1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
sdas [7]
3 years ago
5

Apply Newton’s method to estimate the solution of x3 − x − 1 = 0 by taking x1 = 1 and finding the least n such that xn and xn +

1 agree to three digits after the decimal point.
Mathematics
1 answer:
ss7ja [257]3 years ago
4 0

Solution :

Given

$f(x)=x^3-x-1, x_1=1$

$f'(x)=3x^2-1$

Let the initial approximation is $x_1 =1$

So by Newton's method, we get

$x_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)},n=1,2,...$

$x_2=x_1-\frac{f(x_1)}{f'(x_1)}=1-\frac{1^3-1-1}{3(1)^2-1}=1.5$

$x_3=1.5-\frac{(1.5)^3-1.5-1}{3(1.5)^2-1}=1.34782608$

$x_4=1.34782608-\frac{(1.34782608)^3-1.34782608-1}{3(1.34782608)^2-1}=1.32520039$

$x_5=1.32520039-\frac{(1.32520039)^3-1.32520039-1}{3(1.32520039)^2-1}=1.32471817$

$x_6=1.32471817-\frac{(1.32471817)^3-1.32471817-1}{3(1.32471817)^2-1}=1.32471795$

$x_5 \approx x_6$ are identical up to eight decimal places.

The approximate real root is x ≈ 1.32471795

∴ x = 1.32471795

You might be interested in
Question 1-6
Mumz [18]

i mean ig but 129.... ehh

3 0
3 years ago
Read 2 more answers
A rectangle has side lengths 2x + 3 and 5x - 2.
xz_007 [3.2K]

Answer:

10x² + 11x - 6

Step-by-step explanation:

The area (A) is the product of the sides, that is

A = (2x + 3)(5x - 2) ← expand using FOIL

   = 10x² - 4x + 15x - 6 ← collect like terms

   = 10x² + 11x - 6

5 0
3 years ago
Tommy's wife wants to fence in her circular garden. How many feet of fencing will she need if the diameter of the garden is 16 f
pashok25 [27]

Answer:

C) 16π ft

Step-by-step explanation:

Fencing is perimeter.  The perimeter of a circle is the circumference.

The circumference of a circle is pi time diameter

C= pi*d

We know the diameter is 16

C = 16*pi  ft

We will need 16 pi ft of fencing


4 0
3 years ago
Read 2 more answers
the odds of rolling a certain number on a single die is 1 chance in 6 rolls. in course of a game, someone rolled 3 fives. accord
Zina [86]

Answer:

18

Step-by-step explanation:

The expected value is the probability times the frequency.

3 = 1/6 × n

n = 18

Note: the use of the word "odds" is very misleading here.  Odds are the ratio of number of successes to number of failures:

S / F

Probability is the ratio of number of successes to number of all outcomes:

S / (S + F)

So the probability of rolling a 5 is 1/6.  The odds of rolling a 5 is 1/5.

Furthermore, the word "must" is also incorrect.  The player didn't <em>have</em> to roll 18 times.  They could have rolled three times and gotten a 5 each time.  Or they could have rolled 100 times.  18 is simply the most <em>likely </em>number of rolls needed to get three 5's.

6 0
3 years ago
What value of x is in the solution set of –5x – 15 &gt; 10 + 20x?
Scilla [17]
Hello,

-5x-15>10+20x
==>-15-10>20x+5x
==>-25>25x
==>-1>x
==>x<-1

6 0
3 years ago
Other questions:
  • Emelia earns $8.74 per hour plus a gas allowance of $3.50 per day at her job. How much does Emelia's job pay in a day when she w
    8·1 answer
  • Evaluate the expression a2+6ab for a=−3 and b=4.
    5·1 answer
  • What is the factored form of 6x2 + 13x + 6?
    10·2 answers
  • What does y and z equal. I already got x
    15·1 answer
  • 4x - 3y = 17 5x + 4y = 60
    6·2 answers
  • Factor this polynomial expression.
    6·1 answer
  • If the measure of &lt;1 is 95 degrees what is the measure of &lt;3.​
    13·1 answer
  • To rent a machine for 6 hours, it costs $27. How much will it cost to rent it<br> for 3 hours?
    7·1 answer
  • Find the probability of a choosing a student that is taking a foreign language, given that the student is playing a sport using
    5·1 answer
  • PLEASE HELP ASAP
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!