it can be expressed as a linear
combination of them. In particular, b =
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(Simplify your answers.)
(1) (14 points) Let a = (-2, 10, -4) and b = (3, 1, 1).
(a) (4 points) Using the dot product determine the angle between a and b.
(b) (2 points) Determine the cross product vector axb.
(c) (4 points) Calculate the area of the parallelogram spanned by a and b. Justify
your answer.
1
(d) (4 points) Think of this sheet of paper as the plane containing the vectors a =
(1,1,0) and b = (2,0,0). Sketch the parallelogram P spanned by a and b.
Which diagonal of P represents the vector ab geometrically?
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Chapter 14 Solutions
A Problem Solving Approach to Mathematics for Elementary School Teachers, Books a la Carte Edition plus NEW MyLab Math with Pearson eText - Access Card Package (12th Edition)
Ch. 14.1 - In track, the second lane from the inside of the...Ch. 14.1 - Prob. 3MCCh. 14.1 - Observe that it is possible to build a triangle...Ch. 14.1 - a. Help each person in the group find his or her...Ch. 14.1 - Jerry wants to design a gold chain 60 cm long made...Ch. 14.1 - A student claims that the circumference of a...Ch. 14.1 - A student asks why 227 cannot always be used as...Ch. 14.1 - A Student imagines a wire stretched around Earth....Ch. 14.1 - Which of these units would be the best to use to...Ch. 14.1 - If Freds rope is 12 inches long, about how long is...
Ch. 14.1A - Use the following picture of a ruler to find each...Ch. 14.1A - Prob. 2ACh. 14.1A - Complete each of the following. a. 100 in....Ch. 14.1A - Prob. 4ACh. 14.1A - Estimate the length of the following segment and...Ch. 14.1A - Prob. 6ACh. 14.1A - Repeat exercise 6 using English measures. 6....Ch. 14.1A - Prob. 8ACh. 14.1A - Prob. 9ACh. 14.1A - Prob. 10ACh. 14.1A - List the following in decreasing order: 8 cm,...Ch. 14.1A - Draw a circle as accurately as possible whose...Ch. 14.1A - a. What is the length of a semicircle of a circle...Ch. 14.1A - Prob. 14ACh. 14.1A - Complete each of the following. a. 10 mm =______cm...Ch. 14.1A - Draw a triangle ABC. Measure the length of each of...Ch. 14.1A - Can the following be the lengths of the sides of a...Ch. 14.1A - Prob. 18ACh. 14.1A - Take an 81211-in. piece of paper, fold it as shown...Ch. 14.1A - Prob. 20ACh. 14.1A - Prob. 21ACh. 14.1A - Prob. 22ACh. 14.1A - Prob. 23ACh. 14.1A - Prob. 24ACh. 14.1A - Prob. 25ACh. 14.1A - Prob. 26ACh. 14.1A - Suppose you have three concentric circles and are...Ch. 14.1B - Use the following picture of ruler to find each of...Ch. 14.1B - Estimate and then measure each of the following in...Ch. 14.1B - Convert each of the following to the indicated...Ch. 14.1B - Prob. 5ACh. 14.1B - Prob. 6ACh. 14.1B - Prob. 7ACh. 14.1B - Prob. 8ACh. 14.1B - If eggs were sold in the United States using...Ch. 14.1B - List the following in decreasing order:...Ch. 14.1B - Draw each of the following as accurately as...Ch. 14.1B - The following figure is a circle whose radius is 2...Ch. 14.1B - Prob. 14ACh. 14.1B - Complete each of the following conversions. a. 35...Ch. 14.1B - Prob. 16ACh. 14.1B - Can the following be the lengths of the sides of a...Ch. 14.1B - Prob. 18ACh. 14.1B - Prob. 20ACh. 14.1B - Prob. 21ACh. 14.1B - Prob. 22ACh. 14.1B - Astronomers use a light-year to measure distance....Ch. 14.1B - Give the greatest possible error for each of the...Ch. 14.1B - a. Find the length of a 48 arc of a circle whose...Ch. 14.1B - Find the radius of the circle containing 60 arc...Ch. 14.1B - Prob. 27ACh. 14.2 - Suppose a triangle has sides of lengths 6 in., 11...Ch. 14.2 - Prob. 2MCCh. 14.2 - Prob. 3MCCh. 14.2 - Explain how the rotation in the following drawing...Ch. 14.2 - Prob. 5MCCh. 14.2 - Prob. 6MCCh. 14.2 - Prob. 7MCCh. 14.2 - Prob. 9MCCh. 14.2 - a. Draw a circle of radius 4 cm and divide it into...Ch. 14.2 - Prob. 11MCCh. 14.2 - Prob. 12MCCh. 14.2 - On a field trip, Glenda, a sixth-grade student,...Ch. 14.2 - Prob. 14MCCh. 14.2 - Prob. 15MCCh. 14.2 - Larry and Gary are discussing whose garden has the...Ch. 14.2 - Ori claims that to find the area of a...Ch. 14.2 - Prob. 18MCCh. 14.2 - Prob. 19MCCh. 14.2 - Prob. 21MCCh. 14.2 - Prob. 22MCCh. 14.2 - Prob. 23MCCh. 14.2 - Prob. 24MCCh. 14.2 - Prob. 25MCCh. 14.2 - Prob. 1NAEPCh. 14.2 - Which figure has the greatest area? A. A B. BC....Ch. 14.2 - Prob. 3NAEPCh. 14.2 - Prob. 4NAEPCh. 14.2 - On the scale drawing above, the shaded area...Ch. 14.2A - Choose the most appropriate metric unit cm2, m2 or...Ch. 14.2A - Estimate and then measure the area of the each of...Ch. 14.2A - Prob. 4ACh. 14.2A - Complete the following conversions a. 4000ft2=yd2...Ch. 14.2A - Find the area of each of the following figures if...Ch. 14.2A - Complete each of the following sentences a. A...Ch. 14.2A - Prob. 8ACh. 14.2A - If a triangle is inscribed in a circle so that one...Ch. 14.2A - Prob. 10ACh. 14.2A - Find the area of each of the following...Ch. 14.2A - a. A rectangular piece of land is 1300m1500m i....Ch. 14.2A - Prob. 13ACh. 14.2A - Prob. 14ACh. 14.2A - Find the cost of carpeting the following rectangle...Ch. 14.2A - Prob. 16ACh. 14.2A - Joe uses stick on square carpet tiles to cover his...Ch. 14.2A - Prob. 18ACh. 14.2A - Prob. 19ACh. 14.2A - Prob. 20ACh. 14.2A - Prob. 21ACh. 14.2A - Prob. 22ACh. 14.2A - Prob. 23ACh. 14.2A - Prob. 24ACh. 14.2A - Prob. 25ACh. 14.2A - Prob. 26ACh. 14.2A - Prob. 27ACh. 14.2A - Prob. 28ACh. 14.2A - The radius of a sector is 1 m. a. Find the area of...Ch. 14.2A - Prob. 30ACh. 14.2A - Prob. 31ACh. 14.2A - Prob. 32ACh. 14.2A - Prob. 33ACh. 14.2A - Prob. 34ACh. 14.2A - Prob. 35ACh. 14.2B - Choose the most appropriate metric unit cm2, m2 or...Ch. 14.2B - Prob. 3ACh. 14.2B - Complete the following conversion table m2 cm2 mm2...Ch. 14.2B - Complete the following conversions a. 99ft2=yd2 b....Ch. 14.2B - Find the areas of each of the following figures if...Ch. 14.2B - Prob. 7ACh. 14.2B - Prob. 8ACh. 14.2B - a. If triangle ABC is similar to triangle DEF and...Ch. 14.2B - Find the area of each of the following...Ch. 14.2B - a. A rectangular piece of land is 1.2km by 900m i....Ch. 14.2B - a. If the area of a rectangle remains constant but...Ch. 14.2B - Prob. 14ACh. 14.2B - Prob. 15ACh. 14.2B - Prob. 16ACh. 14.2B - Prob. 17ACh. 14.2B - Prob. 18ACh. 14.2B - Prob. 19ACh. 14.2B - Prob. 21ACh. 14.2B - If the area of a square is 169in2, what is its...Ch. 14.2B - Prob. 23ACh. 14.2B - Prob. 24ACh. 14.2B - Prob. 25ACh. 14.2B - Prob. 26ACh. 14.2B - A store has wrapping paper on sale, One packed is...Ch. 14.2B - Prob. 28ACh. 14.2B - Prob. 29ACh. 14.2B - Prob. 30ACh. 14.2B - Prob. 31ACh. 14.2B - Prob. 32ACh. 14.2B - The radius of a sector is 2 m. a. Find the area of...Ch. 14.2B - Prob. 34ACh. 14.2B - Prob. 35ACh. 14.2B - Prob. 36ACh. 14.2B - What is the length of the side of a square with...Ch. 14.2B - Prob. 38ACh. 14.3 - Mathematical Connections Given a square, describe...Ch. 14.3 - Prob. 2MCCh. 14.3 - Mathematical Connections The sum of the squares of...Ch. 14.3 - Mathematical Connections Explain how to construct...Ch. 14.3 - Mathematical Connections A Pythagorean triple is a...Ch. 14.3 - Mathematical Connections Explain how to adapt the...Ch. 14.3 - The lane of a rural highway may be only 9 ft wide....Ch. 14.3 - Have each person in the group use a 1-m string to...Ch. 14.3 - Prob. 11MCCh. 14.3 - MATHEMATICAL CONNECTIONS One leg of a right...Ch. 14.3 - June wants to know where all the points that...Ch. 14.3 - Prob. 14MCCh. 14.3 - Prob. 15MCCh. 14.3 - Prob. 16MCCh. 14.3 - Prob. 17MCCh. 14.3 - Prob. 18MCCh. 14.3 - Prob. 19MCCh. 14.3 - Prob. 20MCCh. 14.3 - Prob. 21MCCh. 14.3 - Prob. 23MCCh. 14.3 - National Assessment of Educational ProgressNAEP...Ch. 14.3 - Prob. 2NAEPCh. 14.3A - Prob. 1ACh. 14.3A - Prob. 2ACh. 14.3A - On a 5dot5dot geoboard, construct segments of the...Ch. 14.3A - If the hypotenuse of a right is 30 cm long and one...Ch. 14.3A - For each of the following, determine whether the...Ch. 14.3A - Prob. 8ACh. 14.3A - Prob. 9ACh. 14.3A - Prob. 10ACh. 14.3A - Prob. 11ACh. 14.3A - Find the area of each of the following figuresCh. 14.3A - Find the area of each rhombus given below.Ch. 14.3A - Prob. 14ACh. 14.3A - A company wants to lay a string of buoys across a...Ch. 14.3A - Prob. 16ACh. 14.3A - Prob. 17ACh. 14.3A - Prob. 18ACh. 14.3A - Prob. 19ACh. 14.3A - For each of the following pairs of points, find...Ch. 14.3A - If the length of the hypotenuse in a 306090...Ch. 14.3A - Prob. 22ACh. 14.3A - Prob. 23ACh. 14.3A - Prob. 24ACh. 14.3A - Prob. 25ACh. 14.3A - A boat starts at point A, moves 3 km due north,...Ch. 14.3A - Prob. 27ACh. 14.3A - Prob. 28ACh. 14.3A - The diagonals of a rhombus are 8 in. and 12 in....Ch. 14.3A - Prob. 30ACh. 14.3A - Prob. 31ACh. 14.3B - Prob. 1ACh. 14.3B - Prob. 2ACh. 14.3B - Prob. 3ACh. 14.3B - Prob. 5ACh. 14.3B - Prob. 6ACh. 14.3B - For each of the following, determine whether the...Ch. 14.3B - Prob. 8ACh. 14.3B - Prob. 9ACh. 14.3B - Prob. 10ACh. 14.3B - Prob. 11ACh. 14.3B - Prob. 12ACh. 14.3B - Prob. 13ACh. 14.3B - Prob. 14ACh. 14.3B - On a baseball field 90-ft square if a player...Ch. 14.3B - Prob. 16ACh. 14.3B - Prob. 17ACh. 14.3B - Prob. 18ACh. 14.3B - Prob. 19ACh. 14.3B - Prob. 20ACh. 14.3B - Prob. 21ACh. 14.3B - Prob. 22ACh. 14.3B - Prob. 23ACh. 14.3B - Prob. 24ACh. 14.3B - Prob. 25ACh. 14.3B - Prob. 26ACh. 14.3B - Prob. 27ACh. 14.3B - Prob. 28ACh. 14.3B - Prob. 29ACh. 14.3B - Prob. 30ACh. 14.3B - Prob. 31ACh. 14.3B - Prob. 32ACh. 14.4 - Tennis balls are packed tightly three to a can...Ch. 14.4 - Prob. 2MCCh. 14.4 - In the drawing below, cube B was cut from a larger...Ch. 14.4 - Prob. 4MCCh. 14.4 - Prob. 5MCCh. 14.4 - Prob. 6MCCh. 14.4 - a. Shawn used small cubes to build a bigger cube...Ch. 14.4 - Prob. 9MCCh. 14.4 - A student wonders if she triples each measurement...Ch. 14.4 - Prob. 11MCCh. 14.4 - Abi used the formula SA=r(r+l), where r is the...Ch. 14.4 - Prob. 13MCCh. 14.4 - Prob. 14MCCh. 14.4 - Prob. 15MCCh. 14.4 - Prob. 16MCCh. 14.4 - Prob. 17MCCh. 14.4 - Find the perimeters and the areas of the following...Ch. 14.4 - In the following, the length of the diagonal AC of...Ch. 14.4 - Find the length of the diagonal of a cube whose...Ch. 14.4 - Prob. 21MCCh. 14.4 - Convert the following measures. a. 150m=km b....Ch. 14.4 - Which of the following can be folded to form the...Ch. 14.4A - Which of the following nets could be folded along...Ch. 14.4A - Find the surface area of each of the following...Ch. 14.4A - How many litres of paint must you buy to paint the...Ch. 14.4A - Prob. 4ACh. 14.4A - Assume the radius of Earth is 6370 km and Earth is...Ch. 14.4A - Prob. 6ACh. 14.4A - Prob. 7ACh. 14.4A - Prob. 8ACh. 14.4A - The top of a right rectangular box has an area of...Ch. 14.4A - How does the lateral surface area of a right...Ch. 14.4A - Prob. 11ACh. 14.4A - The sector shown is rolled into cone shape so that...Ch. 14.4A - As seen in exercise 12, a sector of a circle can...Ch. 14.4A - Prob. 14ACh. 14.4A - If two right circular cones are similar with radii...Ch. 14.4A - Prob. 16ACh. 14.4A - Prob. 17ACh. 14.4A - Prob. 18ACh. 14.4A - Prob. 19ACh. 14.4A - Prob. 20ACh. 14.4A - Prob. 21ACh. 14.4A - Prob. 22ACh. 14.4B - Prob. 1ACh. 14.4B - Prob. 2ACh. 14.4B - Prob. 3ACh. 14.4B - Prob. 4ACh. 14.4B - Prob. 5ACh. 14.4B - Prob. 6ACh. 14.4B - Prob. 7ACh. 14.4B - Prob. 8ACh. 14.4B - Prob. 10ACh. 14.4B - Prob. 11ACh. 14.4B - Prob. 13ACh. 14.4B - Prob. 14ACh. 14.4B - If two right cones are similar with radii of the...Ch. 14.4B - Prob. 16ACh. 14.4B - Prob. 17ACh. 14.4B - Prob. 18ACh. 14.4B - In the figure shown, a right circular cylinder is...Ch. 14.4B - Find the numerical difference in the surface area...Ch. 14.4B - Prob. 21ACh. 14.4B - Prob. 22ACh. 14.5 - a. Which will increase the volume of a right...Ch. 14.5 - Explain how you would find the volume of an...Ch. 14.5 - Read the following problems i and ii: i. A tank in...Ch. 14.5 - A furniture company gives an estimate for moving...Ch. 14.5 - A cylinder, a cone, and a sphere have the same...Ch. 14.5 - Two stacks of pennies shown are of the same...Ch. 14.5 - A right circular cylinder has a 4-in. diameter, is...Ch. 14.5 - Prob. 8MCCh. 14.5 - Explore Internet sources to determine if it is...Ch. 14.5 - Prob. 11MCCh. 14.5 - Bergmanns rule states that typically species of...Ch. 14.5 - Prob. 13MCCh. 14.5 - Prob. 14MCCh. 14.5 - Prob. 15MCCh. 14.5 - Prob. 16MCCh. 14.5 - Prob. 17MCCh. 14.5 - Prob. 18MCCh. 14.5 - Find the perimeter and area of the following...Ch. 14.5 - Prob. 20MCCh. 14.5 - Prob. 21MCCh. 14.5 - Prob. 22MCCh. 14.5 - Prob. 23MCCh. 14.5 - Prob. 24MCCh. 14.5 - How many 200-milliliter servings can be poured...Ch. 14.5 - Prob. 2NAEPCh. 14.5 - Prob. 3NAEPCh. 14.5A - Prob. 1ACh. 14.5A - Prob. 2ACh. 14.5A - Prob. 3ACh. 14.5A - Find the volume of each of the following figures....Ch. 14.5A - Prob. 5ACh. 14.5A - Prob. 6ACh. 14.5A - Prob. 7ACh. 14.5A - Prob. 8ACh. 14.5A - Prob. 9ACh. 14.5A - Prob. 10ACh. 14.5A - Prob. 11ACh. 14.5A - Prob. 12ACh. 14.5A - Prob. 13ACh. 14.5A - Prob. 14ACh. 14.5A - Prob. 15ACh. 14.5A - Prob. 16ACh. 14.5A - Prob. 17ACh. 14.5A - Prob. 18ACh. 14.5A - A right rectangular prism with base ABCD at the...Ch. 14.5A - Prob. 20ACh. 14.5A - Prob. 21ACh. 14.5A - Prob. 22ACh. 14.5A - Prob. 23ACh. 14.5A - Prob. 24ACh. 14.5A - Prob. 25ACh. 14.5A - Prob. 26ACh. 14.5A - Prob. 27ACh. 14.5A - a. Given any rectangle describe ways to decompose...Ch. 14.5A - Prob. 29ACh. 14.5A - Prob. 30ACh. 14.5A - Prob. 31ACh. 14.5A - Prob. 32ACh. 14.5A - Prob. 33ACh. 14.5A - Prob. 34ACh. 14.5B - Prob. 1ACh. 14.5B - Prob. 2ACh. 14.5B - Prob. 3ACh. 14.5B - Find the volume of each of the following, a. Right...Ch. 14.5B - Prob. 5ACh. 14.5B - Prob. 7ACh. 14.5B - Prob. 8ACh. 14.5B - Prob. 9ACh. 14.5B - Prob. 10ACh. 14.5B - Prob. 11ACh. 14.5B - Prob. 12ACh. 14.5B - Prob. 13ACh. 14.5B - Prob. 14ACh. 14.5B - Prob. 15ACh. 14.5B - Prob. 16ACh. 14.5B - Prob. 17ACh. 14.5B - Prob. 18ACh. 14.5B - Prob. 19ACh. 14.5B - Prob. 20ACh. 14.5B - Prob. 21ACh. 14.5B - Prob. 22ACh. 14.5B - Prob. 23ACh. 14.5B - A paper clip has a mass of about 1 g. Is it...Ch. 14.5B - Prob. 25ACh. 14.5B - Prob. 26ACh. 14.5B - Prob. 27ACh. 14.5B - Prob. 28ACh. 14.5B - Prob. 29ACh. 14.5B - Prob. 30ACh. 14.5B - Prob. 31ACh. 14.5B - Prob. 32ACh. 14.5B - Prob. 33ACh. 14.5B - Prob. 34ACh. 14.CR - Complete the following conversions. a. 50ft=yd b....Ch. 14.CR - Prob. 2CRCh. 14.CR - The diagonal of rectangle has measure 1.3m and a...Ch. 14.CR - Prob. 4CRCh. 14.CR - Prob. 5CRCh. 14.CR - Prob. 6CRCh. 14.CR - Prob. 7CRCh. 14.CR - Prob. 8CRCh. 14.CR - Prob. 9CRCh. 14.CR - Prob. 11CRCh. 14.CR - Prob. 12CRCh. 14.CR - Prob. 13CRCh. 14.CR - Prob. 14CRCh. 14.CR - Find the surface area and volume of each of the...Ch. 14.CR - Prob. 16CRCh. 14.CR - Dougs Dog Food Company wants to impress the public...Ch. 14.CR - Prob. 18CRCh. 14.CR - Prob. 19CRCh. 14.CR - Prob. 20CRCh. 14.CR - Prob. 21CRCh. 14.CR - Prob. 22CRCh. 14.CR - On a 55 geoboard, a. Draw a polygon whose...Ch. 14.CR - Prob. 24CRCh. 14.CR - Prob. 25CRCh. 14.CR - Prob. 26CRCh. 14.CR - Prob. 27CRCh. 14.CR - Prob. 28CRCh. 14.CR - Decide if each of the following situations is...Ch. 14.CR - Prob. 30CRCh. 14.CR - Prob. 31CRCh. 14.CR - Prob. 32CRCh. 14 - NOW TRY THIS To derive the formula for area of a...Ch. 14 - Prob. 6NTCh. 14 - Prob. 7NTCh. 14 - Prob. 8NTCh. 14 - Prob. 9NT
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Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:McDougal Littell
Elementary Geometry For College Students, 7e
Geometry
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Cengage,
Mathematics For Machine Technology
Advanced Math
ISBN:9781337798310
Author:Peterson, John.
Publisher:Cengage Learning,
Elementary Algebra
Algebra
ISBN:9780998625713
Author:Lynn Marecek, MaryAnne Anthony-Smith
Publisher:OpenStax - Rice University
Elementary Geometry for College Students
Geometry
ISBN:9781285195698
Author:Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:Cengage Learning
An Introduction to Area | Teaching Maths | EasyTeaching; Author: EasyTeaching;https://www.youtube.com/watch?v=_uKKl8R1xBM;License: Standard YouTube License, CC-BY
Area of a Rectangle, Triangle, Circle & Sector, Trapezoid, Square, Parallelogram, Rhombus, Geometry; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=JnLDmw3bbuw;License: Standard YouTube License, CC-BY