Prealgebra (6th Edition)
6th Edition
ISBN: 9780134179018
Author: Jamie Blair, John Tobey Jr., Jeffrey Slater, Jenny Crawford
Publisher: PEARSON
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Chapter 10, Problem 33RP
Convert. Do not round your answer.
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Chapter 10 Solutions
Prealgebra (6th Edition)
Ch. 10.1 - Prob. 1ECh. 10.1 - Prob. 2ECh. 10.1 - Prob. 3ECh. 10.1 - Prob. 4ECh. 10.1 - Prob. 5ECh. 10.1 - Prob. 6ECh. 10.1 - Prob. 7ECh. 10.1 - Prob. 8ECh. 10.1 - Prob. 9ECh. 10.1 - Prob. 10E
Ch. 10.1 - Prob. 11ECh. 10.1 - Prob. 12ECh. 10.1 - Prob. 13ECh. 10.1 - Prob. 14ECh. 10.1 - Prob. 15ECh. 10.1 - Convert. 120feet=yardCh. 10.1 - Prob. 17ECh. 10.1 - Prob. 18ECh. 10.1 - Prob. 19ECh. 10.1 - Prob. 20ECh. 10.1 - Prob. 21ECh. 10.1 - Prob. 22ECh. 10.1 - Prob. 23ECh. 10.1 - Prob. 24ECh. 10.1 - Prob. 25ECh. 10.1 - Prob. 26ECh. 10.1 - Prob. 27ECh. 10.1 - Prob. 28ECh. 10.1 - Prob. 29ECh. 10.1 - Prob. 30ECh. 10.1 - Prob. 31ECh. 10.1 - Prob. 32ECh. 10.1 - Prob. 33ECh. 10.1 - Prob. 34ECh. 10.1 - Prob. 35ECh. 10.1 - Prob. 36ECh. 10.1 - Prob. 37ECh. 10.1 - Prob. 38ECh. 10.1 - Prob. 39ECh. 10.1 - Prob. 40ECh. 10.1 - Prob. 41ECh. 10.1 - Prob. 42ECh. 10.1 - Prob. 43ECh. 10.1 - Prob. 44ECh. 10.1 - Prob. 45ECh. 10.1 - Prob. 46ECh. 10.1 - Prob. 47ECh. 10.1 - Prob. 48ECh. 10.1 - Prob. 49ECh. 10.1 - Prob. 50ECh. 10.1 - Prob. 51ECh. 10.1 - Prob. 52ECh. 10.1 - Vaccines A pharmaceutical firm developed a new...Ch. 10.1 - Prob. 54ECh. 10.1 - Rare Flower A very rare essence of an almost...Ch. 10.1 - Longest Train Run The worlds longest train run is...Ch. 10.1 - Highest Railroad The highest railroad line in the...Ch. 10.1 - Prob. 58ECh. 10.1 - 860quarts=gallonsCh. 10.1 - Prob. 60ECh. 10.1 - 4miles=feetCh. 10.1 - Prob. 62ECh. 10.1 - 9gallons=pintsCh. 10.1 - 10hours=secondsCh. 10.1 - 14.6kg=gCh. 10.1 - 0.83kg=mgCh. 10.1 - 3.22kL=LCh. 10.1 - 3607mL=L=kLCh. 10.1 - 7183mg=g=kgCh. 10.1 - Metric prefixes are also used for computers. A...Ch. 10.1 - Prob. 71ECh. 10.1 - Prob. 72ECh. 10.1 - Prob. 73ECh. 10.1 - Prob. 74ECh. 10.1 - Prob. 75ECh. 10.1 - Prob. 76ECh. 10.1 - Prob. 77ECh. 10.1 - Mount Whitney is 14,496 feet high. How many miles...Ch. 10.1 - Prob. 2QQCh. 10.1 - Prob. 3QQCh. 10.1 - Prob. 4QQCh. 10.2 - Prob. 1ECh. 10.2 - Prob. 2ECh. 10.2 - Prob. 3ECh. 10.2 - Prob. 4ECh. 10.2 - Prob. 5ECh. 10.2 - Prob. 6ECh. 10.2 - Prob. 7ECh. 10.2 - Prob. 8ECh. 10.2 - Prob. 9ECh. 10.2 - Prob. 10ECh. 10.2 - Perform each conversion. Round your answer to the...Ch. 10.2 - Prob. 12ECh. 10.2 - Prob. 13ECh. 10.2 - Prob. 14ECh. 10.2 - Prob. 15ECh. 10.2 - Prob. 16ECh. 10.2 - Prob. 17ECh. 10.2 - Prob. 18ECh. 10.2 - Prob. 19ECh. 10.2 - Prob. 20ECh. 10.2 - Prob. 21ECh. 10.2 - Prob. 22ECh. 10.2 - Prob. 23ECh. 10.2 - Prob. 24ECh. 10.2 - Prob. 25ECh. 10.2 - Prob. 26ECh. 10.2 - Prob. 27ECh. 10.2 - Prob. 28ECh. 10.2 - Prob. 29ECh. 10.2 - Prob. 30ECh. 10.2 - Prob. 31ECh. 10.2 - Prob. 32ECh. 10.2 - Prob. 33ECh. 10.2 - Perform each conversion. Round your answer to the...Ch. 10.2 - Prob. 35ECh. 10.2 - Prob. 36ECh. 10.2 - Prob. 37ECh. 10.2 - Prob. 38ECh. 10.2 - Prob. 39ECh. 10.2 - Prob. 40ECh. 10.2 - Prob. 41ECh. 10.2 - Prob. 42ECh. 10.2 - Prob. 43ECh. 10.2 - Prob. 44ECh. 10.2 - Prob. 45ECh. 10.2 - Prob. 46ECh. 10.2 - Prob. 47ECh. 10.2 - Prob. 48ECh. 10.2 - Prob. 49ECh. 10.2 - Prob. 50ECh. 10.2 - Prob. 51ECh. 10.2 - Prob. 52ECh. 10.2 - Prob. 53ECh. 10.2 - Prob. 54ECh. 10.2 - Prob. 55ECh. 10.2 - Prob. 56ECh. 10.2 - Prob. 57ECh. 10.2 - Prob. 58ECh. 10.2 - Prob. 59ECh. 10.2 - Prob. 60ECh. 10.2 - Prob. 61ECh. 10.2 - Prob. 62ECh. 10.2 - Prob. 63ECh. 10.2 - Prob. 64ECh. 10.2 - Prob. 65ECh. 10.2 - Prob. 66ECh. 10.2 - Prob. 67ECh. 10.2 - Prob. 68ECh. 10.2 - Prob. 69ECh. 10.2 - Prob. 70ECh. 10.2 - Prob. 71ECh. 10.2 - Prob. 72ECh. 10.2 - Prob. 1QQCh. 10.2 - Prob. 2QQCh. 10.2 - Prob. 3QQCh. 10.2 - Prob. 4QQCh. 10.3 - Prob. 1ECh. 10.3 - Prob. 2ECh. 10.3 - Prob. 3ECh. 10.3 - Prob. 4ECh. 10.3 - Prob. 5ECh. 10.3 - Prob. 6ECh. 10.3 - Prob. 7ECh. 10.3 - Prob. 8ECh. 10.3 - Choose from the terms below to fill in the blanks...Ch. 10.3 - Prob. 10ECh. 10.3 - Prob. 11ECh. 10.3 - Choose from the terms below to fill in the blanks...Ch. 10.3 - Choose from the terms below to fill in the blanks...Ch. 10.3 - Prob. 14ECh. 10.3 - Prob. 15ECh. 10.3 - Prob. 16ECh. 10.3 - Prob. 17ECh. 10.3 - Choose from the terms below to fill in the blanks...Ch. 10.3 - Prob. 19ECh. 10.3 - Prob. 20ECh. 10.3 - Choose from the terms below to fill in the blanks...Ch. 10.3 - Prob. 22ECh. 10.3 - Prob. 23ECh. 10.3 - Choose from the terms below to fill in the blanks...Ch. 10.3 - Prob. 25ECh. 10.3 - Prob. 26ECh. 10.3 - Prob. 27ECh. 10.3 - Choose from the terms below to fill in the blanks...Ch. 10.3 - Prob. 29ECh. 10.3 - Prob. 30ECh. 10.3 - Prob. 31ECh. 10.3 - Prob. 32ECh. 10.3 - Prob. 33ECh. 10.3 - Prob. 34ECh. 10.3 - Prob. 35ECh. 10.3 - Use the figure to the right to answer exercises 35...Ch. 10.3 - Prob. 37ECh. 10.3 - Prob. 38ECh. 10.3 - Prob. 39ECh. 10.3 - Prob. 40ECh. 10.3 - Given that EFG is a right angle, find the value of...Ch. 10.3 - Prob. 42ECh. 10.3 - Given that STU is a right angle, find the value of...Ch. 10.3 - Given that WXY is a right angle, find the value of...Ch. 10.3 - Prob. 45ECh. 10.3 - Given that LMN is a right angle, find the value of...Ch. 10.3 - Use the figure below to answer exercises 4754....Ch. 10.3 - Use the figure below to answer exercises 4754....Ch. 10.3 - Use the figure below to answer exercises 4754....Ch. 10.3 - Use the figure below to answer exercises 4754....Ch. 10.3 - Prob. 51ECh. 10.3 - Prob. 52ECh. 10.3 - Prob. 53ECh. 10.3 - Prob. 54ECh. 10.3 - In the following figure, xy and the measure of...Ch. 10.3 - In the following figure, mn and the measure of...Ch. 10.3 - In the following figure, mn and the measure of...Ch. 10.3 - Prob. 58ECh. 10.3 - Find the measures of r,s,t,u,v,w,andx given that...Ch. 10.3 - Find the measures of r,s,t,u,v,w,andx given that...Ch. 10.3 - Prob. 61ECh. 10.3 - Find the value of x.Ch. 10.3 - Recall that the sum of the measures of the...Ch. 10.3 - Recall that the sum of the measures of the...Ch. 10.3 - Prob. 65ECh. 10.3 - [1.9.3] Earth-Sun Diameter The approximate size of...Ch. 10.3 - Prob. 1QQCh. 10.3 - Prob. 2QQCh. 10.3 - If PQR is a right angle, find the value of x.Ch. 10.3 - Prob. 4QQCh. 10.4 - Write each of the following as a question. Assume...Ch. 10.4 - Prob. 2ECh. 10.4 - Prob. 3ECh. 10.4 - Prob. 4ECh. 10.4 - Prob. 5ECh. 10.4 - Prob. 6ECh. 10.4 - Prob. 7ECh. 10.4 - Prob. 8ECh. 10.4 - Prob. 9ECh. 10.4 - Prob. 10ECh. 10.4 - Prob. 11ECh. 10.4 - Prob. 12ECh. 10.4 - Prob. 13ECh. 10.4 - Prob. 14ECh. 10.4 - Prob. 15ECh. 10.4 - Prob. 16ECh. 10.4 - Prob. 17ECh. 10.4 - Prob. 18ECh. 10.4 - Prob. 19ECh. 10.4 - Prob. 20ECh. 10.4 - Prob. 21ECh. 10.4 - Prob. 22ECh. 10.4 - Prob. 23ECh. 10.4 - Prob. 24ECh. 10.4 - Prob. 25ECh. 10.4 - Prob. 26ECh. 10.4 - Prob. 27ECh. 10.4 - Prob. 28ECh. 10.4 - Prob. 29ECh. 10.4 - Prob. 30ECh. 10.4 - Prob. 31ECh. 10.4 - Prob. 32ECh. 10.4 - Find the length of the side of a square that has...Ch. 10.4 - Find the length of the side of a square that has...Ch. 10.4 - Find the length of the side of a square that has...Ch. 10.4 - Find the length of the side of a square that has...Ch. 10.4 - Use your calculator to approximate the value....Ch. 10.4 - Use your calculator to approximate the value....Ch. 10.4 - Use your calculator to approximate the value....Ch. 10.4 - Use your calculator to approximate the value....Ch. 10.4 - Use your calculator to approximate the value....Ch. 10.4 - Use your calculator to approximate the value....Ch. 10.4 - Use your calculator to approximate the value....Ch. 10.4 - Use your calculator to approximate the value....Ch. 10.4 - Find the length of the unknown side of each right...Ch. 10.4 - Find the length of the unknown side of each right...Ch. 10.4 - Find the length of the unknown side of each right...Ch. 10.4 - Find the length of the unknown side of each right...Ch. 10.4 - Find the length of the unknown side of each right...Ch. 10.4 - Find the length of the unknown side of each right...Ch. 10.4 - Find the length of the unknown side of each right...Ch. 10.4 - Find the length of the unknown side of each right...Ch. 10.4 - Find the length of the unknown side of each right...Ch. 10.4 - Find the length of the unknown side of each right...Ch. 10.4 - Find the length of the unknown side of each right...Ch. 10.4 - Find the length of the unknown side of each right...Ch. 10.4 - Find the area of each shape made up of squares and...Ch. 10.4 - Prob. 58ECh. 10.4 - Find the area of each shape made up of rectangles...Ch. 10.4 - Find the area of each shape made up of rectangles...Ch. 10.4 - Solve each applied problem. Round your answer to...Ch. 10.4 - Prob. 62ECh. 10.4 - Solve each applied problem. Round your answer to...Ch. 10.4 - Solve each applied problem. Round your answer to...Ch. 10.4 - Prob. 65ECh. 10.4 - Prob. 66ECh. 10.4 - Find the total area of all the vertical areas...Ch. 10.4 - Find the total area of all the vertical areas...Ch. 10.4 - Airplane Wings The top surface of the wings of a...Ch. 10.4 - Airplane Wings The top surface of the wings of a...Ch. 10.4 - [5.1.1] Multiply. 9x221027x2Ch. 10.4 - Prob. 72ECh. 10.4 - Find each square root. Then simplify if possible....Ch. 10.4 - Prob. 2QQCh. 10.4 - Find the length of one leg of a right triangle...Ch. 10.4 - Concept Check State the Pythagorean Theorem and...Ch. 10.5 - Prob. 1ECh. 10.5 - Prob. 2ECh. 10.5 - Prob. 3ECh. 10.5 - Prob. 4ECh. 10.5 - Prob. 5ECh. 10.5 - Prob. 6ECh. 10.5 - Prob. 7ECh. 10.5 - Prob. 8ECh. 10.5 - In exercises 924, use. Round your answer to the...Ch. 10.5 - Prob. 10ECh. 10.5 - Prob. 11ECh. 10.5 - Prob. 12ECh. 10.5 - Prob. 13ECh. 10.5 - In exercises 924, use. Round your answer to the...Ch. 10.5 - Prob. 15ECh. 10.5 - In exercises 924, use. Round your answer to the...Ch. 10.5 - Prob. 17ECh. 10.5 - Prob. 18ECh. 10.5 - Prob. 19ECh. 10.5 - Prob. 20ECh. 10.5 - Prob. 21ECh. 10.5 - In exercises 924, use. Round your answer to the...Ch. 10.5 - Prob. 23ECh. 10.5 - In exercises 924, use. Round your answer to the...Ch. 10.5 - Prob. 25ECh. 10.5 - Prob. 26ECh. 10.5 - In exercises 2534, use. Round your answer to the...Ch. 10.5 - Prob. 28ECh. 10.5 - Prob. 29ECh. 10.5 - Prob. 30ECh. 10.5 - Prob. 31ECh. 10.5 - In exercises 2534, use. Round your answer to the...Ch. 10.5 - Prob. 33ECh. 10.5 - Prob. 34ECh. 10.5 - Use 3.14 in exercises 35 and 36. Round your answer...Ch. 10.5 - Use 3.14 in exercises 35 and 36. Round your answer...Ch. 10.5 - Round your answer to the nearest hundredth for...Ch. 10.5 - Round your answer to the nearest hundredth for...Ch. 10.5 - Find the volume of each rectangular box. [3.3.3]...Ch. 10.5 - Find the volume of each rectangular box. [3.3.3]...Ch. 10.5 - For each of the following, use 3.14 and round to...Ch. 10.5 - Prob. 2QQCh. 10.5 - For each of the following, use 3.14 and round to...Ch. 10.5 - For each of the following, use 3.14 and round to...Ch. 10.6 - Name the figure that matches the volume formula....Ch. 10.6 - Prob. 2ECh. 10.6 - Name the figure that matches the volume formula....Ch. 10.6 - Name the figure that matches the volume formula....Ch. 10.6 - Name the figure that matches the volume formula....Ch. 10.6 - Prob. 6ECh. 10.6 - Find each volume. Use 3.14. Round each answer to...Ch. 10.6 - Find each volume. Use 3.14. Round each answer to...Ch. 10.6 - Find each volume. Use 3.14. Round each answer to...Ch. 10.6 - Find each volume. Use 3.14. Round each answer to...Ch. 10.6 - Find each volume. Use 3.14. Round each answer to...Ch. 10.6 - Find each volume. Use 3.14. Round each answer to...Ch. 10.6 - Find each volume. Use 3.14. Round each answer to...Ch. 10.6 - Prob. 14ECh. 10.6 - Exercises 15 and 16 involve hemispheres. A...Ch. 10.6 - Exercises 15 and 16 involve hemispheres. A...Ch. 10.6 - Find each volume. Use. Round each answer to the...Ch. 10.6 - Find each volume. Use. Round each answer to the...Ch. 10.6 - Find each volume. Use. Round each answer to the...Ch. 10.6 - Prob. 20ECh. 10.6 - Prob. 21ECh. 10.6 - Prob. 22ECh. 10.6 - Prob. 23ECh. 10.6 - Prob. 24ECh. 10.6 - Prob. 25ECh. 10.6 - Prob. 26ECh. 10.6 - Prob. 27ECh. 10.6 - A collar of Styrofoam is made to insulate a pipe....Ch. 10.6 - Prob. 29ECh. 10.6 - Prob. 30ECh. 10.6 - Prob. 31ECh. 10.6 - Prob. 32ECh. 10.6 - Prob. 33ECh. 10.6 - Prob. 34ECh. 10.6 - Use the following formulas for surface area for...Ch. 10.6 - Use the following formulas for surface area for...Ch. 10.6 - Solve each proportion. [4.6.3] 2440=x120Ch. 10.6 - Solve each proportion. [4.6.3] 18x=1210Ch. 10.6 - Solve each proportion. [5.4.2] Multiply. 212334Ch. 10.6 - Solve each proportion. [5.4.2] 712435Ch. 10.6 - Prob. 1QQCh. 10.6 - Find the volume of a cone of radius 3 inches and...Ch. 10.6 - Prob. 3QQCh. 10.6 - Prob. 4QQCh. 10.7 - Fill in the blanks. The corresponding angles of...Ch. 10.7 - Fill in the blanks. The lengths of _______ sides...Ch. 10.7 - Fill in the blanks. The ________ of similar...Ch. 10.7 - Fill in the blanks. The corresponding sides of...Ch. 10.7 - Prob. 5ECh. 10.7 - Prob. 6ECh. 10.7 - Prob. 7ECh. 10.7 - Prob. 8ECh. 10.7 - Prob. 9ECh. 10.7 - Prob. 10ECh. 10.7 - Prob. 11ECh. 10.7 - Prob. 12ECh. 10.7 - Two triangles are similar. The smaller triangle...Ch. 10.7 - Two triangles are similar. The smaller triangle...Ch. 10.7 - Two triangles are similar. The larger triangle has...Ch. 10.7 - Prob. 16ECh. 10.7 - Prob. 17ECh. 10.7 - Prob. 18ECh. 10.7 - A flagpole casts a shadow. At the same time, a...Ch. 10.7 - Prob. 20ECh. 10.7 - Shadow Cast Lola is standing outside of a...Ch. 10.7 - Shadow Cast Huy is rock climbing in Utah. He is 6...Ch. 10.7 - Prob. 23ECh. 10.7 - Each pair of figures is similar. Find the length...Ch. 10.7 - Each pair of figures is similar. Find the length...Ch. 10.7 - Each pair of figures is similar. Find the length...Ch. 10.7 - Blueprints The blueprints for a home being built...Ch. 10.7 - Miniature Model Van A plastic model of a van that...Ch. 10.7 - How would you find the relationship between the...Ch. 10.7 - How would you find the relationship between the...Ch. 10.7 - Perform the operations indicated. Use the correct...Ch. 10.7 - Prob. 32ECh. 10.7 - Perform the operations indicated. Use the correct...Ch. 10.7 - Perform the operations indicated. Use the correct...Ch. 10.7 - These two triangles are similar. Find the length...Ch. 10.7 - Prob. 2QQCh. 10.7 - The width of a rectangle is 8 feet and its length...Ch. 10.7 - Concept Check Refer to Quick Quiz 2 to answer the...Ch. 10 - Fill in the blank with the definition for each...Ch. 10 - Fill in the blank with the definition for each...Ch. 10 - Fill in the blank with the definition for each...Ch. 10 - Fill in the blank with the definition for each...Ch. 10 - Prob. 5RPCh. 10 - Prob. 6RPCh. 10 - Prob. 7RPCh. 10 - Prob. 8RPCh. 10 - Prob. 9RPCh. 10 - Fill in the blank with the definition for each...Ch. 10 - Fill in the blank with the definition for each...Ch. 10 - Fill in the blank with the definition for each...Ch. 10 - Write each formula using symbols and numbers. Area...Ch. 10 - Write each formula using symbols and numbers....Ch. 10 - Write each formula using symbols and numbers. Area...Ch. 10 - Write each formula using symbols and numbers....Ch. 10 - Write each formula using symbols and numbers....Ch. 10 - Write each formula using symbols and numbers....Ch. 10 - Write each formula using symbols and numbers....Ch. 10 - Prob. 20RPCh. 10 - Convert. When necessary, express your answer as a...Ch. 10 - Convert. When necessary, express your answer as a...Ch. 10 - Convert. When necessary, express your answer as a...Ch. 10 - Convert. When necessary, express your answer as a...Ch. 10 - Prob. 25RPCh. 10 - Prob. 26RPCh. 10 - Prob. 27RPCh. 10 - Prob. 28RPCh. 10 - Prob. 29RPCh. 10 - Convert. Do not round your answer. 2598mm=cmCh. 10 - Prob. 31RPCh. 10 - Convert. Do not round your answer. 6.3m=cmCh. 10 - Convert. Do not round your answer. 5km=mCh. 10 - Convert. Do not round your answer. 15kL=LCh. 10 - Convert. Do not round your answer. 473m=kmCh. 10 - Convert. Do not round your answer. 196kg=gCh. 10 - Convert. Do not round your answer. 721kg=gCh. 10 - Solve each problem. Round your answer to the...Ch. 10 - Solve each problem. Round your answer to the...Ch. 10 - Prob. 40RPCh. 10 - Perform each conversion. Round your answer to the...Ch. 10 - Perform each conversion. Round your answer to the...Ch. 10 - Perform each conversion. Round your answer to the...Ch. 10 - Prob. 44RPCh. 10 - Perform each conversion. Round your answer to the...Ch. 10 - Prob. 46RPCh. 10 - Prob. 47RPCh. 10 - Distance Traveled Keshia traveled at 90 km/hr for...Ch. 10 - Cereal Cost The unit price on a box of breakfast...Ch. 10 - Prob. 50RPCh. 10 - Use the figure to the right to answer exercises 50...Ch. 10 - Prob. 52RPCh. 10 - In the figure to the right, given that ABC is a...Ch. 10 - Use the figure to the right to answer exercises...Ch. 10 - Prob. 55RPCh. 10 - Prob. 56RPCh. 10 - In the following figure, ab and the measure of w...Ch. 10 - Find each square root without using a calculator....Ch. 10 - Find each square root without using a calculator....Ch. 10 - Approximate using a calculator. Round your answer...Ch. 10 - Approximate using a calculator. Round your answer...Ch. 10 - Find each square root and then simplify. 6425Ch. 10 - Find each square root and then simplify. 121+16Ch. 10 - Prob. 64RPCh. 10 - Find the length of the unknown side of the right...Ch. 10 - Prob. 66RPCh. 10 - For exercises 6771, use 3.14. Round your answer to...Ch. 10 - Prob. 68RPCh. 10 - For exercises 6771, use 3.14. Round your answer to...Ch. 10 - Prob. 70RPCh. 10 - For exercises 6771, use 3.14. Round your answer to...Ch. 10 - Find the volume of each object. Use 3.14 and round...Ch. 10 - Find the volume of each object. Use 3.14 and round...Ch. 10 - Prob. 74RPCh. 10 - Prob. 75RPCh. 10 - Prob. 76RPCh. 10 - Find the volume of each object. Use 3.14 and round...Ch. 10 - Find the volume of each object. Use 3.14 and round...Ch. 10 - Convert each of the following. a. 145 ounces to...Ch. 10 - Convert each of the following. a. 162 grams to...Ch. 10 - Prob. 3TCh. 10 - Prob. 4TCh. 10 - Fred is traveling through Europe. After driving 4...Ch. 10 - Prob. 6TCh. 10 - Prob. 7TCh. 10 - Prob. 8TCh. 10 - In the following figure, xy and the measure of w...Ch. 10 - Determine if the following are perfect squares. 81Ch. 10 - Determine if the following are perfect squares. 24Ch. 10 - Determine if the following are perfect squares. 18Ch. 10 - Find the length of the side of a square that has...Ch. 10 - Simplify. 49Ch. 10 - Simplify. 916Ch. 10 - Find the approximate value. Round your answer to...Ch. 10 - Find the approximate value. Round your answer to...Ch. 10 - Find the approximate value. Round your answer to...Ch. 10 - Prob. 19TCh. 10 - Prob. 20TCh. 10 - Find the approximate value. Round your answer to...Ch. 10 - Prob. 22TCh. 10 - Prob. 23TCh. 10 - For questions 2228, use 3.14. Find the area of a...Ch. 10 - For questions 2228, use 3.14. Joe wants to buy a...Ch. 10 - Prob. 26TCh. 10 - For questions 2228, use 3.14. How much air is...Ch. 10 - For questions 2228, use 3.14. Find the volume of a...Ch. 10 - Prob. 29TCh. 10 - These two triangles are similar. Find the length...Ch. 10 - A flagpole casts a shadow of 2.5 feet. At the same...Ch. 10 - The two rectangles shown here are similar. Find...
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- 3. (a) Let A be an algebra. Define the notion of an A-module M. When is a module M a simple module? (b) State and prove Schur's Lemma for simple modules. (c) Let AM(K) and M = K" the natural A-module. (i) Show that M is a simple K-module. (ii) Prove that if ƒ € Endд(M) then ƒ can be written as f(m) = am, where a is a matrix in the centre of M, (K). [Recall that the centre, Z(M,(K)) == {a Mn(K) | ab M,,(K)}.] = ba for all bЄ (iii) Explain briefly why this means End₁(M) K, assuming that Z(M,,(K))~ K as K-algebras. Is this consistent with Schur's lemma?arrow_forward(a) State, without proof, Cauchy's theorem, Cauchy's integral formula and Cauchy's integral formula for derivatives. Your answer should include all the conditions required for the results to hold. (8 marks) (b) Let U{z EC: |z| -1}. Let 12 be the triangular contour with vertices at 0, 2-2 and 2+2i, parametrized in the anticlockwise direction. Calculate dz. You must check the conditions of any results you use. (d) Let U C. Calculate Liz-1ym dz, (z - 1) 10 (5 marks) where 2 is the same as the previous part. You must check the conditions of any results you use. (4 marks)arrow_forward(a) Suppose a function f: C→C has an isolated singularity at wЄ C. State what it means for this singularity to be a pole of order k. (2 marks) (b) Let f have a pole of order k at wЄ C. Prove that the residue of f at w is given by 1 res (f, w): = Z dk (k-1)! >wdzk−1 lim - [(z — w)* f(z)] . (5 marks) (c) Using the previous part, find the singularity of the function 9(z) = COS(πZ) e² (z - 1)²' classify it and calculate its residue. (5 marks) (d) Let g(x)=sin(211). Find the residue of g at z = 1. (3 marks) (e) Classify the singularity of cot(z) h(z) = Z at the origin. (5 marks)arrow_forward
- 1. Let z = x+iy with x, y Є R. Let f(z) = u(x, y) + iv(x, y) where u(x, y), v(x, y): R² → R. (a) Suppose that f is complex differentiable. State the Cauchy-Riemann equations satisfied by the functions u(x, y) and v(x,y). (b) State what it means for the function (2 mark) u(x, y): R² → R to be a harmonic function. (3 marks) (c) Show that the function u(x, y) = 3x²y - y³ +2 is harmonic. (d) Find a harmonic conjugate of u(x, y). (6 marks) (9 marks)arrow_forwardPlease could you provide a step by step solutions to this question and explain every step.arrow_forwardCould you please help me with question 2bii. If possible could you explain how you found the bounds of the integral by using a graph of the region of integration. Thanksarrow_forward
- Let A be a vector space with basis 1, a, b. Which (if any) of the following rules turn A into an algebra? (You may assume that 1 is a unit.) (i) a² = a, b² = ab = ba = 0. (ii) a²=b, b² = ab = ba = 0. (iii) a²=b, b² = b, ab = ba = 0.arrow_forwardNo chatgpt pls will upvotearrow_forward= 1. Show (a) Let G = Z/nZ be a cyclic group, so G = {1, 9, 92,...,g" } with g": that the group algebra KG has a presentation KG = K(X)/(X” — 1). (b) Let A = K[X] be the algebra of polynomials in X. Let V be the A-module with vector space K2 and where the action of X is given by the matrix Compute End(V) in the cases (i) x = p, (ii) xμl. (67) · (c) If M and N are submodules of a module L, prove that there is an isomorphism M/MON (M+N)/N. (The Second Isomorphism Theorem for modules.) You may assume that MON is a submodule of M, M + N is a submodule of L and the First Isomorphism Theorem for modules.arrow_forward
- (a) Define the notion of an ideal I in an algebra A. Define the product on the quotient algebra A/I, and show that it is well-defined. (b) If I is an ideal in A and S is a subalgebra of A, show that S + I is a subalgebra of A and that SnI is an ideal in S. (c) Let A be the subset of M3 (K) given by matrices of the form a b 0 a 0 00 d Show that A is a subalgebra of M3(K). Ꮖ Compute the ideal I of A generated by the element and show that A/I K as algebras, where 0 1 0 x = 0 0 0 001arrow_forward(a) Let HI be the algebra of quaternions. Write out the multiplication table for 1, i, j, k. Define the notion of a pure quaternion, and the absolute value of a quaternion. Show that if p is a pure quaternion, then p² = -|p|². (b) Define the notion of an (associative) algebra. (c) Let A be a vector space with basis 1, a, b. Which (if any) of the following rules turn A into an algebra? (You may assume that 1 is a unit.) (i) a² = a, b²=ab = ba 0. (ii) a² (iii) a² = b, b² = abba = 0. = b, b² = b, ab = ba = 0. (d) Let u1, 2 and 3 be in the Temperley-Lieb algebra TL4(8). ገ 12 13 Compute (u3+ Augu2)² where A EK and hence find a non-zero x € TL4 (8) such that ² = 0.arrow_forwardQ1: Solve the system x + x = t², x(0) = (9)arrow_forward
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