The function F of v if the actual frequency of sound emitted by the ambulance is 560 H z when an ambulance is moving toward an observer and the frequency of a sound relative to an observer is given by F v = f a s 0 s 0 − v , where f a is the actual frequency of the sound at the source, s 0 is the speed of the sound in air 772.4 mph , and v is the speed at which the source of sound is moving toward the observer.
The function F of v if the actual frequency of sound emitted by the ambulance is 560 H z when an ambulance is moving toward an observer and the frequency of a sound relative to an observer is given by F v = f a s 0 s 0 − v , where f a is the actual frequency of the sound at the source, s 0 is the speed of the sound in air 772.4 mph , and v is the speed at which the source of sound is moving toward the observer.
Solution Summary: The author explains the cost function F of v if the actual frequency of sound emitted by the ambulance is 560Hz.
The function F of v if the actual frequency of sound emitted by the ambulance is 560Hz when an ambulance is moving toward an observer and the frequency of a sound relative to an observer is given by Fv=fas0s0−v , where fa is the actual frequency of the sound at the source, s0 is the speed of the sound in air 772.4mph , and v is the speed at which the source of sound is moving toward the observer.
(b)
To determine
To graph: The sketch of a function given by Fv=560772.4772.4−v on the window 0,1000,100by0,5000,1000 .
(c)
To determine
The effect of the frequency of sound when the speed of the ambulance increases.
A factorization A = PDP 1 is not unique. For A=
7 2
-4 1
1
1
5 0
2
1
one factorization is P =
D=
and P-1
30
=
Use this information with D₁
=
to find a matrix P₁ such that
-
-1 -2
0 3
1
-
- 1
05
A-P,D,P
P1
(Type an integer or simplified fraction for each matrix element.)
Matrix A is factored in the form PDP 1. Use the Diagonalization Theorem to find the eigenvalues of A and a basis for each eigenspace.
30 -1
-
1 0 -1
400
0
0 1
A=
3 4 3
0 1 3
040
3 1 3
0 0
4
1
0
0
003
-1 0 -1
Select the correct choice below and fill in the answer boxes to complete your choice.
(Use a comma to separate vectors as needed.)
A basis for the corresponding eigenspace is {
A. There is one distinct eigenvalue, λ =
B. In ascending order, the two distinct eigenvalues are λ₁
...
=
and 2
=
Bases for the corresponding eigenspaces are {
and ( ), respectively.
C. In ascending order, the three distinct eigenvalues are λ₁ =
=
12/2
=
and 3 = Bases for the corresponding eigenspaces are
{}, }, and {
respectively.
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