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 14.5, Problem 6MC
Two stacks of pennies shown are of the same height.
a. Explain which has the greater surface area and why.
b. Explain which has the greater volume and why.
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Given: AABE ~ ACDE.
Prove: AC bisects BD.
Note: quadrilateral properties are not permitted in this proof.
Step
Statement
Reason
AABE ACDE
Given
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Vertical angles are congruent
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Type of Statement
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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
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○ 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
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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ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Algebra: Structure And Method, Book 1
Algebra
ISBN:9780395977224
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,
Elementary Algebra
Algebra
ISBN:9780998625713
Author:Lynn Marecek, MaryAnne Anthony-Smith
Publisher:OpenStax - Rice University
The surface area and volume of cone, cylinder, prism and pyramid; Author: AtHome Tuition;https://www.youtube.com/watch?v=SlaQmaJCOt8;License: Standard YouTube License, CC-BY