The tortoise versus the hare: The speed of the hare is given by the sinusoidal function H ( t ) = 1 − cos ( ( π t ) / 2 ) whereas the speed of the tortoise is T ( t ) = ( 1 / 2 ) tan − 1 ( t / 4 ) , where t is time measured in hours and the speed is measured in miles per hour. Find the area between the curves from time t = 0 to the first time after one hour when the tortoise and hare are traveling at the same speed. What does it represent? Use a calculator to determine the intersection points, if necessary, accurate to three decimal places.
The tortoise versus the hare: The speed of the hare is given by the sinusoidal function H ( t ) = 1 − cos ( ( π t ) / 2 ) whereas the speed of the tortoise is T ( t ) = ( 1 / 2 ) tan − 1 ( t / 4 ) , where t is time measured in hours and the speed is measured in miles per hour. Find the area between the curves from time t = 0 to the first time after one hour when the tortoise and hare are traveling at the same speed. What does it represent? Use a calculator to determine the intersection points, if necessary, accurate to three decimal places.
The tortoise versus the hare: The speed of the hare is given by the sinusoidal function
H
(
t
)
=
1
−
cos
(
(
π
t
)
/
2
)
whereas the speed of the tortoise is
T
(
t
)
=
(
1
/
2
)
tan
−
1
(
t
/
4
)
, where t is time measured in hours and the speed is measured in miles per hour. Find the area between the curves from time t = 0 to the first time after one hour when the tortoise and hare are traveling at the same speed. What does it represent? Use a calculator to determine the intersection points, if necessary, accurate to three decimal places.
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.
University Calculus: Early Transcendentals (4th Edition)
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Area Between The Curve Problem No 1 - Applications Of Definite Integration - Diploma Maths II; Author: Ekeeda;https://www.youtube.com/watch?v=q3ZU0GnGaxA;License: Standard YouTube License, CC-BY