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
Lunna [17]
1 year ago
5

Use Newton’s Method to find the solution to x^3+1=2x+3 use x_1=2 and find x_4 accurate to six decimal places. Hint use x^3-2x-2=

0 as your equation.
Mathematics
1 answer:
luda_lava [24]1 year ago
4 0

Let f(x) = x^3 - 2x - 2. Then differentiating, we get

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

We approximate f(x) at x_1=2 with the tangent line,

f(x) \approx f(x_1) + f'(x_1) (x - x_1) = 10x - 18

The x-intercept for this approximation will be our next approximation for the root,

10x - 18 = 0 \implies x_2 = \dfrac95

Repeat this process. Approximate f(x) at x_2 = \frac95.

f(x) \approx f(x_2) + f'(x_2) (x-x_2) = \dfrac{193}{25}x - \dfrac{1708}{125}

Then

\dfrac{193}{25}x - \dfrac{1708}{125} = 0 \implies x_3 = \dfrac{1708}{965}

Once more. Approximate f(x) at x_3.

f(x) \approx f(x_3) + f'(x_3) (x - x_3) = \dfrac{6,889,342}{931,225}x - \dfrac{11,762,638,074}{898,632,125}

Then

\dfrac{6,889,342}{931,225}x - \dfrac{11,762,638,074}{898,632,125} = 0 \\\\ \implies x_4 = \dfrac{5,881,319,037}{3,324,107,515} \approx 1.769292663 \approx \boxed{1.769293}

Compare this to the actual root of f(x), which is approximately <u>1.76929</u>2354, matching up to the first 5 digits after the decimal place.

You might be interested in
What is the value of f(x) when x = 3?
Maksim231197 [3]
It's not specific enough to solve...so far it would only be f(3)
4 0
3 years ago
Given 3 sides of a triangle - how to tell it right, acute, or obtuse 8,11, 16
user100 [1]
Using Pythagorean theorem, we can justify our answer.
if c^2 = a^2 + b^2 then triangle is right one,
if c^2 > a^2 + b^2 then triangle is obtuse and
if c^2 < a^2 + b^2 then triangle is acute triangle.

Here a=8, b=11 and c=16
Put these values in the equation
16^2 = 8 ^2 + 11^2
256 = 64 +121
256> 185
So here c^2 > a^2 + b^2  Which means triangle is obtuse triangle.

Answer: Obtuse Triangle


6 0
3 years ago
Oliver downloaded 15 apps for her phone that altogether, used 2,806 MB of space. If each app used the same amount of space, abou
shepuryov [24]

Step-by-step explanation:

I guess the answer is 187MB

4 0
2 years ago
Find the perimeter of a rectangle that has a length of 2x +7 and a width of 5x.
Harlamova29_29 [7]

Answer:

14x + 14

Step-by-step explanation:

Perimeter = 2( L + W)

2(2x+7 + 5x) = 2(7x + 7)

distributive property

= 14x + 14

3 0
3 years ago
Read 2 more answers
A washer and dryer cost $989 combined. The washer costs $89 more then the dryer. What is the cost of the dryer?
Stells [14]

Answer The washer costs $539.  The dryer cost $450

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
Other questions:
  • I can't solve this please help me
    6·1 answer
  • y2−10y+25=−49 Solve the following quadratic equation by the square root method. If needed, write your answer as a fraction reduc
    13·1 answer
  • Which graph represents the solution for the open sentence 3|p| – 5 &lt; 7.
    5·2 answers
  • After taking a test, mias grade dropped from 85% to 81%
    9·2 answers
  • Please help me please
    12·1 answer
  • Super easy plz answer all for 20 points just adding
    9·1 answer
  • Rewrite 4/10 1/25 as a unit rate <br> 1. 2:125?<br> 2.100.1?<br> 3. 10.1?<br> 4.25.4?
    6·2 answers
  • Y'all I need help asap
    15·1 answer
  • Whats 4 1/5% of 50?Write your answer as a decimal.Make sure your answer is fully reduced.
    10·2 answers
  • I need this answer asap please helppppp
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!