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
Enter 52.16 in expanded form.
ivolga24 [154]

Answer:

50 + 2 + 0.1 + 0.06

5 0
3 years ago
Read 2 more answers
I need help with this!
monitta
Eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
5 0
3 years ago
Pls help i will give u brianliest
Fynjy0 [20]

Answer:

Slope = -3

y-intercept = (0,-4)

Equation: y = -3x-4

Step-by-step explanation:

We can take any two input-output pairs from the table to find the equation of given function.

Linear function is given by:

y =mx+b

Here m is the gradient of the functions which is defined as:

m = \frac{rise}{run} = \frac{y_2-y_1}{x_2-x_1}

The input-output pairs are:

(x1,y1) = (-1,-1)

(x2,y2) = (0,-4)

First of all,

m = \frac{-4-(-1)}{0-(-1)}\\= \frac{-4+1}{1} = -3

Putting the value of slope in the equation

y = -3x+b

Putting (-1,-1) in the equation

-1 = -3(-1)+b\\-1 = 3+b\\b = -1-3\\b = -4

The equation will be:

y = -3x-4

Hence,

Slope = -3

y-intercept = (0,-4)

Equation: y = -3x-4

7 0
3 years ago
Jose has $45 to spend at the mall. He buys a toy for $18.63, two candy bars at $0.47 EACH, and a shirt for $12.64 (All prices in
GREYUIT [131]

Answer:

$12.79

Step-by-step explanation:

$45 - $18.63 = $26.37

$26.37 - ($.47 x 2) = $26.37 - $.94 = $25.43

$25.43 - $12.64 = $12.79

6 0
3 years ago
What is Question I (if m&lt;EBF = 117°, fine m&lt;ABE)​
Natasha_Volkova [10]

Answer:

m∠ABE = 27°

Step-by-step explanation:

* Lets look to the figure to solve the problem

- AC is a line

- Ray BF intersects the line AC at B

- Ray BF ⊥ line AC

∴ ∠ABF and ∠CBF are right angles

∴ m∠ABF = m∠CBF = 90°

- Rays BE and BD intersect the line AC at B

∵ m∠ABE = m∠DBE ⇒ have same symbol on the figure

∴ BE is the bisector of angle ABD

∵ m∠EBF = 117°

∵ m∠EBF = m∠ABE + m∠ABF

∵ m∠ABF = 90°

∴ 117° = m∠ABE + 90°

- Subtract 90 from both sides

∴ m∠ABE = 27°

4 0
3 years ago
Read 2 more answers
Other questions:
  • Use an algebraic rule to describe a translation right 4 units and down 2 units.
    12·1 answer
  • A rectangular field is eleven times as long as it is wide. If the perimeter of the field is 1560 feet, what are the dimensions o
    6·1 answer
  • Given the function g(x)=x^2+10x+23g(x)=x
    13·1 answer
  • Which of the following quotients are negative? Check all that apply. 1: 2.2 ÷ 9.5 2:–0.5 ÷ 0.021 3: –1.3 ÷ –54.321 0.4 ÷ –0.4 4:
    13·2 answers
  • An item is regularly priced at $51. Amanda bought it on sale for 85% off the regular price. How much did Amanda pay?
    9·1 answer
  • The overall pass rate for law school graduates taking the Maryland bar exam has been reported as 76%. Assume that a certain Mary
    10·1 answer
  • In a linear equation relating income and consumption, you know that the intercept is $1,000 and the slope of the line is 4. if i
    10·1 answer
  • The cafeteria has 6 round tables and 23 rectangular tables. If each round table has 7 chairs and each rectangular table has 18 c
    14·1 answer
  • A professional football field is 160 feet wide. What is the width of the field in yards? *
    8·1 answer
  • The length of a rectangle is 2 centimeters longer than its width.
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!