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nlexa [21]
3 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]3 years ago
6 0

Answer:

[deleted]

Step-by-step explanation:

Masja [62]3 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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Rainbow [258]

Answer:

3

Step-by-step explanation:

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8 0
3 years ago
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The ratio of chicken to vegetables in a soup is 2:3. If there are 9 cups of chicken, how many cups of vegetables are in the soup
zlopas [31]

Answer:

13.5

Step-by-step explanation:

2/3=9/x

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2x=27

x=27÷2

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4 0
3 years ago
ARE YOU GOOD AT GEOMETRY?? WILLING TO HELP SOMEONE OUT?? NEED EASY POINTS AND BRAINLIEST?? COME RIGHT THIS WAY ALL HELP IS APPRE
BlackZzzverrR [31]

Answer:

C: (-8,3) R:5

Step-by-step explanation:

The equation of a circle can be written as:

(x-h)^2+(y-k)^2=r^2

where (h,k) is the center, and r is the radius

We have the equation:

(x+8)^2+(y-3)^2=25

Center:

The center is (-8,3)

(x+8)^2--> (x-h)^2

Therefore the x coordinate of the center is -8

(y-3)^2-->(y-k)^2

Therefore the y coordinate of the center is 3

Radius

r^2=25

Take the square root of both sides

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4 0
3 years ago
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At noon, ship a is 30 nautical miles due west of ship
Dmitry_Shevchenko [17]
Let the origin of the coordinate system be the position of ship B at noon. Then the distance between the ships as a function of t (in hours) is
.. d = √((30 +23t)² +(17t)²)
.. = √(818t² +1380t +900)

The rate of change of distance with respect to time is
.. d' = (1/2)(2*818*t +1380)/√(818t² +1380t +900)
.. = (818t +690)/√(818t² +1380t +900)

At t=4, this is
.. d' = (818*4 +690)/√(818*16 +1380*4 +900)
.. = 3962/√19508
.. ≈ 28.37 . . . . . knots

The distance between the ships is increasing at about 28.37 knots at 4 pm.

8 0
3 years ago
Can someone help please
SIZIF [17.4K]
I believe the answer is B. The y intercept is when x is 0.
5 0
3 years ago
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