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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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NECESITO AYUDA EN ESTOS EJERCIICIOS DE MATES NIVEL SEGUNDO ESO
Kay [80]

Answer: 49/60

Step-by-step explanation:

(1/3+2/5)-1/4-(5/6-7/6)

Primero  (5/6-7/6)

5/6-7/6=-2/6

1/3+2/5-1/4-(-2/6)

1/3+2/5-1/4+2/6

2/6=1/3

1/3+2/5-1/4+1/3

2/3+2/5-1/4

2/3=10/15

2/5=6/15

10/15+6/15-1/4

16/15-1/4

16/15=64/60

1/4=15/60

64/60-15/60=49/60

4 0
3 years ago
10. Express the following as a single fraction.<br> x-1 +x+2 + x<br>2<br>5<br>4<br>​
Margaret [11]

Answer:

x+x+x=3x

2-1=1

3x+1

this is ansver

3 0
2 years ago
Is the GCF (greatest common factor) of a pair of numbers ever equal to one of the numbers? Explain why or why not.
FrozenT [24]

Answer:

Yes

Step-by-step explanation:

Yes, that is possible because whenever one number is a factor of the other one, it's their greatest common factor. Here are some examples.

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