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
horrorfan [7]
2 years ago
13

What is an approximate solution to this equation? 4/x-5=√x+3+2

Mathematics
1 answer:
maw [93]2 years ago
3 0

The approximate solution to the equation \dfrac{4}{x - 5} = \sqrt{x + 3} +2 found using

the Newton-Raphson method is option B.

B. 5.81

<h3>How can the Newton-Raphson method be used?</h3>

The given function is presented as follows;

\dfrac{4}{x - 5} = \mathbf{ \sqrt{x + 3} +2}

Which gives;

\dfrac{4}{x - 5} -2= \sqrt{x + 3}

<em />\left(\dfrac{14-2\cdot x}{x-5} \right)^2 = \sqrt{x+3} ^2 = x+3

\mathbf{\dfrac{4\cdot x^2 - 56 \cdot x + 196}{x^2-10\cdot x + 25}} = x + 3

Therefore;

\mathbf{\dfrac{4\cdot x^2 - 56 \cdot x + 196}{x^2-10\cdot x + 25} - (x + 3)} = 0

\dfrac{- x^3 + 11 \cdot x^2 - 51 \cdot x + 121}{x^2-10\cdot x + 25}  = 0

x³ - 11·x² + 51·x - 121 = 0

Using the Newton Raphson method, with x₀ = 6, we have;

x_1 = x_0- \dfrac{x^3 - 11 \cdot x^2 + 51 \cdot x - 121}{3 \cdot x^2 - 22 \cdot x + 51}

Which gives;

x_1 = 6- \dfrac{6^3 - 11 \times 6^2 + 51 \times 6 - 121}{3 \times 6^2 - 22 \times 6 + 51} \approx \mathbf{ 5.81}

The correct option is <u>B. 5.81</u>

Learn more about the roots polynomial functions here:

brainly.com/question/25956931

You might be interested in
Is the triangle obtuse, acute, equilateral or right?
Stells [14]

9514 1404 393

Answer:

  obtuse

Step-by-step explanation:

The law of cosines tells you ...

  b² = a² +c² -2ac·cos(B)

Substituting for a²+c² using the given equation, we have ...

  b² = b²·cos(B)² -2ac·cos(B)

We can subtract b² to get a quadratic in standard form for cos(B).

  b²·cos(B)² -2ac·cos(B) -b² = 0

Solving this using the quadratic formula gives ...

  \cos(B)=\dfrac{-(-2ac)\pm\sqrt{(-2ac)^2-4(b^2)(-b^2)}}{2b^2}\\\\\cos(B)=\dfrac{ac}{b^2}\pm\sqrt{\left(\dfrac{ac}{b^2}\right)^2+1}

The fraction ac/b² is always positive, so the term on the right (the square root) is always greater than 1. The value of cos(B) cannot be greater than 1, so the only viable value for cos(B) is ...

  \cos(B)=\dfrac{ac}{b^2}-\sqrt{\left(\dfrac{ac}{b^2}\right)^2+1}

The value of the radical is necessarily greater than ac/b², so cos(B) is necessarily negative. When cos(B) < 0, B > 90°. The triangle is obtuse.

4 0
3 years ago
Read 2 more answers
I need help it’s due soon and i need help please also i solved one but i need three solved thanksssss
mel-nik [20]

Answer:

6) b = -13.55

8) p = -1

9) x = 7

4 0
3 years ago
Please help me with this!!
SashulF [63]

Answer:

Step-by-step explanation:

4 0
3 years ago
What is the initial value of the function represented by this table?
klemol [59]

Check the picture below.

7 0
3 years ago
The number of marbles of different colors stored in a hat is listed below:
ivann1987 [24]

Answer:

12.5%

Step-by-step explanation:

I warn you, I'm not positive I'm correct.

First I added 8+10+6 and got 24

I divided that by 3 and got 8

I divided 100 by 8 because if you cross multiply 1/8 and x/100 you would get 8x = 100

100 ÷ 8 = 12.5

So I got 12.5%

5 0
3 years ago
Other questions:
  • 8, Draw a Picture Draw a quadrilateral that has neither line<br> symmetry nor rotational symmetry.
    10·1 answer
  • Your friend Bob makes a triangle out of a pen, a pencil, a small ruler. Using the same three school supplies, you try to make a
    15·1 answer
  • Which is equivalent to 5/9-3/8+(-1/4)+1 4/9+1 5/8
    11·1 answer
  • A musician uploads a music video to the Internet and sends a link to the video to 4 friends. Each friend then sends the link to
    14·2 answers
  • Tomas needs exactly 666 potatoes to make 121212 potato pancakes.
    5·1 answer
  • 6. If Scott Hoff has a balance of $429.50 on a credit card that charges a finance charge computed at 2.5%, what is the
    5·2 answers
  • 3 1/3 + (-2 1/4) + 1 5/6=
    7·1 answer
  • Find the domain and range of the relation.<br> please please help me
    12·1 answer
  • How did Confucianism make an impact on Chinese culture?
    9·2 answers
  • Three vertices of a parallelogram are (0,6), (1,6), and (9,10). Graph the parallelogram.
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!