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nlexa [21]
2 years ago
15

Consider the following equations. f(x)= x^3 +3x^2 -2x+1 g(x)= x^2-5x+4 Approximate the solution to the equation f(x) = g(x) usin

g three iterations of successive approximation.
A. x =11/16

B. x=13/16

C. x=3/8

D. x= 7/8

Mathematics
2 answers:
Mashcka [7]2 years ago
6 0

Answer:

[deleted]

Step-by-step explanation:

Masja [62]2 years ago
5 0

Answer:

A. x = 11/16

Step-by-step explanation:

For the purpose here, it is convenient to rearrange the equation to f(x) -g(x) = 0. We know the root will be in the interval [0, 1] because (f-g)(0) = -3 and (f-g)(1) = +3. At each iteration, we evaluate (f-g)(x) at the midpoint of the interval to see which of the interval end points can be moved and still bracket the root.

Using the bisection method starting with the interval [0, 1] we find f(1/2)-g(1/2) < 0, so we can move the interval limits to [1/2, 1].

For the next iteration, we find f(3/4) -g(3/4) > 0, so we can move the interval limits to [1/2, 3/4].

For the third iteration, we find f(5/8) -g(5/8) < 0, so we can move the interval limits to [5/8, 3/4].

Then the root is approximately the middle of that interval:

x ≈ (5/8 +3/4)/2 = 11/16

_____

This value of x is 0.6875. The root is closer to 0.639802004233. The bisection method takes about 3 iterations for each decimal place of accuracy. Other methods can nearly double the number of accurate decimal places on each iteration.

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iogann1982 [59]

Answer:

D is the right one

Step-by-step explanation:

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Citrus2011 [14]

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2 years ago
If 75% of a number is 15, 15% of that number
natta225 [31]

Answer:

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2 years ago
Solve for y Please help I need a tip
Gwar [14]

Answer:

y = 4

Step-by-step explanation:

Step 1: Write equation

9/4y - 12 = 1/4y - 4

Step 2: Solve for <em>y</em>

  1. Subtract 1/4y on both sides: 8/4y - 12 = -4
  2. Simplify: 2y - 12 = -4
  3. Add 12 to both sides: 2y = 8
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Step 3: Check

<em>Plug in x to verify it's a solution.</em>

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2 years ago
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