College Mathematics for Trades and Technologies (10th Edition) (What's New in Trade Math)
10th Edition
ISBN: 9780134690339
Author: Cheryl Cleaves, Margie Hobbs
Publisher: PEARSON
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Chapter 8, Problem 15RE
To determine
To solve: The proportion
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Find the most general real-valued solution to the linear system of differential equations
x(t)
-2
7-730
--8-8
y(t)
=
In the phase plane, this system is best described as a
source/unstable node
sink / stable node
saddle
center point / ellipses
spiral source
spiral sink
☐ none of these
Book: Section 3.5 of Notes on Diffy Qs
1
help (formulas)
help (matrices)
Consider the system of differential equations
dx
8
3
x
Y
dt
4
-- (0) + (1) (음)- (0)
dy
18
y.
dt
For this system, the eigenvalues are help (numbers)
Enter as a comma separated list.
How do the solution curves of the system above behave?
All of the solutions curves would converge towards 0 (sink/stable node).
All of the solution curves would run away from 0 (source/unstable node).
The solution curves would race towards zero and then veer away towards infinity (saddle point).
The solution curves converge to different points.
The solution to the above differential equation with initial values x(0) = 5, y(0) = 3 is
x(t)
=
help (formulas)
y(t)
=
help (formulas)
Book: Section 3.5 of Notes on Diffy Qs
Consider the system of differential equations
Verify that
x'
x,
x(0)
=
x(t) = c1e5t
H
+ Cze³t
[]
is a solution to the system of differential equations for any choice of the constants C1 and C2. Find values of C1 and
C2 that solve the given initial value problem. (According to the uniqueness theorem, you have found the unique
solution of ' = Px, x(0) = 0).
H
e³t
(t) = ( \ ) · e³ {}] + () ·³ [1]
Book: Section 3.3 of Notes on Diffy Qs
help (numbers)
Chapter 8 Solutions
College Mathematics for Trades and Technologies (10th Edition) (What's New in Trade Math)
Ch. 8.1 - Evaluate:
Ch. 8.1 - Prob. 2LCCh. 8.1 - Prob. 1ECh. 8.1 - Prob. 2ECh. 8.1 - Evaluate the formulas.
A = 4πr2 if π = 3.14 and r...Ch. 8.1 - Prob. 4ECh. 8.1 - Prob. 5ECh. 8.1 - Prob. 6ECh. 8.1 - Evaluate the formulas.
CON Evaluate the formula...Ch. 8.1 - Evaluate the formulas.
ELEC Use the formula to...
Ch. 8.1 - Evaluate the formulas.
CAD/ARC Find the length of...Ch. 8.1 - Evaluate the simple interest formula I = PRT using...Ch. 8.1 - Evaluate the simple interest formula I = PRT using...Ch. 8.1 - Evaluate the simple interest formula I = PRT using...Ch. 8.1 - Evaluate the simple interest formula I = PRT using...Ch. 8.1 - Prob. 14ECh. 8.1 - Prob. 15ECh. 8.1 - Prob. 16ECh. 8.1 - Prob. 17ECh. 8.1 - Prob. 18ECh. 8.1 - Prob. 19ECh. 8.1 - Prob. 20ECh. 8.1 - BUS Using the markup formula, M = S − C, find the...Ch. 8.1 - Prob. 22ECh. 8.1 - Using the formula for the side of a square, , find...Ch. 8.1 - Prob. 24ECh. 8.1 - Prob. 25ECh. 8.1 - INDTEC According to Boyle’s law, if temperature is...Ch. 8.1 - Prob. 27ECh. 8.1 - Use the formula to find the number of cylinders...Ch. 8.1 - Prob. 29ECh. 8.1 - Prob. 30ECh. 8.1 - Prob. 31ECh. 8.1 - Prob. 32ECh. 8.1 - Prob. 33ECh. 8.1 - Prob. 34ECh. 8.1 - Rearrange the formulas.
Solve S = C + M for C.
Ch. 8.1 - Rearrange the formulas.
Solve V = πr2k for h.
Ch. 8.1 - Prob. 37ECh. 8.1 - Prob. 38ECh. 8.1 - Prob. 39ECh. 8.1 - Prob. 40ECh. 8.1 - Prob. 41ECh. 8.1 - Rearrange the formulas.
Solve S = 2πrh for h.
Ch. 8.1 - Prob. 43ECh. 8.1 - Prob. 44ECh. 8.1 - Prob. 45ECh. 8.1 - Rearrange the formulas.
Solve for R.
Ch. 8.1 - Prob. 47ECh. 8.1 - Prob. 48ECh. 8.1 - Prob. 49ECh. 8.1 - Prob. 50ECh. 8.2 - Prob. 1LCCh. 8.2 - Prob. 2LCCh. 8.2 - Solve the proportions. Round to four significant...Ch. 8.2 - Prob. 2ECh. 8.2 - Prob. 3ECh. 8.2 - Prob. 4ECh. 8.2 - Prob. 5ECh. 8.2 - Prob. 6ECh. 8.2 - Prob. 7ECh. 8.2 - Prob. 8ECh. 8.2 - Prob. 9ECh. 8.2 - Prob. 10ECh. 8.2 - Prob. 11ECh. 8.2 - Prob. 12ECh. 8.2 - Prob. 13ECh. 8.2 - Prob. 14ECh. 8.2 - Prob. 15ECh. 8.2 - Prob. 16ECh. 8.2 - Prob. 17ECh. 8.2 - Prob. 18ECh. 8.2 - Prob. 19ECh. 8.2 - Prob. 20ECh. 8.2 - Prob. 21ECh. 8.2 - Prob. 22ECh. 8.2 - Prob. 23ECh. 8.2 - Prob. 24ECh. 8.2 - Prob. 25ECh. 8.2 - Prob. 26ECh. 8.2 - Prob. 27ECh. 8.2 - Prob. 28ECh. 8.2 - Prob. 29ECh. 8.2 - Prob. 30ECh. 8.2 - Prob. 31ECh. 8.2 - Prob. 32ECh. 8.2 - Prob. 33ECh. 8.2 - Prob. 34ECh. 8.2 - Prob. 35ECh. 8.2 - Prob. 36ECh. 8.2 - Prob. 37ECh. 8.2 - Prob. 38ECh. 8.2 - Prob. 39ECh. 8.2 - Prob. 40ECh. 8.2 - Prob. 41ECh. 8.2 - Prob. 42ECh. 8.2 - Prob. 43ECh. 8.2 - Prob. 44ECh. 8.2 - Prob. 45ECh. 8.2 - Prob. 46ECh. 8.2 - Prob. 47ECh. 8.2 - Prob. 48ECh. 8.2 - Prob. 49ECh. 8.2 - Prob. 50ECh. 8.2 - Prob. 51ECh. 8.2 - Prob. 52ECh. 8.2 - Prob. 53ECh. 8.2 - Prob. 54ECh. 8.3 - Prob. 1LCCh. 8.3 - Prob. 1ECh. 8.3 - Prob. 2ECh. 8.3 - Solve using proportions. See Example 1.
AUTO A...Ch. 8.3 - Prob. 4ECh. 8.3 - Prob. 5ECh. 8.3 - Prob. 6ECh. 8.3 - Prob. 7ECh. 8.3 - Prob. 8ECh. 8.3 - Prob. 9ECh. 8.3 - Prob. 10ECh. 8.3 - Prob. 11ECh. 8.3 - Prob. 12ECh. 8.3 - Prob. 13ECh. 8.3 - Prob. 14ECh. 8.3 - Prob. 15ECh. 8.3 - Prob. 16ECh. 8.3 - Prob. 17ECh. 8.3 - Prob. 18ECh. 8.3 - Prob. 19ECh. 8.3 - Prob. 20ECh. 8.3 - Prob. 21ECh. 8.3 - Solve using a constant of variation. See Example...Ch. 8.3 - Prob. 23ECh. 8.3 - Prob. 24ECh. 8.3 - Prob. 25ECh. 8.3 - Prob. 26ECh. 8.3 - Prob. 27ECh. 8.3 - Prob. 28ECh. 8.3 - Prob. 29ECh. 8.3 - Prob. 30ECh. 8.3 - Prob. 31ECh. 8.3 - Prob. 32ECh. 8.3 - Prob. 33ECh. 8.3 - Prob. 34ECh. 8.3 - Prob. 35ECh. 8.3 - Prob. 36ECh. 8.3 - Prob. 37ECh. 8.3 - Prob. 38ECh. 8.3 - Prob. 39ECh. 8.3 - Prob. 40ECh. 8.3 - Prob. 41ECh. 8.3 - Prob. 47ECh. 8.3 - Prob. 48ECh. 8.3 - Prob. 49ECh. 8.3 - Prob. 50ECh. 8.3 - Prob. 51ECh. 8.3 - Prob. 52ECh. 8.4 - If it takes 5 hours for 3 workers to load a truck,...Ch. 8.4 - Solve using proportions. See Example 1.
AG/H Two...Ch. 8.4 - Solve using proportions. See Example 1.
INDTR The...Ch. 8.4 - Solve using proportions. See Example...Ch. 8.4 - Prob. 4ECh. 8.4 - Prob. 5ECh. 8.4 - Prob. 6ECh. 8.4 - The fan pulley and alternator pulley are connected...Ch. 8.4 - Prob. 8ECh. 8.4 - Prob. 9ECh. 8.4 - Prob. 10ECh. 8.4 - Prob. 11ECh. 8.4 - Prob. 12ECh. 8.4 - Prob. 13ECh. 8.4 - Prob. 14ECh. 8.4 - Prob. 15ECh. 8.4 - Prob. 16ECh. 8.4 - Prob. 17ECh. 8.4 - Prob. 18ECh. 8.4 - Prob. 19ECh. 8.4 - Prob. 20ECh. 8.4 - Prob. 21ECh. 8.4 - Prob. 22ECh. 8.4 - Prob. 23ECh. 8.4 - Prob. 24ECh. 8.4 - Prob. 25ECh. 8.4 - Prob. 26ECh. 8.4 - Prob. 27ECh. 8.4 - Prob. 28ECh. 8.4 - Prob. 29ECh. 8.4 - Prob. 30ECh. 8.4 - Prob. 31ECh. 8.4 - Prob. 32ECh. 8.4 - Prob. 33ECh. 8.4 - Prob. 34ECh. 8.4 - Prob. 35ECh. 8.4 - Prob. 36ECh. 8.4 - Prob. 37ECh. 8.4 - Prob. 38ECh. 8 - Prob. 1RECh. 8 - PFIN Find the rate if I = $2,484, P = $4,600, and...Ch. 8 - Prob. 3RECh. 8 - Prob. 4RECh. 8 - Prob. 5RECh. 8 - Prob. 6RECh. 8 - Prob. 7RECh. 8 - Prob. 8RECh. 8 - Prob. 9RECh. 8 - Prob. 10RECh. 8 - Prob. 11RECh. 8 - Prob. 12RECh. 8 - Prob. 13RECh. 8 - Prob. 14RECh. 8 - Prob. 15RECh. 8 - Prob. 16RECh. 8 - Prob. 17RECh. 8 - Prob. 18RECh. 8 - Prob. 19RECh. 8 - Prob. 20RECh. 8 - Prob. 21RECh. 8 - Prob. 22RECh. 8 - Prob. 23RECh. 8 - Prob. 24RECh. 8 - Prob. 25RECh. 8 - Prob. 26RECh. 8 - Prob. 27RECh. 8 - Prob. 28RECh. 8 - Prob. 29RECh. 8 - Prob. 30RECh. 8 - Prob. 31RECh. 8 - Prob. 32RECh. 8 - Prob. 33RECh. 8 - Prob. 34RECh. 8 - Prob. 35RECh. 8 - Prob. 36RECh. 8 - Prob. 37RECh. 8 - Prob. 38RECh. 8 - Prob. 39RECh. 8 - Prob. 40RECh. 8 - Prob. 41RECh. 8 - Prob. 42RECh. 8 - Prob. 43RECh. 8 - Prob. 44RECh. 8 - Prob. 45RECh. 8 - Prob. 46RECh. 8 - Prob. 47RECh. 8 - Prob. 48RECh. 8 - Prob. 49RECh. 8 - Prob. 50RECh. 8 - Prob. 51RECh. 8 - Prob. 52RECh. 8 - Prob. 1CACh. 8 - Prob. 2CACh. 8 - Prob. 3CACh. 8 - Prob. 4CACh. 8 - Prob. 5CACh. 8 - Prob. 6CACh. 8 - Prob. 7CACh. 8 - Prob. 8CACh. 8 - Prob. 9CACh. 8 - Prob. 10CACh. 8 - Prob. 1PTCh. 8 - The formula for the volume (V) of a solid...Ch. 8 - Prob. 3PTCh. 8 - Prob. 4PTCh. 8 - Prob. 5PTCh. 8 - Prob. 6PTCh. 8 - Prob. 7PTCh. 8 - Prob. 8PTCh. 8 - Prob. 9PTCh. 8 - Prob. 10PTCh. 8 - Prob. 11PTCh. 8 - Prob. 12PTCh. 8 - Prob. 13PTCh. 8 - Prob. 14PTCh. 8 - Prob. 15PTCh. 8 - Prob. 16PTCh. 8 - Prob. 17PTCh. 8 - Prob. 18PTCh. 8 - Prob. 19PTCh. 8 - Prob. 20PTCh. 8 - Prob. 21PTCh. 8 - Prob. 22PTCh. 8 - Prob. 23PTCh. 8 - Prob. 24PTCh. 8 - Prob. 25PTCh. 8 - Prob. 26PT
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- Find the most general real-valued solution to the linear system of differential equations [5 -6 x = -10|| x(t) [*] [B] • [8] = C1 y(t) In the phase plane, this system is best described as a source/unstable node O sink / stable node saddle center point / ellipses spiral source spiral sink none of these Book: Section 3.5 of Notes on Diffy Qs help (formulas) help (matrices)arrow_forwardConsider the system of higher order differential equations y″ = t¯¹y' + 7y – tz + (sint)z' + e5t, z" = y — 3z'. Rewrite the given system of two second order differential equations as a system of four first order linear differential equations of the form ÿ' = P(t)ÿ+ g(t). Use the following change of variables y' [Y] Y1 Y2 Y3 LY4_ help (formulas) help (matrices) Book: Section 3.3 of Notes on Diffy Qs [y1(t)] [ y(t)] Y2(t) y' (t) ÿ(t) = = Y3(t) z(t) Y₁(t)] [z'(t)]arrow_forwardCalculate the eigenvalues of this matrix: [21 12 A 24 -21 You'll probably want to use a calculator or computer to estimate the roots of the polynomial that defines the eigenvalues. The system has two real eigenvalues 1 and 2 where \1<\2 smaller eigenvalue \1 = help (numbers) associated eigenvector v1 larger eigenvalue 2 = = help (matrices) help (numbers) associated eigenvector v2 If x' = = B help (matrices) A is a differential equation, how do the solution curves behave? A. The solution curves diverge from different points on parallel paths. B. The solution curves would race towards zero and then veer away towards infinity. (saddle point) C. The solution curves converge to different points on parallel paths. D. All of the solution curves would run away from 0. (source / unstable node) E. All of the solutions curves would converge towards 0. (sink / stable node) Book: Section 3.5 of Notes on Diffy Qsarrow_forward
- Suppose x = C1e2t [x(0)] Ly(0). Find C1 and C2. H == + C₂et [ - C1 = help (numbers) C₂ = help (numbers) 3 5 2 1 -3 -2 -1 2 3 -1 -2 -3 A 5 * x = Sketch the phase plane trajectory that satisfies the given initial condition. Which graph most closely resembles the graph you drew? Choose ✰ Is the solution curve headed toward or away from the origin as t increases? A. toward B. away C. neither toward nor away -3 N -1 3 2 1 -1 -2 -3 Book: Section 3.5 of Notes on Diffy Qs 0 3 5 2 1 -3 -2 -1 -1 -2 -3 - B 3 2 2 1 3 x * x * х 2 3 -3 -2 -1 2 3 -1 -2 -3 Darrow_forwardShow that 2et |x(t) = is a solution to the system of linear homogeneous differential equations x'₁ = 2x1 + x2 x3, x2 = x1 + x2 + 2x3, x3 = x = x1 + 2x2 x3. Find the value of each term in the equation x1 order given.) = 2x1 x2 x3 in terms of the variable t. (Enter the terms in the ☐ = 0 + 0 + ☐ help (formulas) Find the value of each term in the equation x 2 = x1 + x2+2x3 terms of the variable t. (Enter the terms in the order given.) ☐ = 0 + 0 + help (formulas) Find the value of each term in the equation x3 = x1 + 2x2 + x3 in terms of the variable t. (Enter the terms in the order given.) ☐ = 0 + 0 + ☐ help (formulas) Book: Section 3.3 of Notes on Diffy Qsarrow_forwardLet P-L 1 2e3t+8e- = t 15 +], x2(t) = [3e³t + 20e-t -8e³t + 2e-t -12e³t +5e-t P by evaluating derivatives and the matrix product 1(t) = = Show that 1(t) is a solution to the system ' = #³½ (t) = [ 15 9 1(t) Enter your answers in terms of the variable t. [8]·[8] help (formulas) help (matrices) Show that 2(t) is a solution to the system ' = P by evaluating derivatives and the matrix product Enter your answers in terms of the variable t. [8]-[8] help (formulas) help (matrices) Book: Section 3.3 of Notes on Diffy Qs 9 코일(t)= [15-3]교2(t)arrow_forward
- Find the most general real-valued solution to the linear system of differential equations x [✓] - [2 -25 = 2 7-8-8 In the phase plane, this system is best described as a source/unstable node O sink / stable node saddle center point / ellipses spiral source spiral sink none of these Book: Section 3.5 of Notes on Diffy Qs help (formulas) help (matrices)arrow_forwardLet Find A' (t) = A" (t) = = In(|t|)] A(t) = 4-t e2t 0 11 t help (formulas) help (matrices) 2e2t help (formulas) help (matrices) A(t) is defined for all t in the interval(s) help (intervals) A'(t) is defined for all t in the interval(s) A" (t) is defined for all t in the interval(s) Book: Section 3.3 of Notes on Diffy Qs help (intervals) help (intervals)arrow_forwardAnswer the boxes and box the answers if possible list the answers and answer it.arrow_forward
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