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nikklg [1K]
3 years ago
11

Help please I do t have lot of time

Mathematics
1 answer:
lys-0071 [83]3 years ago
4 0
It’s b my good friend
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Ex 7) Imagine a mile-long bar of metal such as the rail along railroad tracks. Suppose that the rail is anchored on both ends an
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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.

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Alayaa crashed her car through a fence, ran over a garbage can and ran into a tree. The fence will cost $550 to repair, $50 to r
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Which equation is equivalent to<br><br> f(x) = 16x4 – 81 = 0?
Vesna [10]

Answer:

The equivalent expression is:

16x^4-81=(4x^2-9)(4x^2+9)

Step-by-step explanation:

We have been given the equation:

f(x)=16x^4-81=0

Equivalent expression can be computed by solving the expression ai its maximum.

We can factorize the given equation:

By using a^2-b^2=(a+b)(a-b)

Here, a=4x^2,b=9

Hence, we get the equation below:

16x^4-81=(4x^2-9)(4x^2+9)

Therefore, the equivalent expression is:

16x^4-81=(4x^2-9)(4x^2+9)

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