Basic Technical Mathematics
11th Edition
ISBN: 9780134437705
Author: Washington
Publisher: PEARSON
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Chapter 26, Problem 12RE
To determine
The acceleration of a plane taking off from the flight deck.
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16. Solve the given differential equation:
y" + 4y sin (t)u(t 2π),
-
y(0) = 1, y'(0) = 0
Given,
1
(x² + 1)(x²+4)
1/3
-1/3
=
+
x²+1 x² +4
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R denotes the field of real numbers, Q denotes the field of rationals, and
Fp denotes the field of p elements given by integers modulo p. You may refer to general
results from lectures.
Question 1
For each non-negative integer m, let R[x]m denote the
vector space consisting of the polynomials in x with coefficients in R and of degree ≤ m.
x²+2, V3 = 5. Prove that (V1, V2, V3) is a linearly independent
(a) Let vi = x, V2 =
list in R[x] 3.
(b) Let V1, V2, V3 be as defined in (a). Find a vector v € R[×]3 such that (V1, V2, V3, V4)
is a basis of R[x] 3.
[8]
[6]
(c) Prove that the map ƒ from R[x] 2 to R[x]3 given by f(p(x)) = xp(x) — xp(0) is a
linear map.
[6]
(d) Write down the matrix for the map ƒ defined in (c) with respect to the basis
(2,2x + 1, x²) of R[x] 2 and the basis (1, x, x², x³) of R[x] 3.
[5]
Question 4
(a) The following matrices represent linear maps on R² with respect to an
orthonormal basis:
=
[1/√5 2/√5
[2/√5 -1/√5]
"
[1/√5 2/√5]
A =
B =
[2/√5 1/√5] 1
C =
D =
=
=
[ 1/3/5 2/35]
1/√5 2/√5
-2/√5 1/√5'
For each of the matrices A, B, C, D, state whether it represents a self-adjoint
linear map, an orthogonal linear map, both, or neither.
(b) For the quadratic form
q(x, y, z) = y² + 2xy +2yz
over R, write down a linear change of variables to u, v, w such that q in these
terms is in canonical form for Sylvester's Law of Inertia.
[6]
[4]
Chapter 26 Solutions
Basic Technical Mathematics
Ch. 26.1 - In Example 4, change the acceleration to a = 4...Ch. 26.1 - Prob. 2PECh. 26.1 - In Example 3, change 5.0 s to 2.5 s and then solve...Ch. 26.1 - Prob. 2ECh. 26.1 - What is the velocity (in ft/s) of a sandbag 1.5 s...Ch. 26.1 - Prob. 4ECh. 26.1 - A conveyor belt 8.00 m long moves at 0.25 m/s. If...Ch. 26.1 - Prob. 6ECh. 26.1 - The velocity (in km/h) of a plane flying into an...Ch. 26.1 - A cyclist goes downhill for 15 min with a velocity...
Ch. 26.1 - A car crosses an intersection as a fire engine...Ch. 26.1 - In designing a highway, a civil engineer must...Ch. 26.1 - Prob. 11ECh. 26.1 - Prob. 12ECh. 26.1 - A certain Chevrolet Corvette goes from 0 mi/h to...Ch. 26.1 - Prob. 14ECh. 26.1 - Prob. 15ECh. 26.1 - Prob. 16ECh. 26.1 - Prob. 17ECh. 26.1 - Prob. 18ECh. 26.1 - Prob. 19ECh. 26.1 - Prob. 20ECh. 26.1 - Prob. 21ECh. 26.1 - Prob. 22ECh. 26.1 - Prob. 23ECh. 26.1 - Prob. 24ECh. 26.1 - Prob. 25ECh. 26.1 - Prob. 26ECh. 26.1 - The voltage across a 3.75-μF capacitor in a...Ch. 26.1 - Prob. 28ECh. 26.1 - Prob. 29ECh. 26.1 - Prob. 30ECh. 26.1 - Prob. 31ECh. 26.1 - Prob. 32ECh. 26.1 - Prob. 33ECh. 26.1 - Prob. 34ECh. 26.1 - Prob. 35ECh. 26.1 - Prob. 36ECh. 26.2 - Find the area in the first quadrant bounded by y =...Ch. 26.2 - Prob. 2PECh. 26.2 - In Exercises 1 and 2, make the given changes in...Ch. 26.2 - In Exercises 1 and 2, make the given changes in...Ch. 26.2 - Prob. 3ECh. 26.2 - Prob. 4ECh. 26.2 - Prob. 5ECh. 26.2 - Prob. 6ECh. 26.2 - In Exercises 3–28, find the areas bounded by the...Ch. 26.2 - Prob. 8ECh. 26.2 - Prob. 9ECh. 26.2 - Prob. 10ECh. 26.2 - Prob. 11ECh. 26.2 - Prob. 12ECh. 26.2 - Prob. 13ECh. 26.2 - Prob. 14ECh. 26.2 - Prob. 15ECh. 26.2 - Prob. 16ECh. 26.2 - Prob. 17ECh. 26.2 - Prob. 18ECh. 26.2 - Prob. 19ECh. 26.2 - Prob. 20ECh. 26.2 - Prob. 21ECh. 26.2 - Prob. 22ECh. 26.2 - Prob. 23ECh. 26.2 - Prob. 24ECh. 26.2 - Prob. 25ECh. 26.2 - Prob. 26ECh. 26.2 - Prob. 27ECh. 26.2 - Prob. 28ECh. 26.2 - Prob. 29ECh. 26.2 - Prob. 30ECh. 26.2 - Prob. 31ECh. 26.2 - In Exercises 29–38, solve the given problems.
32....Ch. 26.2 - Prob. 33ECh. 26.2 - Prob. 34ECh. 26.2 - Prob. 35ECh. 26.2 - Prob. 36ECh. 26.2 - Prob. 37ECh. 26.2 - Prob. 38ECh. 26.2 - Prob. 39ECh. 26.2 - Prob. 40ECh. 26.2 - Prob. 41ECh. 26.2 - Prob. 42ECh. 26.2 - Prob. 43ECh. 26.2 - Prob. 44ECh. 26.2 - Prob. 45ECh. 26.2 - Prob. 46ECh. 26.2 - Prob. 47ECh. 26.2 - Prob. 48ECh. 26.2 - Prob. 49ECh. 26.2 - Prob. 50ECh. 26.3 - Find the volume of the solid generated by...Ch. 26.3 - Prob. 2PECh. 26.3 - Prob. 1ECh. 26.3 - Prob. 2ECh. 26.3 - Prob. 3ECh. 26.3 - Prob. 4ECh. 26.3 - Prob. 5ECh. 26.3 - Prob. 6ECh. 26.3 - Prob. 7ECh. 26.3 - Prob. 8ECh. 26.3 - In Exercises 7–16, find the volume generated by...Ch. 26.3 - Prob. 10ECh. 26.3 - In Exercises 7–16, find the volume generated by...Ch. 26.3 - Prob. 12ECh. 26.3 - Prob. 13ECh. 26.3 - Prob. 14ECh. 26.3 - Prob. 15ECh. 26.3 - Prob. 16ECh. 26.3 - Prob. 17ECh. 26.3 - Prob. 18ECh. 26.3 - Prob. 19ECh. 26.3 - Prob. 20ECh. 26.3 - In Exercises 17–26, find the volume generated by...Ch. 26.3 - In Exercises 17–26, find the volume generated by...Ch. 26.3 - In Exercises 17–26, find the volume generated by...Ch. 26.3 - In Exercises 17–26, find the volume generated by...Ch. 26.3 - In Exercises 17–26, find the volume generated by...Ch. 26.3 - In Exercises 17–26, find the volume generated by...Ch. 26.3 - In Exercises 27–40, find the indicated volumes by...Ch. 26.3 - Prob. 28ECh. 26.3 - Prob. 29ECh. 26.3 - Prob. 30ECh. 26.3 - Prob. 31ECh. 26.3 - Prob. 32ECh. 26.3 - Prob. 33ECh. 26.3 - Prob. 34ECh. 26.3 - Prob. 35ECh. 26.3 - Prob. 36ECh. 26.3 - Prob. 37ECh. 26.3 - Prob. 38ECh. 26.3 - Prob. 39ECh. 26.3 - Prob. 40ECh. 26.4 - In Example 4, change y = 4 to y = 1 and solve the...Ch. 26.4 - Prob. 1ECh. 26.4 - Prob. 2ECh. 26.4 - In Exercises 3–6, find the center of mass (in cm)...Ch. 26.4 - Prob. 4ECh. 26.4 - Prob. 5ECh. 26.4 - Prob. 6ECh. 26.4 - Prob. 7ECh. 26.4 - Prob. 8ECh. 26.4 - Prob. 9ECh. 26.4 - Prob. 10ECh. 26.4 - Prob. 11ECh. 26.4 - Prob. 12ECh. 26.4 - Prob. 13ECh. 26.4 - Prob. 14ECh. 26.4 - Prob. 15ECh. 26.4 - Prob. 16ECh. 26.4 - Prob. 17ECh. 26.4 -
In Exercises 11–34, find the coordinates of the...Ch. 26.4 - Prob. 19ECh. 26.4 -
In Exercises 11–34, find the coordinates of the...Ch. 26.4 - Prob. 21ECh. 26.4 -
In Exercises 11–34, find the coordinates of the...Ch. 26.4 -
In Exercises 11–34, find the coordinates of the...Ch. 26.4 -
In Exercises 11–34, find the coordinates of the...Ch. 26.4 - Prob. 25ECh. 26.4 - Prob. 26ECh. 26.4 - Prob. 27ECh. 26.4 - Prob. 28ECh. 26.4 - Prob. 29ECh. 26.4 -
In Exercises 11–34, find the coordinates of the...Ch. 26.4 - Prob. 31ECh. 26.4 - Prob. 32ECh. 26.4 - Prob. 33ECh. 26.4 - Prob. 34ECh. 26.5 - EXAMPLE 1 Moment of inertia and radius of...Ch. 26.5 - Prob. 1ECh. 26.5 - Prob. 2ECh. 26.5 - Prob. 3ECh. 26.5 - Prob. 4ECh. 26.5 - Prob. 5ECh. 26.5 - Prob. 6ECh. 26.5 - Prob. 7ECh. 26.5 - Prob. 8ECh. 26.5 - Prob. 9ECh. 26.5 - Prob. 10ECh. 26.5 - In Exercises 7–28, find the indicated moment of...Ch. 26.5 - In Exercises 7–28, find the indicated moment of...Ch. 26.5 - Prob. 13ECh. 26.5 - Prob. 14ECh. 26.5 - Prob. 15ECh. 26.5 - In Exercises 7–28, find the indicated moment of...Ch. 26.5 - Prob. 17ECh. 26.5 - Prob. 18ECh. 26.5 - Prob. 19ECh. 26.5 - Prob. 20ECh. 26.5 -
In Exercises 7–28, find the indicated moment of...Ch. 26.5 - Prob. 22ECh. 26.5 - Prob. 23ECh. 26.5 - Prob. 24ECh. 26.5 - Prob. 25ECh. 26.5 - Prob. 26ECh. 26.5 - Prob. 27ECh. 26.5 - Prob. 28ECh. 26.6 - Prob. 1PECh. 26.6 - Prob. 2PECh. 26.6 - Prob. 1ECh. 26.6 - Prob. 2ECh. 26.6 - Prob. 3ECh. 26.6 - Prob. 4ECh. 26.6 - Prob. 5ECh. 26.6 - Prob. 6ECh. 26.6 - An electron has a 1.6 × 10–19 C negative charge....Ch. 26.6 - Prob. 8ECh. 26.6 - Prob. 9ECh. 26.6 - Prob. 10ECh. 26.6 - Prob. 11ECh. 26.6 - Prob. 12ECh. 26.6 - At liftoff, a rocket weighs 32.5 tons, including...Ch. 26.6 - Prob. 14ECh. 26.6 - Prob. 15ECh. 26.6 - Prob. 16ECh. 26.6 - Prob. 17ECh. 26.6 - Prob. 18ECh. 26.6 - Prob. 19ECh. 26.6 - Prob. 20ECh. 26.6 - Prob. 21ECh. 26.6 - Prob. 22ECh. 26.6 - Prob. 23ECh. 26.6 - Prob. 24ECh. 26.6 - Prob. 25ECh. 26.6 - Prob. 26ECh. 26.6 - Prob. 27ECh. 26.6 - Prob. 28ECh. 26.6 - Prob. 29ECh. 26.6 - Prob. 30ECh. 26.6 - Prob. 31ECh. 26.6 - Prob. 32ECh. 26.6 - Prob. 33ECh. 26.6 - Prob. 34ECh. 26.6 - Prob. 35ECh. 26.6 - Prob. 36ECh. 26.6 - Prob. 37ECh. 26.6 - Prob. 38ECh. 26 - Prob. 1RECh. 26 - Prob. 2RECh. 26 - Prob. 3RECh. 26 - Prob. 4RECh. 26 - Prob. 5RECh. 26 - Prob. 6RECh. 26 - Prob. 7RECh. 26 - Prob. 8RECh. 26 - Prob. 9RECh. 26 - Prob. 10RECh. 26 - Prob. 11RECh. 26 - Prob. 12RECh. 26 - Prob. 13RECh. 26 - Prob. 14RECh. 26 - Prob. 15RECh. 26 - Prob. 16RECh. 26 - Prob. 17RECh. 26 - Prob. 18RECh. 26 - Prob. 19RECh. 26 - Prob. 20RECh. 26 - Prob. 21RECh. 26 - Prob. 22RECh. 26 - Prob. 23RECh. 26 - Prob. 24RECh. 26 - Prob. 25RECh. 26 - Prob. 26RECh. 26 - Prob. 27RECh. 26 - Prob. 28RECh. 26 - Prob. 29RECh. 26 - Prob. 30RECh. 26 - Prob. 31RECh. 26 - Prob. 32RECh. 26 - Prob. 33RECh. 26 - Prob. 34RECh. 26 - Prob. 35RECh. 26 - Prob. 36RECh. 26 - Prob. 37RECh. 26 - Prob. 38RECh. 26 - Prob. 39RECh. 26 - Prob. 40RECh. 26 - Prob. 41RECh. 26 - Prob. 42RECh. 26 - Prob. 43RECh. 26 - Prob. 44RECh. 26 - Prob. 45RECh. 26 - Prob. 46RECh. 26 - Prob. 47RECh. 26 - Prob. 48RECh. 26 - Prob. 49RECh. 26 - Prob. 50RECh. 26 - Prob. 51RECh. 26 - Prob. 52RECh. 26 - Prob. 53RECh. 26 - Prob. 54RECh. 26 - Prob. 55RECh. 26 - Prob. 56RECh. 26 - Prob. 57RECh. 26 - Prob. 58RECh. 26 - Prob. 59RECh. 26 - Prob. 60RECh. 26 - Prob. 61RECh. 26 - Prob. 62RECh. 26 - Prob. 63RECh. 26 - Prob. 64RECh. 26 - Prob. 65RECh. 26 - Prob. 1PTCh. 26 - Prob. 2PTCh. 26 - Prob. 3PTCh. 26 - Prob. 4PTCh. 26 - Prob. 5PTCh. 26 - Prob. 6PTCh. 26 - Prob. 7PTCh. 26 - Prob. 8PTCh. 26 - Prob. 9PTCh. 26 - Prob. 10PT
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