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
serg [7]
2 years ago
9

Use the Newton-Raphson method to find the root of the equation f(x) = In(3x) + 5x2, using an initial guess of x = 0.5 and a stop

ping criterion of &= 0.1%. Report your answer to 3 decimal places. What is the estimate for the root? What is the approximate relative error? %
Mathematics
1 answer:
xxMikexx [17]2 years ago
7 0

Answer with explanation:

The equation which we have to solve by Newton-Raphson Method is,

 f(x)=log (3 x) +5 x²

f'(x)=\frac{1}{3x}+10 x

Initial Guess =0.5

Formula to find Iteration by Newton-Raphson method

  x_{n+1}=x_{n}-\frac{f(x_{n})}{f'(x_{n})}\\\\x_{1}=x_{0}-\frac{f(x_{0})}{f'(x_{0})}\\\\ x_{1}=0.5-\frac{\log(1.5)+1.25}{\frac{1}{1.5}+10 \times 0.5}\\\\x_{1}=0.5- \frac{0.1760+1.25}{0.67+5}\\\\x_{1}=0.5-\frac{1.426}{5.67}\\\\x_{1}=0.5-0.25149\\\\x_{1}=0.248

x_{2}=0.248-\frac{\log(0.744)+0.30752}{\frac{1}{0.744}+10 \times 0.248}\\\\x_{2}=0.248- \frac{-0.128+0.30752}{1.35+2.48}\\\\x_{2}=0.248-\frac{0.17952}{3.83}\\\\x_{2}=0.248-0.0468\\\\x_{2}=0.2012

x_{3}=0.2012-\frac{\log(0.6036)+0.2024072}{\frac{1}{0.6036}+10 \times 0.2012}\\\\x_{3}=0.2012- \frac{-0.2192+0.2025}{1.6567+2.012}\\\\x_{3}=0.2012-\frac{-0.0167}{3.6687}\\\\x_{3}=0.2012+0.0045\\\\x_{3}=0.2057

x_{4}=0.2057-\frac{\log(0.6171)+0.21156}{\frac{1}{0.6171}+10 \times 0.2057}\\\\x_{4}=0.2057- \frac{-0.2096+0.21156}{1.6204+2.057}\\\\x_{4}=0.2057-\frac{0.0019}{3.6774}\\\\x_{4}=0.2057-0.0005\\\\x_{4}=0.2052

So, root of the equation =0.205 (Approx)

Approximate relative error

                =\frac{\text{Actual value}}{\text{Given Value}}\\\\=\frac{0.205}{0.5}\\\\=0.41

 Approximate relative error in terms of Percentage

   =0.41 × 100

   = 41 %

You might be interested in
Which number line can be used to find the distance between (4, –1) and (8, –1)
podryga [215]

Answer:

The distance between the two points is 4

Step-by-step explanation:

(8, -1) - (4, -1) is 4, so I’d say the answer is four.

5 0
3 years ago
Can someone help me match these
zavuch27 [327]

1. x^2 + y^2 - 4x + 12y - 20 = 0 ---- (x-2)^2 + (y+6)^2 = 60

3. 3x^2+ 3y^2 + 12x +18y - 15 = 0 --- (x+2)^2 + (y+3)^2 = 18

5. 2x^2 + 2y^2 - 24x - 16y - 8 = 0 --- (x-6)^2 + (y-4)^2 = 56

I don't know the other two, hope I helped though.

8 0
2 years ago
Solve the equation. <br><br> 2x+4+8x=24
Rasek [7]

2x + 4 + 8x = 24

2x + 8x = 24 - 4

10x = 20

x = 20 ÷ 10

x = 2

____

Hope it helps!

꧁✿ ᴿᴬᴵᴺᴮᴼᵂˢᴬᴸᵀ2222 ✬꧂ ❤

3 0
2 years ago
Read 2 more answers
Need help plz plz thx
Vera_Pavlovna [14]
The answer is D. To solve 3/5 ÷ 4/7 you would change it to 3/5 × 7/4.
5 0
3 years ago
Point K is on line segment JL. Given JK = 2x – 2, KL
Scorpion4ik [409]

Answer:

KL = 10

Step-by-step explanation:

JK + KL = JL

2x – 2 + x – 9 =  2x + 8

Combine like terms

3x -11 = 2x+8

Subtract 2x from each side

3x-2x -11 = 2x+8-2x

x-11 = 8

Add 11 to each side

x-11+11 = 8+11

x = 19

KL = x – 9

     = 19-9

     = 10

8 0
3 years ago
Other questions:
  • What type of research relies on the researcher's first-hand observations of participants in naturally occurring contexts?
    8·1 answer
  • Please answer asap, i need to turn it in by the end of the day.
    7·1 answer
  • What's the prime factorization of 180 &amp; how do I explain it in exponential form ???
    14·1 answer
  • The slope of TX is 2/7 and
    6·1 answer
  • A scatter plot is made to model the amount of money left to pay on a car loan. The data used for the scatter plot are shown in t
    12·2 answers
  • Find the slope of (-14, -1),(-5,5)
    10·1 answer
  • 19. Students at a certain school can enroll in one elective course: painting, theater, choir, or band. This two-way frequency
    14·1 answer
  • Karen picked apples at the Carter Apple Orchard this weekend. She made a graph to show how many apples she picked.
    13·2 answers
  • X=2 And x+3^2 I do not understand
    7·1 answer
  • PPPPPLLLLLLZZZZZZZ HEEEELLP
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!