Elementary Technical Mathematics
12th Edition
ISBN: 9781337630580
Author: Dale Ewen
Publisher: Cengage Learning
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Chapter 2.2, Problem 37E
To determine
To calculate: The simplified value of the expression
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(7) (12 points) Let F(x, y, z) = (y, x+z cos yz, y cos yz).
Ꮖ
(a) (4 points) Show that V x F = 0.
(b) (4 points) Find a potential f for the vector field F.
(c) (4 points) Let S be a surface in R3 for which the Stokes' Theorem is valid. Use
Stokes' Theorem to calculate the line integral
Jos
F.ds;
as denotes the boundary of S. Explain your answer.
(3) (16 points) Consider
z = uv,
u = x+y,
v=x-y.
(a) (4 points) Express z in the form z = fog where g: R² R² and f: R² →
R.
(b) (4 points) Use the chain rule to calculate Vz = (2, 2). Show all intermediate
steps otherwise no credit.
(c) (4 points) Let S be the surface parametrized by
T(x, y) = (x, y, ƒ (g(x, y))
(x, y) = R².
Give a parametric description of the tangent plane to S at the point p = T(x, y).
(d) (4 points) Calculate the second Taylor polynomial Q(x, y) (i.e. the quadratic
approximation) of F = (fog) at a point (a, b). Verify that
Q(x,y) F(a+x,b+y).
=
Chapter 2 Solutions
Elementary Technical Mathematics
Ch. 2.1 - Add the following signed number: (+4)+(+5)Ch. 2.1 - Add the following signed number: (6)+(2)Ch. 2.1 - Add the following signed number: (+7)+(3)Ch. 2.1 - Add the following signed number: (8)+(+1)Ch. 2.1 - Add the following signed number: (3)+(+9)Ch. 2.1 - Prob. 6SNDCh. 2.1 - Prob. 7SNDCh. 2.1 - Add the following signed number: (0)+(+8)Ch. 2.1 - Add the following signed number: (+2)+(+1)Ch. 2.1 - Prob. 10SND
Ch. 2.1 - Prob. 11SNDCh. 2.1 - Prob. 12SNDCh. 2.1 - Add the following signed number: (10)+(+8)Ch. 2.1 - Prob. 14SNDCh. 2.1 - Prob. 15SNDCh. 2.1 - Prob. 16SNDCh. 2.1 - Add the following signed number: (+4)+(4)Ch. 2.1 - Add the following signed number: (7)+(+8)Ch. 2.1 - Prob. 19SNDCh. 2.1 - Prob. 20SNDCh. 2.1 - Add the following signed number: (+3)+(2)Ch. 2.1 - Prob. 22SNDCh. 2.1 - Prob. 23SNDCh. 2.1 - Prob. 24SNDCh. 2.1 - Add the following signed number: (+7)+(8)Ch. 2.1 - Prob. 26SNDCh. 2.1 - Prob. 27SNDCh. 2.1 - Add the following signed number: (2)+(2)Ch. 2.1 - Add the following signed number: (3)+(+4)Ch. 2.1 - Prob. 30SNDCh. 2.1 - Find the absolute value of each number: 3Ch. 2.1 - Prob. 2ECh. 2.1 - Prob. 3ECh. 2.1 - Prob. 4ECh. 2.1 - Find the absolute value of each number: +4Ch. 2.1 - Prob. 6ECh. 2.1 - Prob. 7ECh. 2.1 - Find the absolute value of each number: 37Ch. 2.1 - Find the absolute value of each number: 15Ch. 2.1 - Prob. 10ECh. 2.1 - Prob. 11ECh. 2.1 - Prob. 12ECh. 2.1 - Add: (+9)+(2)Ch. 2.1 - Prob. 14ECh. 2.1 - Prob. 15ECh. 2.1 - Prob. 16ECh. 2.1 - Add: (3)+(9)Ch. 2.1 - Prob. 18ECh. 2.1 - Prob. 19ECh. 2.1 - Prob. 20ECh. 2.1 - Add: (4)+(5)Ch. 2.1 - Prob. 22ECh. 2.1 - Prob. 23ECh. 2.1 - Add: (+8)+(+2)Ch. 2.1 - Add: (5)+(+2)Ch. 2.1 - Prob. 26ECh. 2.1 - Prob. 27ECh. 2.1 - Prob. 28ECh. 2.1 - Add: (10)+(6)Ch. 2.1 - Prob. 30ECh. 2.1 - Prob. 31ECh. 2.1 - Prob. 32ECh. 2.1 - Add: (2)+(0)Ch. 2.1 - Prob. 34ECh. 2.1 - Prob. 35ECh. 2.1 - Prob. 36ECh. 2.1 - Add: (16)+(7)Ch. 2.1 - Prob. 38ECh. 2.1 - Prob. 39ECh. 2.1 - Prob. 40ECh. 2.1 - Add: (1)+(3)+(+8)Ch. 2.1 - Prob. 42ECh. 2.1 - Prob. 43ECh. 2.1 - Prob. 44ECh. 2.1 - Add: (9)+(+6)+(4)Ch. 2.1 - Prob. 46ECh. 2.1 - Prob. 47ECh. 2.1 - Add: (4)+(+5)+(8)+(+4)Ch. 2.1 - Add: (4)+(7)+(7)+(2)Ch. 2.1 - Prob. 50ECh. 2.1 - Prob. 51ECh. 2.1 - Add: (+6)+(+5)+(7)+(3)Ch. 2.1 - Add: (6)+(+2)+(+7)+(3)Ch. 2.1 - Prob. 54ECh. 2.1 - Prob. 55ECh. 2.1 - Add: (+5)+(+2)+(3)+(9)+(9)Ch. 2.1 - Add: (5)+(+6)+(9)+(4)+(7)Ch. 2.1 - Add: (9)+(+7)+(6)+(+5)+(8)Ch. 2.1 - Prob. 59ECh. 2.1 - Prob. 60ECh. 2.1 - Prob. 61ECh. 2.1 - Add: 14+(5)+(1)+6+(3)Ch. 2.1 - Prob. 63ECh. 2.1 - Add: (5)+4+(1)+6+(7)Ch. 2.1 - Add: (3)+8+(4)+(7)+10Ch. 2.1 - Prob. 66ECh. 2.1 - Prob. 67ECh. 2.1 - Prob. 68ECh. 2.1 - Add: (5)+5+(7)+2+(8)Ch. 2.1 - Add: 7+9+(6)+(4)+9+(2)Ch. 2.2 - Add or subtract the following signed numbers:...Ch. 2.2 - Prob. 2SNDCh. 2.2 - Prob. 3SNDCh. 2.2 - Prob. 4SNDCh. 2.2 - Prob. 5SNDCh. 2.2 - Prob. 6SNDCh. 2.2 - Prob. 7SNDCh. 2.2 - Prob. 8SNDCh. 2.2 - Prob. 9SNDCh. 2.2 - Prob. 10SNDCh. 2.2 - Prob. 11SNDCh. 2.2 - Prob. 12SNDCh. 2.2 - Prob. 13SNDCh. 2.2 - Prob. 14SNDCh. 2.2 - Prob. 15SNDCh. 2.2 - Prob. 16SNDCh. 2.2 - Add or subtract the following signed numbers:...Ch. 2.2 - Prob. 18SNDCh. 2.2 - Prob. 19SNDCh. 2.2 - Prob. 20SNDCh. 2.2 - Prob. 21SNDCh. 2.2 - Prob. 22SNDCh. 2.2 - Prob. 23SNDCh. 2.2 - Prob. 24SNDCh. 2.2 - Prob. 25SNDCh. 2.2 - Prob. 26SNDCh. 2.2 - Prob. 27SNDCh. 2.2 - Prob. 28SNDCh. 2.2 - Prob. 29SNDCh. 2.2 - Prob. 30SNDCh. 2.2 - Subtract: (+4)(+6)Ch. 2.2 - Prob. 2ECh. 2.2 - Prob. 3ECh. 2.2 - Subtract: (10)(+4)Ch. 2.2 - Subtract: (+5)(7)Ch. 2.2 - Prob. 6ECh. 2.2 - Prob. 7ECh. 2.2 - Subtract: (+4)(9)Ch. 2.2 - Subtract: (12)(6)Ch. 2.2 - Subtract: (12)(6)Ch. 2.2 - Prob. 11ECh. 2.2 - Prob. 12ECh. 2.2 - Subtract: (0)(4)Ch. 2.2 - Prob. 14ECh. 2.2 - Prob. 15ECh. 2.2 - Prob. 16ECh. 2.2 - Subtract: (4)(5)Ch. 2.2 - Prob. 18ECh. 2.2 - Prob. 19ECh. 2.2 - Prob. 20ECh. 2.2 - Subtract: (5)(+2)Ch. 2.2 - Prob. 22ECh. 2.2 - Prob. 23ECh. 2.2 - Subtract: (8)(3)Ch. 2.2 - Subtract: (10)(6)Ch. 2.2 - Prob. 26ECh. 2.2 - Prob. 27ECh. 2.2 - Prob. 28ECh. 2.2 - Subtract: (2)(0)Ch. 2.2 - Prob. 30ECh. 2.2 - Prob. 31ECh. 2.2 - Prob. 32ECh. 2.2 - Subtract: (16)(7)Ch. 2.2 - Subtract: (19)(12)Ch. 2.2 - Subtract: (6)(+9)Ch. 2.2 - Prob. 36ECh. 2.2 - Prob. 37ECh. 2.2 - Prob. 38ECh. 2.2 - Prob. 39ECh. 2.2 - Perform the indicated operations: (+3)(4)(9)Ch. 2.2 - Prob. 41ECh. 2.2 - Perform the indicated operations: (+10)(4)(6)(9)Ch. 2.2 - Prob. 43ECh. 2.2 - Prob. 44ECh. 2.2 - Prob. 45ECh. 2.2 - Prob. 46ECh. 2.2 - Prob. 47ECh. 2.2 - Prob. 48ECh. 2.2 - Perform the indicated operations:...Ch. 2.2 - Prob. 50ECh. 2.2 - Prob. 51ECh. 2.2 - Perform the indicated operations: 12+2+306Ch. 2.2 - Prob. 53ECh. 2.2 - Prob. 54ECh. 2.2 - Perform the indicated operations: 1618+472+9Ch. 2.2 - Prob. 56ECh. 2.2 - Prob. 57ECh. 2.2 - Prob. 58ECh. 2.2 - Perform the indicated operations: 97+4+2966+1Ch. 2.2 - Perform the indicated operations: 4+675+671Ch. 2.3 - Add, subtract, or multiply the following signed...Ch. 2.3 - Prob. 2SNDCh. 2.3 - Prob. 3SNDCh. 2.3 - Prob. 4SNDCh. 2.3 - Prob. 5SNDCh. 2.3 - Prob. 6SNDCh. 2.3 - Prob. 7SNDCh. 2.3 - Prob. 8SNDCh. 2.3 - Prob. 9SNDCh. 2.3 - Prob. 10SNDCh. 2.3 - Prob. 11SNDCh. 2.3 - Prob. 12SNDCh. 2.3 - Prob. 13SNDCh. 2.3 - Prob. 14SNDCh. 2.3 - Prob. 15SNDCh. 2.3 - Prob. 16SNDCh. 2.3 - Add, subtract, or multiply the following signed...Ch. 2.3 - Prob. 18SNDCh. 2.3 - Prob. 19SNDCh. 2.3 - Prob. 20SNDCh. 2.3 - Add, subtract, or multiply the following signed...Ch. 2.3 - Prob. 22SNDCh. 2.3 - Prob. 23SNDCh. 2.3 - Prob. 24SNDCh. 2.3 - Prob. 25SNDCh. 2.3 - Prob. 26SNDCh. 2.3 - Prob. 27SNDCh. 2.3 - Prob. 28SNDCh. 2.3 - Prob. 29SNDCh. 2.3 - Prob. 30SNDCh. 2.3 - Multiply: (+4)(+6)Ch. 2.3 - Prob. 2ECh. 2.3 - Prob. 3ECh. 2.3 - Prob. 4ECh. 2.3 - Multiply: (+5)(7)Ch. 2.3 - Prob. 6ECh. 2.3 - Prob. 7ECh. 2.3 - Prob. 8ECh. 2.3 - Multiply: (12)(6)Ch. 2.3 - Prob. 10ECh. 2.3 - Prob. 11ECh. 2.3 - Prob. 12ECh. 2.3 - Multiply: (0)(4)Ch. 2.3 - Multiply: (5)(10)Ch. 2.3 - Prob. 15ECh. 2.3 - Prob. 16ECh. 2.3 - Multiply: (+15)(20)Ch. 2.3 - Prob. 18ECh. 2.3 - Prob. 19ECh. 2.3 - Prob. 20ECh. 2.3 - Multiply: (+3)(2)Ch. 2.3 - Prob. 22ECh. 2.3 - Prob. 23ECh. 2.3 - Prob. 24ECh. 2.3 - Multiply: (7)(3)Ch. 2.3 - Prob. 26ECh. 2.3 - Prob. 27ECh. 2.3 - Multiply: (+5)(3)Ch. 2.3 - Multiply: (6)(9)Ch. 2.3 - Prob. 30ECh. 2.3 - Prob. 31ECh. 2.3 - Prob. 32ECh. 2.3 - Multiply: (8)(3)Ch. 2.3 - Prob. 34ECh. 2.3 - Prob. 35ECh. 2.3 - Prob. 36ECh. 2.3 - Multiply: (9)(7)Ch. 2.3 - Prob. 38ECh. 2.3 - Prob. 39ECh. 2.3 - Prob. 40ECh. 2.3 - Multiply: (+3)(2)(+1)Ch. 2.3 - Multiply: (5)(9)(+2)Ch. 2.3 - Prob. 43ECh. 2.3 - Prob. 44ECh. 2.3 - Multiply: (+5)(+2)(+3)Ch. 2.3 - Prob. 46ECh. 2.3 - Prob. 47ECh. 2.3 - Multiply: (3)(1)(+1)(+2)Ch. 2.3 - Multiply: (9)(2)(+3)(+1)(3)Ch. 2.3 - Prob. 50ECh. 2.3 - Prob. 51ECh. 2.3 - Prob. 52ECh. 2.3 - Divide: +273Ch. 2.3 - Divide: 48+6Ch. 2.3 - Prob. 55ECh. 2.3 - Prob. 56ECh. 2.3 - Divide: +14+7Ch. 2.3 - Prob. 58ECh. 2.3 - Prob. 59ECh. 2.3 - Divide: +729Ch. 2.3 - Divide: 100+25Ch. 2.3 - Prob. 62ECh. 2.3 - Prob. 63ECh. 2.3 - Divide: +366Ch. 2.3 - Divide: +85+5Ch. 2.3 - Prob. 66ECh. 2.3 - Prob. 67ECh. 2.3 - Prob. 68ECh. 2.3 - Divide: 90060Ch. 2.3 - Prob. 70ECh. 2.3 - Prob. 71ECh. 2.3 - Prob. 72ECh. 2.3 - Prob. 73ECh. 2.3 - Prob. 74ECh. 2.3 - Prob. 75ECh. 2.3 - Divide: (+120)(6)Ch. 2.3 - Divide: (110)(11)Ch. 2.3 - Prob. 78ECh. 2.3 - Divide: (96)(12)Ch. 2.3 - Prob. 80ECh. 2.4 - Perform the indicated operations and simplify:...Ch. 2.4 - Perform the indicated operations and simplify:...Ch. 2.4 - Prob. 3ECh. 2.4 - Perform the indicated operations and simplify:...Ch. 2.4 - Perform the indicated operations and simplify:...Ch. 2.4 - Prob. 6ECh. 2.4 - Prob. 7ECh. 2.4 - Prob. 8ECh. 2.4 - Perform the indicated operations and simplify:...Ch. 2.4 - Perform the indicated operations and simplify:...Ch. 2.4 - Prob. 11ECh. 2.4 - Prob. 12ECh. 2.4 - Perform the indicated operations and simplify:...Ch. 2.4 - Prob. 14ECh. 2.4 - Perform the indicated operations and simplify:...Ch. 2.4 - Perform the indicated operations and simplify:...Ch. 2.4 - Perform the indicated operations and simplify:...Ch. 2.4 - Perform the indicated operations and simplify:...Ch. 2.4 - Prob. 19ECh. 2.4 - Prob. 20ECh. 2.4 - Perform the indicated operations and simplify:...Ch. 2.4 - Perform the indicated operations and simplify:...Ch. 2.4 - Prob. 23ECh. 2.4 - Perform the indicated operations and simplify:...Ch. 2.4 - Perform the indicated operations and simplify:...Ch. 2.4 - Prob. 26ECh. 2.4 - Prob. 27ECh. 2.4 - Prob. 28ECh. 2.4 - Perform the indicated operations and simplify:...Ch. 2.4 - Perform the indicated operations and simplify:...Ch. 2.4 - Prob. 31ECh. 2.4 - Prob. 32ECh. 2.4 - Perform the indicated operations and simplify:...Ch. 2.4 - Prob. 34ECh. 2.4 - Prob. 35ECh. 2.4 - Prob. 36ECh. 2.4 - Perform the indicated operations and simplify:...Ch. 2.4 - Prob. 38ECh. 2.4 - Prob. 39ECh. 2.4 - Prob. 40ECh. 2.4 - Prob. 41ECh. 2.4 - Perform the indicated operations and simplify:...Ch. 2.4 - Perform the indicated operations and simplify:...Ch. 2.4 - Perform the indicated operations and simplify:...Ch. 2.4 - Perform the indicated operations and simplify:...Ch. 2.4 - Perform the indicated operations and simplify:...Ch. 2.5 - Perform the indicated operations using the laws of...Ch. 2.5 - Perform the indicated operations using the laws of...Ch. 2.5 - Perform the indicated operations using the laws of...Ch. 2.5 - Prob. 4ECh. 2.5 - Perform the indicated operations using the laws of...Ch. 2.5 - Perform the indicated operations using the laws of...Ch. 2.5 - Perform the indicated operations using the laws of...Ch. 2.5 - Perform the indicated operations using the laws of...Ch. 2.5 - Perform the indicated operations using the laws of...Ch. 2.5 - Perform the indicated operations using the laws of...Ch. 2.5 - Prob. 11ECh. 2.5 - Prob. 12ECh. 2.5 - Perform the indicated operations using the laws of...Ch. 2.5 - Perform the indicated operations using the laws of...Ch. 2.5 - Prob. 15ECh. 2.5 - Perform the indicated operations using the laws of...Ch. 2.5 - Perform the indicated operations using the laws of...Ch. 2.5 - Prob. 18ECh. 2.5 - Prob. 19ECh. 2.5 - Perform the indicated operations using the laws of...Ch. 2.5 - Perform the indicated operations using the laws of...Ch. 2.5 - Perform the indicated operations using the laws of...Ch. 2.5 - Perform the indicated operations using the laws of...Ch. 2.5 - Perform the indicated operations using the laws of...Ch. 2.5 - Perform the indicated operations using the laws of...Ch. 2.5 - Perform the indicated operations using the laws of...Ch. 2.5 - Perform the indicated operations using the laws of...Ch. 2.5 - Prob. 28ECh. 2.5 - Perform the indicated operations using the laws of...Ch. 2.5 - Prob. 30ECh. 2.6 - Writhe each number in scientific notation: 356Ch. 2.6 - Writhe each number in scientific notation: 15,600Ch. 2.6 - Writhe each number in scientific notation: 634.8Ch. 2.6 - Writhe each number in scientific notation: 24.85Ch. 2.6 - Writhe each number in scientific notation: 0.00825Ch. 2.6 - Writhe each number in scientific notation: 0.00063Ch. 2.6 - Prob. 7ECh. 2.6 - Writhe each number in scientific notation: 377,000Ch. 2.6 - Writhe each number in scientific notation:...Ch. 2.6 - Writhe each number in scientific notation: 0.00335Ch. 2.6 - Prob. 11ECh. 2.6 - Prob. 12ECh. 2.6 - Writhe each number in scientific notation:...Ch. 2.6 - Writhe each number in scientific notation:...Ch. 2.6 - Writhe each number in scientific notation:...Ch. 2.6 - Writhe each number in scientific notation:...Ch. 2.6 - Writhe each number in scientific notation: 640,000Ch. 2.6 - Writhe each number in scientific notation: 85,009Ch. 2.6 - Prob. 19ECh. 2.6 - Prob. 20ECh. 2.6 - Prob. 21ECh. 2.6 - Prob. 22ECh. 2.6 - Prob. 23ECh. 2.6 - Prob. 24ECh. 2.6 - Prob. 25ECh. 2.6 - Prob. 26ECh. 2.6 - Prob. 27ECh. 2.6 - Prob. 28ECh. 2.6 - Prob. 29ECh. 2.6 - Prob. 30ECh. 2.6 - Prob. 31ECh. 2.6 - Prob. 32ECh. 2.6 - Prob. 33ECh. 2.6 - Prob. 34ECh. 2.6 - Prob. 35ECh. 2.6 - Prob. 36ECh. 2.6 - Prob. 37ECh. 2.6 - Prob. 38ECh. 2.6 - Prob. 39ECh. 2.6 - Prob. 40ECh. 2.6 - Prob. 41ECh. 2.6 - Prob. 42ECh. 2.6 - Prob. 43ECh. 2.6 - Prob. 44ECh. 2.6 - Find the larger number: 0.000043; 0.00091Ch. 2.6 - Prob. 46ECh. 2.6 - Prob. 47ECh. 2.6 - Prob. 48ECh. 2.6 - Find the larger number: 0.0613; 0.00812Ch. 2.6 - Find the larger number: 0.0000613; 0.01200Ch. 2.6 - Find the smaller number: 0.008; 0.0009Ch. 2.6 - Prob. 52ECh. 2.6 - Find the smaller number: 1.003; 1.0009Ch. 2.6 - Prob. 54ECh. 2.6 - Prob. 55ECh. 2.6 - Prob. 56ECh. 2.6 - Find the smaller number: 0.000314; 0.000371Ch. 2.6 - Prob. 58ECh. 2.6 - Perform the indicated operation (write each result...Ch. 2.6 - Perform the indicated operation (write each result...Ch. 2.6 - Perform the indicated operation (write each result...Ch. 2.6 - Prob. 62ECh. 2.6 - Prob. 63ECh. 2.6 - Prob. 64ECh. 2.6 - Perform the indicated operation (write each result...Ch. 2.6 - Prob. 66ECh. 2.6 - Perform the indicated operation (write each result...Ch. 2.6 - Prob. 68ECh. 2.6 - Perform the indicated operation (write each result...Ch. 2.6 - Perform the indicated operation (write each result...Ch. 2.6 - Prob. 71ECh. 2.6 - Perform the indicated operation (write each result...Ch. 2.6 - Perform the indicated operation (write each result...Ch. 2.6 - Prob. 74ECh. 2.6 - Prob. 75ECh. 2.6 - Prob. 76ECh. 2.6 - Perform the indicated operation (write each result...Ch. 2.6 - Prob. 78ECh. 2.6 - Perform the indicated operation (write each result...Ch. 2.6 - Prob. 80ECh. 2.6 - Prob. 81ECh. 2.6 - Prob. 82ECh. 2.7 - Write each number in engineering notation: 28,000Ch. 2.7 - Prob. 2ECh. 2.7 - Write each number in engineering notation:...Ch. 2.7 - Prob. 4ECh. 2.7 - Prob. 5ECh. 2.7 - Prob. 6ECh. 2.7 - Prob. 7ECh. 2.7 - Write each number in engineering notation: 0.00015Ch. 2.7 - Prob. 9ECh. 2.7 - Prob. 10ECh. 2.7 - Prob. 11ECh. 2.7 - Write each number in engineering notation:...Ch. 2.7 - Prob. 13ECh. 2.7 - Prob. 14ECh. 2.7 - Prob. 15ECh. 2.7 - Prob. 16ECh. 2.7 - Prob. 17ECh. 2.7 - Prob. 18ECh. 2.7 - Prob. 19ECh. 2.7 - Prob. 20ECh. 2.7 - Prob. 21ECh. 2.7 - Prob. 22ECh. 2.7 - Prob. 23ECh. 2.7 - Prob. 24ECh. 2.7 - Prob. 25ECh. 2.7 - Prob. 26ECh. 2.7 - Prob. 27ECh. 2.7 - Prob. 28ECh. 2.7 - Prob. 29ECh. 2.7 - Prob. 30ECh. 2.7 - Prob. 31ECh. 2.7 - Prob. 32ECh. 2.7 - Prob. 33ECh. 2.7 - Prob. 34ECh. 2.7 - Prob. 35ECh. 2.7 - Prob. 36ECh. 2.7 - Prob. 37ECh. 2.7 - Prob. 38ECh. 2.7 - Prob. 39ECh. 2.7 - Prob. 40ECh. 2 - Find the absolute value of each number: +5Ch. 2 - Find the absolute value of each number: 16Ch. 2 - Prob. 3RCh. 2 - Prob. 4RCh. 2 - Prob. 5RCh. 2 - Prob. 6RCh. 2 - Prob. 7RCh. 2 - Prob. 8RCh. 2 - Prob. 9RCh. 2 - Prob. 10RCh. 2 - Prob. 11RCh. 2 - Prob. 12RCh. 2 - Prob. 13RCh. 2 - Prob. 14RCh. 2 - Prob. 15RCh. 2 - Prob. 16RCh. 2 - Prob. 17RCh. 2 - Prob. 18RCh. 2 - Prob. 19RCh. 2 - Prob. 20RCh. 2 - Prob. 21RCh. 2 - Prob. 22RCh. 2 - Prob. 23RCh. 2 - Prob. 24RCh. 2 - Prob. 25RCh. 2 - Prob. 26RCh. 2 - Prob. 27RCh. 2 - Prob. 28RCh. 2 - Write each number in scientific notation: 476,000Ch. 2 - Write each number in scientific notation: 0.0014Ch. 2 - Prob. 31RCh. 2 - Prob. 32RCh. 2 - Prob. 33RCh. 2 - Prob. 34RCh. 2 - Find the smaller number: 0.000075; 0.0006Ch. 2 - Prob. 36RCh. 2 - Prob. 37RCh. 2 - Prob. 38RCh. 2 - Prob. 39RCh. 2 - Prob. 40RCh. 2 - Perform the indicated operation and write each...Ch. 2 - Perform the indicated operation and write each...Ch. 2 - Write each number in engineering notation: 275,000Ch. 2 - Write each number in engineering notation:...Ch. 2 - Write each number in engineering notation: 0.00045Ch. 2 - Prob. 46RCh. 2 - Prob. 47RCh. 2 - Perform the indicated operations and write each...Ch. 2 - Prob. 49RCh. 2 - Prob. 50RCh. 2 - Perform the indicated operations: 7+(+9)Ch. 2 - Perform the indicated operations: 28+(11)Ch. 2 - Perform the indicated operations: 18+(6)Ch. 2 - Perform the indicated operations: 65+42Ch. 2 - Prob. 5TCh. 2 - Perform the indicated operations: 6(10)Ch. 2 - Prob. 7TCh. 2 - Prob. 8TCh. 2 - Perform the indicated operations: (+15)(22)Ch. 2 - Perform the indicated operations: (+17)(8)Ch. 2 - Perform the indicated operations: +204Ch. 2 - Prob. 12TCh. 2 - Perform the indicated operations:...Ch. 2 - Perform the indicated operations:...Ch. 2 - Prob. 15TCh. 2 - Prob. 16TCh. 2 - Perform the indicated operations: 8+5+212+53Ch. 2 - Perform the indicated operations and simplify:...Ch. 2 - Prob. 19TCh. 2 - Prob. 20TCh. 2 - Write 0.000182 in scientific notation.Ch. 2 - Prob. 22TCh. 2 - Prob. 23TCh. 2 - Prob. 24TCh. 2 - Prob. 25TCh. 2 - Prob. 26TCh. 2 - Prob. 27TCh. 2 - Prob. 28TCh. 2 - Prob. 29TCh. 2 - Prob. 30TCh. 2 - Prob. 31TCh. 2 - Prob. 32TCh. 2 - Prob. 33TCh. 2 - Prob. 34TCh. 2 - Prob. 35TCh. 2 - Prob. 1CRCh. 2 - Prob. 2CRCh. 2 - Prob. 3CRCh. 2 - Prob. 4CRCh. 2 - Prob. 5CRCh. 2 - Prob. 6CRCh. 2 - Prob. 7CRCh. 2 - Prob. 8CRCh. 2 - Perform the indicated operations and simplify:...Ch. 2 - Prob. 10CRCh. 2 - Prob. 11CRCh. 2 - Perform the indicated operations and simplify:...Ch. 2 - Prob. 13CRCh. 2 - Prob. 14CRCh. 2 - Prob. 15CRCh. 2 - Prob. 16CRCh. 2 - To the nearest hundredth, 58 is what percent of...Ch. 2 - Prob. 18CRCh. 2 - Prob. 19CRCh. 2 - Prob. 20CRCh. 2 - Prob. 21CRCh. 2 - Prob. 22CRCh. 2 - Prob. 23CRCh. 2 - Prob. 24CRCh. 2 - Prob. 25CRCh. 2 - Prob. 26CRCh. 2 - Write each number in engineering notation: 0.00027Ch. 2 - Prob. 28CRCh. 2 - Prob. 29CRCh. 2 - Prob. 30CRCh. 2 - Prob. 31CRCh. 2 - Prob. 32CRCh. 2 - Perform the indicated operations and write each...
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- (6) (8 points) Change the order of integration and evaluate (z +4ry)drdy . So S√ ² 0arrow_forward(10) (16 points) Let R>0. Consider the truncated sphere S given as x² + y² + (z = √15R)² = R², z ≥0. where F(x, y, z) = −yi + xj . (a) (8 points) Consider the vector field V (x, y, z) = (▼ × F)(x, y, z) Think of S as a hot-air balloon where the vector field V is the velocity vector field measuring the hot gasses escaping through the porous surface S. The flux of V across S gives the volume flow rate of the gasses through S. Calculate this flux. Hint: Parametrize the boundary OS. Then use Stokes' Theorem. (b) (8 points) Calculate the surface area of the balloon. To calculate the surface area, do the following: Translate the balloon surface S by the vector (-15)k. The translated surface, call it S+ is part of the sphere x² + y²+z² = R². Why do S and S+ have the same area? ⚫ Calculate the area of S+. What is the natural spherical parametrization of S+?arrow_forward(1) (8 points) Let c(t) = (et, et sint, et cost). Reparametrize c as a unit speed curve starting from the point (1,0,1).arrow_forward
- (9) (16 points) Let F(x, y, z) = (x² + y − 4)i + 3xyj + (2x2 +z²)k = - = (x²+y4,3xy, 2x2 + 2²). (a) (4 points) Calculate the divergence and curl of F. (b) (6 points) Find the flux of V x F across the surface S given by x² + y²+2² = 16, z ≥ 0. (c) (6 points) Find the flux of F across the boundary of the unit cube E = [0,1] × [0,1] x [0,1].arrow_forward(8) (12 points) (a) (8 points) Let C be the circle x² + y² = 4. Let F(x, y) = (2y + e²)i + (x + sin(y²))j. Evaluate the line integral JF. F.ds. Hint: First calculate V x F. (b) (4 points) Let S be the surface r² + y² + z² = 4, z ≤0. Calculate the flux integral √(V × F) F).dS. Justify your answer.arrow_forwardDetermine whether the Law of Sines or the Law of Cosines can be used to find another measure of the triangle. a = 13, b = 15, C = 68° Law of Sines Law of Cosines Then solve the triangle. (Round your answers to four decimal places.) C = 15.7449 A = 49.9288 B = 62.0712 × Need Help? Read It Watch Itarrow_forward
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