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Liula [17]
3 years ago
15

-2x+2y=6 7x-8y=-27 what is the solution

Mathematics
1 answer:
navik [9.2K]3 years ago
8 0
-2x+2y=6
7x-8y=-27
5x-6y=-21
-x+y=3
6x-7y=-24
6x-7y=-4(-2x+2y)
6x-7y=8x-8y
-6x from both sides:
-7y=2x-8y
add 8y to both sides:
y=2x
-2x+2y=6
2y-6=2x
2y-6=-12
-6-6=-12
y=-3
x=-6

Hope this helps :)

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F(x)=x^3+3
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Answer:

  (a)   -3/4

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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 ...

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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.

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(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.

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

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

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See the attached table for function values.

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<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.

5 0
3 years ago
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Answer:

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Step-by-step explanation:

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2 years ago
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5 0
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nata0808 [166]
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