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nordsb [41]
3 years ago
5

Use Newton's Method to approximate the zero(s) of the function. Continue the iterations until two successive approximations diff

er by less than 0.001. Then find the zero(s) to three decimal places using a graphing utility and compare the results. f(x) = x5 + x − 6
Mathematics
1 answer:
liubo4ka [24]3 years ago
5 0

Answer:

There is only one real zero and it is located at x = 1.359

Step-by-step explanation:

After the 4th iteration the solution was repeating the first 3 decimal places.  The formula for Newton's Method is

x_{n}-\frac{f(x_{n}) }{f'(x_{n}) }

If our function is

f(x)=x^5+x-6

then the first derivative is

f'(x)=5x^4+1

I graphed this on my calculator to see where the zero(s) looked like they might be, and saw there was only one real one, somewhere between 1 and 2.  I started with my first guess being x = 1.

When I plugged in a 1 for x, I got a zero of 5/3.  

Plugging in 5/3 and completing the process again gave me 997/687

Plugging in 997/687 and completing the process again gave me 1.36976

Plugging in 1.36976 and completing the process again gave me 1.359454

Plugging in 1.359454 and completing the process again gave me 1.359304

Since we are looking for accuracy to 3 decimal places, there was no need to go further.

Checking the zeros on the calculator graphing program gave me a zero of 1.3593041 which is exactly the same as my 5th iteration!

Newton's Method is absolutely amazing!!!

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NOT NECESSARILY would a triangle be equilateral if one of its angles is 60 degrees. To be an equilateral triangle (a triangle in which all 3 sides have the same length), all 3 angles of the triangle would have to be 60°-angles; however, the triangle could be a 30°-60°-90° right triangle in which the side opposite the 30 degree angle is one-half as long as the hypotenuse, and the length of the side opposite the 60 degree angle is √3/2 as long as the hypotenuse. Another of possibly many examples would be a triangle with angles of 60°, 40°, and 80° which has opposite sides of lengths 2, 1.4845 (rounded to 4 decimal places), and 2.2743 (rounded to 4 decimal places), respectively, the last two of which were determined by using the Law of Sines: "In any triangle ABC, having sides of length a, b, and c, the following relationships are true: a/sin A = b/sin B = c/sin C."¹

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3 years ago
In circle O below, AB is a diameter and m
Neko [114]

Answer:

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Step-by-step explanation:

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4 0
3 years ago
On the distant plant, Mathology, a sports area covers 7400 yodels2. How many square deckles would this be if 1 deckle = 75.9 yod
STatiana [176]

Answer:

It would be <u>97.50</u> square deckles.

Step-by-step explanation:

Given:

On the distant plant, Mathology, a sports area covers 7400 yodels².

1 deckle = 75.9 yodels.

Now, to get the square deckles.

As given, 1 deckle = 75.9 yodels.

So, to get the square deckles by using conversion factor:

<em>75.9 yodels = 1 deckle.</em>

7400 yodels² = 7400\div 75.9

                       = 97.50\ deckels ^2.

Therefore, it would be 97.50 square deckles.

8 0
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In the right triangle ABC shown, c=17ft and angle A=30 degrees Determine side a
jekas [21]

Using relations in a right triangle, considering c as the hypotenuse, we have that the length of side A is: a = 8.5\sqrt{3}

<h3>What are the relations in a right triangle?</h3>

The relations in a right triangle are given as follows:

  • The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.
  • The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.
  • The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.

From the information given, we can build the following relation:

cos(A) = a/c.

\frac{\sqrt{3}}{2} = \frac{a}{17}

a = \frac{17\sqrt{3}}{2}

a = 8.5\sqrt{3}

More can be learned about relations in a right triangle at brainly.com/question/26396675

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6 0
1 year ago
Jim has 12 colored papers 8 bows 2 different colored markers and 2 envelopes How many different cards can Jim make
ikadub [295]
384 because 12*8=96*2=192*2=384
8 0
3 years ago
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