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Leno4ka [110]
3 years ago
14

Solve this equation using elimination: 4x-y=8;6x+y=2

Mathematics
1 answer:
fomenos3 years ago
7 0
Solve simultaneously.

4x - y = 8
6x + y = 2


Multiply top equation by 6, and bottom equation by 4, to eliminate x, so that we can find y.
~
24x - 6y = 48
24x - 4y = 8

Subtract top from bottom to form one equation.
~
-2y = 40
Therefore y is 20.

Put y back in to an equation, such as 4x - y = 8.
~
4x - 20 = 8
4x = 28
x = 7
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F(x)=x^3+3
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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 ...

  • 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.

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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.

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inna [77]

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Step-by-step explanation:

4 0
3 years ago
Last week Jonas spent 9 1/6 hours working on his homework over a period of 4 2/3 days. Approximately how many hours a day, on av
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The selling price is greater than the buying price of the house by $4,950

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