One division of a large defense contractor manufactures telecommunication equipment for the military. This division reports that
2 answers:
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<u><em>Answer:</em></u>
The longest bread stick is approximately 16 in
<u><em>Explanation:</em></u>
The diagram representing the tray is shown in the attached image
From the diagram, we can note that the diagonal of the tray represents the hypotenuse of a right-angled triangle having legs 9.5 in and 13 in
<u>Therefore, to get the length of the hypotenuse, we can use the Pythagorean equation which is as follows:</u>
c² = a² + b²
where c is the length of the hypotenuse and a and b are the length of the two legs
<u>Substitute with the givens in the above equation to get the length of the hypotenuse as follows:</u>
c² = (9.5)² + (13)² = 259.25
c = 16.1 in which is approximately 16 in
<u>From the above, we can conclude that:</u>
The longest bread stick that can be fit straight along the diagonal of the tray is approximately 16 in
Hope this helps :)
Answer:
the P matrix you are looking for is P=(1/) · [[1 1 0 0],[1 -1 0 0],[0 0 1 1],[0 0 1 -1]]
Step-by-step explanation:
Answer:
For an orthogonal diagonalization of any matrix you have to:
1º) Find the matrix eigenvalues in a set order.
2º) Find the eigenvectors of each respective eigenvalues.
Tip: You can write the matrix A like A = D P
3º) D is the diagonal matrix with each eigenvalue (in order) in the diagonal.
4º) Write P as the normalized eigenvectors in order (in columns).
Tip 2: Remember, ·P = I, so if A =
D P, then:
P A = P
D P
= I D I = D
So the P we are looking for is the of the diagonalization.
Tip 3: In this case, A is a block matrix with null nondiagonal submatrixes, therefore its eigenvalues can be calculated by using the diagonal submatrixes. The problem is reduced to calculate the eigenvalues of A₁₁ = A ₂₂ = [[5 3],[3 5]]
Solving:
1º)the eigenvalues of A₁₁ are {8,2}, therefore the D matrix is
2º) the eigenvectors of A₁₁ are P₈= {[1 1]T} P₂= {[1 -1]T}, therefore normalizing the eigenvectors you obtain P = (1/) · [[1 1 0 0],[1 -1 0 0],[0 0 1 1],[0 0 1 -1]] (you can see that P =
in this case).
As said in "tip 2": P A = P
D P
= I D I = D
So the P obtained is the one you are looking for.