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SashulF [63]
3 years ago
5

F(x)=x^3+3

Mathematics
1 answer:
lawyer [7]3 years ago
5 0

Answer:

  (a)   -3/4

  (b)  -0.75

  (c)  -0.75

Step-by-step explanation:

It's a bit hard to tell what constitutes an "iteration" when using the bisection method to approximate a polynomial root. For the purpose here, we'll say one iteration consists of ...

  • evaluating the function at the midpoint of the bracketing interval
  • choosing a smaller bracketing interval
  • identifying the x-value known to be closest to the solution

Thus, the result of the iteration consists of a bracketing interval and the choice of one of the interval's ends as the solution approximation.

__

(a) We observe that the graphs intersect in the interval (-1, 0). For the first iteration, we evaluate f(x)-g(x) at x=-1/2. This tells us the solution is in the interval (-1, -1/2). The x-value closest to the root is x=-1/2.

For the second iteration, we evaluate the function f(x)-g(x) at x=-3/4. This tells us the solution is in the interval (-1, -3/4). The x-value closest to the root is x=-3/4.

For the third iteration, we evaluate the function f(x)-g(x) at x=-7/8. This tells us the solution is in the interval (-7/8, -3/4). The x-value closest to the root is x=-3/4.

__

(b) The graph tells us the solution is approximately 0.7549. Rounded to 2 decimal places, the solution is approximately 0.75.

__

(c) The above solution found after 3 iterations rounded to 2 decimal places is exactly 0.75.

__

See the attached table for function values.

_____

<em>Comment on bisection iteration</em>

Since you cut the interval containing the root in half with each iteration, you gain approximately one decimal place for each 3 iterations. When the function value is very nearly zero at one of the interval endpoints, it can take many more iterations to achieve a better result.

Here, it takes 4 more iterations before an x-value becomes closer to the solution (x≈-97/128). And it takes one more iteration to move the end of the interval away from -3/4. After these 5 more iterations (8 total), the solution is known to lie in the interval (-97/128, -193/256). The corresponding solution approximation is -193/256. It is still only correct to 2 decimal places.

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The correct answer is a. In the left-hand column, each number goes up by one. In the right hand column, each number goes up by 1120. Each number on the left can be multiplied by 1120 to get the number on the right.
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Mr. Jimerson records the amount of snowfall that the local area recieves. 12am-1am: 0.3 inches | 1am-2am: 0.8 inches | 2am-3am:
MatroZZZ [7]

Answer:

5.781 inches.

Step-by-step explanation:

Since Mr. Jimerson records the amount of snowfall that the local area recieves, recording the following data: 12 am-1am: 0.3 inches | 1 am-2am: 0.8 inches | 2 am-3am: 1.36 inches | 3 am-4am: 2.019, if the total amount of snowfall at 7am is 7.8 inches, to determine how much snow fell between 4 am-7am the following calculation must be performed:

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Therefore, since the amount of snow accumulated at 7 am was 7.8 inches, the snowfall between 4 and 7 am was 5.781 inches.

6 0
2 years ago
PLEASE HELP!!!!
scZoUnD [109]

Answer:

(D) 1+0.06m

Step-by-step explanation:

Let's say that m=$120

(A)= $127.2

(B)= $127.2

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(D)= $8.2

As you can see after I substituted in 120 for (m) and solved, D is the only equation that did not represent her current balance.

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3 0
3 years ago
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Hey! i’ll give brainliest please help.
xeze [42]
I think the answer is A sorry if I’m wrong
7 0
2 years ago
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ratelena [41]

Answer:

b

Step-by-step explanation:

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3 years ago
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