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Answer:
Firstly, it is important to note that the multiplication of matrices is done in this way:
Columns x Rows or viceversa
Now, two matrices can be multiplied only if their dimensions are compatible, which means that the number of columns in the first matrix must be equal to the number of rows in the second matrix.
In other words:
Two matrices A and B are said to be multiplies if the number of columns in A coincides with the number of rows in B.
In this context, the correct option is:
Where A is:
And B is:
As you can see, the number of columns in A coincides with the number of rows in B
9514 1404 393
Answer:
about 44.5 feet
Step-by-step explanation:
We can write relations for the height of the rail as a function of initial length and expanded length, but the solution cannot be found algebraically. A graphical solution or iterative solution is possible.
Referring to the figure in the second attachment, we can write a relation between the angle value α and the height of the circular arc as ...
h = c·tan(α) . . . . . . where c = half the initial rail length
Then the length of the expanded rail is ...
s = r(2α) = (c/sin(2α)(2α) . . . . . . where s = half the expanded rail length
Rearranging this last equation, we have ...
sin(2α)/(2α) = c/s
It is this equation that must be solved iteratively. We find the solution to be ...
α ≈ 0.0168538794049 radians
So, the height of the circular arc is ...
h = 2640.5·tan(0.0168538794049) ≈ 44.4984550191 . . . feet
The rail will bow upward by about 44.5 feet.
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<em>Additional comments</em>
Note that s and c in the diagram are half the lengths of the arc and the chord, respectively. The ratio of half-lengths is the same as the ratio of full lengths: c/s = 2640/2640.5 = 5280/5281.
We don't know the precise shape the arc will take, but we suspect is is not a circular arc. It seems likely to be a catenary, or something similar.
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We used Newton's method iteration to refine the estimate of the angle from that shown on the graph. The iterator used is x' = x -f(x)/f'(x), where x' is the next guess based on the previous guess of x. Only a few iterations are required obtain an angle value to full calculator precision.
