Math in Our World
3rd Edition
ISBN: 9780073519678
Author: David Sobecki Professor, Allan G. Bluman
Publisher: McGraw-Hill Education
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Chapter 15.3, Problem 2E
To determine
To describe: The process for finding the number congruent to 25 in the mod 7 system.
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(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).
=
(6) (8 points) Change the order of integration and evaluate
(z +4ry)drdy .
So S√ ²
0
(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+?
Chapter 15 Solutions
Math in Our World
Ch. 15.1 - Use Table 15-1 to find the result of each...Ch. 15.1 - Which properties does the following system...Ch. 15.1 - Prob. 3TTOCh. 15.1 - Prob. 4TTOCh. 15.1 - Prob. 1ECh. 15.1 - Prob. 2ECh. 15.1 - Prob. 3ECh. 15.1 - Prob. 4ECh. 15.1 - Prob. 5ECh. 15.1 - Prob. 6E
Ch. 15.1 - Prob. 7ECh. 15.1 - Prob. 8ECh. 15.1 - Prob. 9ECh. 15.1 - Prob. 10ECh. 15.1 - Prob. 11ECh. 15.1 - Prob. 12ECh. 15.1 - For Exercises 724, use the elements C, D, E, and...Ch. 15.1 - For Exercises 724, use the elements C, D, E, and...Ch. 15.1 - For Exercises 724, use the elements C, D, E, and...Ch. 15.1 - For Exercises 724, use the elements C, D, E, and...Ch. 15.1 - For Exercises 724, use the elements C, D, E, and...Ch. 15.1 - For Exercises 724, use the elements C, D, E, and...Ch. 15.1 - Prob. 19ECh. 15.1 - Prob. 20ECh. 15.1 - For Exercises 724, use the elements C, D, E, and...Ch. 15.1 - Prob. 22ECh. 15.1 - Prob. 23ECh. 15.1 - Prob. 24ECh. 15.1 - Prob. 25ECh. 15.1 - Prob. 26ECh. 15.1 - Prob. 27ECh. 15.1 - Prob. 28ECh. 15.1 - Prob. 29ECh. 15.1 - For Exercises 2540, use the elements and the...Ch. 15.1 - Prob. 31ECh. 15.1 - Prob. 32ECh. 15.1 - For Exercises 2540, use the elements and the...Ch. 15.1 - For Exercises 2540, use the elements and the...Ch. 15.1 - For Exercises 2540, use the elements and the...Ch. 15.1 - Prob. 36ECh. 15.1 - Prob. 37ECh. 15.1 - Prob. 38ECh. 15.1 - For Exercises 2540, use the elements and the...Ch. 15.1 - Prob. 40ECh. 15.1 - Prob. 41ECh. 15.1 - Prob. 42ECh. 15.1 - Prob. 43ECh. 15.1 - Prob. 44ECh. 15.1 - Prob. 45ECh. 15.1 - Prob. 46ECh. 15.1 - Prob. 47ECh. 15.1 - For Exercises 4150, determine which properties the...Ch. 15.1 - Prob. 49ECh. 15.1 - Prob. 50ECh. 15.1 - Prob. 51ECh. 15.1 - Prob. 52ECh. 15.1 - Prob. 53ECh. 15.1 - Prob. 54ECh. 15.1 - Prob. 55ECh. 15.1 - Prob. 56ECh. 15.1 - For exercises 5160, determine whether the given...Ch. 15.1 - Prob. 58ECh. 15.1 - For exercises 5160, determine whether the given...Ch. 15.1 - Prob. 60ECh. 15.1 - Exercises 6166 use the mathematical system...Ch. 15.1 - Prob. 62ECh. 15.1 - Prob. 63ECh. 15.1 - Prob. 64ECh. 15.1 - Prob. 65ECh. 15.1 - Prob. 66ECh. 15.1 - Prob. 67ECh. 15.1 - Prob. 68ECh. 15.1 - Prob. 69ECh. 15.1 - Prob. 70ECh. 15.1 - Prob. 71ECh. 15.1 - Prob. 72ECh. 15.1 - Prob. 73ECh. 15.1 - Prob. 74ECh. 15.1 - Prob. 75ECh. 15.1 - Prob. 76ECh. 15.1 - Prob. 77ECh. 15.1 - Prob. 78ECh. 15.1 - Prob. 79ECh. 15.1 - Prob. 80ECh. 15.1 - Prob. 81ECh. 15.1 - Prob. 82ECh. 15.1 - Exercises 8184 are based on the classic game of...Ch. 15.1 - Exercises 8184 are based on the classic game of...Ch. 15.1 - Suppose that a mathematical system consists of the...Ch. 15.2 - Using the 12-hour clock, find these sums. (a)3+12...Ch. 15.2 - Prob. 2TTOCh. 15.2 - Prob. 3TTOCh. 15.2 - Prob. 4TTOCh. 15.2 - Prob. 1ECh. 15.2 - Prob. 2ECh. 15.2 - Prob. 3ECh. 15.2 - Prob. 4ECh. 15.2 - Prob. 5ECh. 15.2 - Prob. 6ECh. 15.2 - Prob. 7ECh. 15.2 - Prob. 8ECh. 15.2 - Prob. 9ECh. 15.2 - Prob. 10ECh. 15.2 - Prob. 11ECh. 15.2 - Prob. 12ECh. 15.2 - Prob. 13ECh. 15.2 - Prob. 14ECh. 15.2 - Prob. 15ECh. 15.2 - Prob. 16ECh. 15.2 - For Exercises 920, find the equivalent number on...Ch. 15.2 - For Exercises 920, find the equivalent number on...Ch. 15.2 - Prob. 19ECh. 15.2 - Prob. 20ECh. 15.2 - For Exercises 2130, perform the additions on the...Ch. 15.2 - Prob. 22ECh. 15.2 - For Exercises 2130, perform the additions on the...Ch. 15.2 - Prob. 24ECh. 15.2 - For Exercises 2130, perform the additions on the...Ch. 15.2 - Prob. 26ECh. 15.2 - For Exercises 2130, perform the additions on the...Ch. 15.2 - Prob. 28ECh. 15.2 - For Exercises 2130, perform the additions on the...Ch. 15.2 - Prob. 30ECh. 15.2 - For Exercises 3140, perform the subtractions on...Ch. 15.2 - Prob. 32ECh. 15.2 - For Exercises 3140, perform the subtractions on...Ch. 15.2 - Prob. 34ECh. 15.2 - For Exercises 3140, perform the subtractions on...Ch. 15.2 - Prob. 36ECh. 15.2 - For Exercises 3140, perform the subtractions on...Ch. 15.2 - Prob. 38ECh. 15.2 - For Exercises 3140, perform the subtractions on...Ch. 15.2 - Prob. 40ECh. 15.2 - For Exercises 4150, perform the multiplications on...Ch. 15.2 - Prob. 42ECh. 15.2 - For Exercises 4150, perform the multiplications on...Ch. 15.2 - Prob. 44ECh. 15.2 - For Exercises 4150, perform the multiplications on...Ch. 15.2 - Prob. 46ECh. 15.2 - For Exercises 4150, perform the multiplications on...Ch. 15.2 - Prob. 48ECh. 15.2 - For Exercises 4150, perform the multiplications on...Ch. 15.2 - Prob. 50ECh. 15.2 - In Exercises 5162, perform the indicated operation...Ch. 15.2 - Prob. 52ECh. 15.2 - In Exercises 5162, perform the indicated operation...Ch. 15.2 - Prob. 54ECh. 15.2 - In Exercises 5162, perform the indicated operation...Ch. 15.2 - Prob. 56ECh. 15.2 - Prob. 57ECh. 15.2 - Prob. 58ECh. 15.2 - Prob. 59ECh. 15.2 - Prob. 60ECh. 15.2 - In Exercises 5162, perform the indicated operation...Ch. 15.2 - Prob. 62ECh. 15.2 - For Exercises 6370, find the additive inverse for...Ch. 15.2 - Prob. 64ECh. 15.2 - Prob. 65ECh. 15.2 - Prob. 66ECh. 15.2 - Prob. 67ECh. 15.2 - For Exercises 6370, find the additive inverse for...Ch. 15.2 - Prob. 69ECh. 15.2 - For Exercises 6370, find the additive inverse for...Ch. 15.2 - For Exercises 7176, find the multiplicative...Ch. 15.2 - Prob. 72ECh. 15.2 - For Exercises 7176, find the multiplicative...Ch. 15.2 - Prob. 74ECh. 15.2 - Prob. 75ECh. 15.2 - Prob. 76ECh. 15.2 - Prob. 77ECh. 15.2 - Prob. 78ECh. 15.2 - Prob. 79ECh. 15.2 - Prob. 80ECh. 15.2 - Prob. 81ECh. 15.2 - Prob. 82ECh. 15.2 - Prob. 83ECh. 15.2 - Prob. 84ECh. 15.2 - Prob. 85ECh. 15.2 - Prob. 86ECh. 15.2 - Prob. 87ECh. 15.2 - Prob. 88ECh. 15.2 - For Exercises 8190, find the value of y using the...Ch. 15.2 - Prob. 90ECh. 15.2 - Prob. 91ECh. 15.2 - Prob. 92ECh. 15.2 - Prob. 93ECh. 15.2 - Prob. 94ECh. 15.2 - Prob. 95ECh. 15.2 - Prob. 96ECh. 15.2 - Prob. 97ECh. 15.2 - Prob. 98ECh. 15.2 - Prob. 99ECh. 15.2 - Prob. 100ECh. 15.2 - Prob. 101ECh. 15.2 - Prob. 102ECh. 15.2 - Prob. 103ECh. 15.2 - Prob. 104ECh. 15.2 - Prob. 105ECh. 15.2 - Prob. 106ECh. 15.2 - Prob. 107ECh. 15.2 - Prob. 108ECh. 15.2 - Prob. 109ECh. 15.2 - Prob. 110ECh. 15.2 - Prob. 111ECh. 15.2 - Prob. 112ECh. 15.2 - Prob. 113ECh. 15.2 - Prob. 114ECh. 15.2 - Prob. 115ECh. 15.2 - Prob. 116ECh. 15.2 - Prob. 117ECh. 15.2 - Prob. 118ECh. 15.2 - Prob. 119ECh. 15.2 - Prob. 120ECh. 15.2 - Prob. 121ECh. 15.3 - Prob. 1TTOCh. 15.3 - Prob. 2TTOCh. 15.3 - Prob. 3TTOCh. 15.3 - Prob. 4TTOCh. 15.3 - Prob. 5TTOCh. 15.3 - Find all natural number solutions to 4x 24 mod 8.Ch. 15.3 - Prob. 1ECh. 15.3 - Prob. 2ECh. 15.3 - Prob. 3ECh. 15.3 - Prob. 4ECh. 15.3 - Prob. 5ECh. 15.3 - Prob. 6ECh. 15.3 - Prob. 7ECh. 15.3 - Prob. 8ECh. 15.3 - Prob. 9ECh. 15.3 - Prob. 10ECh. 15.3 - For Exercises 516, find the values of each number...Ch. 15.3 - For Exercises 516, find the values of each number...Ch. 15.3 - Prob. 13ECh. 15.3 - Prob. 14ECh. 15.3 - Prob. 15ECh. 15.3 - Prob. 16ECh. 15.3 - Prob. 17ECh. 15.3 - Prob. 18ECh. 15.3 - Prob. 19ECh. 15.3 - Prob. 20ECh. 15.3 - Prob. 21ECh. 15.3 - For Exercises 1746, perform the following...Ch. 15.3 - Prob. 23ECh. 15.3 - Prob. 24ECh. 15.3 - Prob. 25ECh. 15.3 - Prob. 26ECh. 15.3 - Prob. 27ECh. 15.3 - Prob. 28ECh. 15.3 - Prob. 29ECh. 15.3 - Prob. 30ECh. 15.3 - Prob. 31ECh. 15.3 - Prob. 32ECh. 15.3 - Prob. 33ECh. 15.3 - Prob. 34ECh. 15.3 - For Exercises 1746, perform the following...Ch. 15.3 - Prob. 36ECh. 15.3 - Prob. 37ECh. 15.3 - For Exercises 1746, perform the following...Ch. 15.3 - Prob. 39ECh. 15.3 - Prob. 40ECh. 15.3 - Prob. 41ECh. 15.3 - Prob. 42ECh. 15.3 - Prob. 43ECh. 15.3 - Prob. 44ECh. 15.3 - Prob. 45ECh. 15.3 - Prob. 46ECh. 15.3 - Prob. 47ECh. 15.3 - Prob. 48ECh. 15.3 - Prob. 49ECh. 15.3 - Prob. 50ECh. 15.3 - Prob. 51ECh. 15.3 - Prob. 52ECh. 15.3 - Prob. 53ECh. 15.3 - For Exercises 4754, find all natural number...Ch. 15.3 - Prob. 55ECh. 15.3 - Prob. 56ECh. 15.3 - Prob. 57ECh. 15.3 - Prob. 58ECh. 15.3 - Prob. 59ECh. 15.3 - Prob. 60ECh. 15.3 - Prob. 61ECh. 15.3 - Prob. 62ECh. 15.3 - Prob. 63ECh. 15.3 - Prob. 64ECh. 15.3 - Prob. 65ECh. 15.3 - Prob. 66ECh. 15.3 - Prob. 67ECh. 15.3 - Prob. 68ECh. 15.3 - Prob. 69ECh. 15.3 - Prob. 70ECh. 15.3 - Prob. 71ECh. 15.3 - Prob. 72ECh. 15.3 - Prob. 73ECh. 15.3 - Prob. 74ECh. 15.3 - Prob. 75ECh. 15.3 - Prob. 76ECh. 15.3 - Prob. 77ECh. 15.3 - Prob. 78ECh. 15.3 - Prob. 79ECh. 15.3 - Prob. 80ECh. 15.3 - Prob. 81ECh. 15.3 - Write a congruence that solves each conversion...Ch. 15.3 - Prob. 83ECh. 15.3 - Prob. 85ECh. 15.3 - Prob. 86ECh. 15.3 - Prob. 87ECh. 15.3 - Prob. 88ECh. 15.3 - Prob. 89ECh. 15.3 - Consider the congruence x2 4 mod 5. (a)Check that...Ch. 15.3 - Prob. 91ECh. 15.3 - For each congruence, find all possible values for...Ch. 15 - For Exercises 111, use the elements A, B, C and...Ch. 15 - Prob. 2RECh. 15 - For Exercises 111, use the elements A, B, C and...Ch. 15 - Prob. 4RECh. 15 - Prob. 5RECh. 15 - Prob. 6RECh. 15 - Prob. 7RECh. 15 - Prob. 8RECh. 15 - Prob. 9RECh. 15 - Prob. 10RECh. 15 - Prob. 11RECh. 15 - Prob. 12RECh. 15 - For Exercises 1216, determine if the given system...Ch. 15 - Prob. 14RECh. 15 - Prob. 15RECh. 15 - Prob. 16RECh. 15 - Prob. 17RECh. 15 - Prob. 18RECh. 15 - Prob. 19RECh. 15 - Prob. 20RECh. 15 - Prob. 21RECh. 15 - Prob. 22RECh. 15 - For Exercises 2328, perform the indicated...Ch. 15 - Prob. 24RECh. 15 - Prob. 25RECh. 15 - Prob. 26RECh. 15 - Prob. 27RECh. 15 - Prob. 28RECh. 15 - Prob. 29RECh. 15 - Prob. 30RECh. 15 - Prob. 31RECh. 15 - Prob. 32RECh. 15 - Prob. 33RECh. 15 - Prob. 34RECh. 15 - For Exercises 3142, find the equivalent number for...Ch. 15 - Prob. 36RECh. 15 - Prob. 37RECh. 15 - Prob. 38RECh. 15 - Prob. 39RECh. 15 - Prob. 40RECh. 15 - Prob. 41RECh. 15 - Prob. 42RECh. 15 - Prob. 43RECh. 15 - Prob. 44RECh. 15 - Prob. 45RECh. 15 - Prob. 46RECh. 15 - Prob. 47RECh. 15 - Prob. 48RECh. 15 - Prob. 49RECh. 15 - Prob. 50RECh. 15 - Prob. 51RECh. 15 - Prob. 52RECh. 15 - Prob. 53RECh. 15 - Prob. 54RECh. 15 - Prob. 55RECh. 15 - Prob. 56RECh. 15 - Prob. 57RECh. 15 - Prob. 58RECh. 15 - Prob. 59RECh. 15 - Prob. 60RECh. 15 - Prob. 61RECh. 15 - Prob. 62RECh. 15 - Prob. 63RECh. 15 - Prob. 64RECh. 15 - Prob. 65RECh. 15 - Prob. 66RECh. 15 - Prob. 1CTCh. 15 - Prob. 2CTCh. 15 - Prob. 3CTCh. 15 - Prob. 4CTCh. 15 - Prob. 5CTCh. 15 - Prob. 6CTCh. 15 - Prob. 7CTCh. 15 - Prob. 8CTCh. 15 - Prob. 9CTCh. 15 - Prob. 10CTCh. 15 - Prob. 11CTCh. 15 - Prob. 12CTCh. 15 - Prob. 13CTCh. 15 - Prob. 14CTCh. 15 - Prob. 15CTCh. 15 - Prob. 16CTCh. 15 - Prob. 17CTCh. 15 - Prob. 18CTCh. 15 - Prob. 19CTCh. 15 - Prob. 20CTCh. 15 - Prob. 21CTCh. 15 - Prob. 22CTCh. 15 - Prob. 23CTCh. 15 - Prob. 24CTCh. 15 - An entire baseball league is signed up for an...Ch. 15 - Prob. 26CT
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