Using Newton-Raphson method to find the approximate root of the equation x log_{10}x=1.2
( Carry out three iterations ). [tex] \\ \\ [/tex]
Thank uh!

Answers

Answer 1

Answer:

[tex]x \approx 2.740646096[/tex]

Step-by-step explanation:

Given:

[tex]x\log_{10}x=1.2[/tex]

Rewrite so that it's equal to zero:

[tex]\implies x\log_{10}x-1.2=0[/tex]

Therefore:

[tex]\implies f(x)=x\log_{10}(x)-1.2[/tex]

Differentiate the function:

Use the product rule to differentiate [tex]x\log_{10}(x)[/tex]:

[tex]\textsf{Let }u=x \implies \dfrac{du}{dx}=1[/tex]

[tex]\textsf{Let }v=\log_{10}(x) \implies \dfrac{dv}{dx}=\dfrac{1}{x \ln 10}[/tex]

[tex]\begin{aligned}\implies \dfrac{dy}{dx} & = u\dfrac{dv}{dx}+v \dfrac{du}{dx}\\& = \dfrac{x}{x \ln 10}+\log_{10}(x)\\& = \dfrac{1}{\ln 10}+\log_{10}(x)\end{aligned}[/tex]

[tex]\implies f'(x)=\dfrac{1}{\ln 10}+\log_{10}(x)[/tex]

[tex]\implies f'(x)=\dfrac{1+\ln 10 \log_{10}(x)}{\ln 10}[/tex]

Newton-Rhapson iteration formula

[tex]x_{n+1}=x_n-\dfrac{f(x_n)}{f'(x_n)}[/tex]

Substitute the function and its derivative into the formula, replacing x with [tex]x_n[/tex]:

[tex]\implies x_{n+1}=x_n-\dfrac{x_n\log_{10}(x_n)-1.2}{\dfrac{1+\ln 10 \log_{10}(x)}{\ln 10}}[/tex]

[tex]\implies x_{n+1}=x_n-\dfrac{x_n\ln 10\log_{10}(x_n)-1.2\ln 10}{1+\ln 10 \log_{10}(x_n)}[/tex]

Therefore, the iteration formula is:

[tex]x_{n+1}=x_n-\dfrac{x_n\ln 10\log_{10}(x_n)-1.2\ln 10}{1+\ln 10 \log_{10}(x_n)}[/tex]

Let [tex]x_0=3[/tex]

Substitute this into the formula and carry out 3 iterations:

[tex]\implies x_{1}=3-\dfrac{3\ln 10\log_{10}(3)-1.2\ln 10}{1+\ln 10 \log_{10}(3)}=2.746149035[/tex]

[tex]\implies x_2=2.740648841[/tex]

[tex]\implies x_3= 2.740646096[/tex]


Related Questions

What is the value of StartFraction 6 Over x EndFraction + 2x2, when x = 3?

Answers

D. 20
(6/X) + 2x^2 =
(6/3) + 2(3^2) =
2 + 2(9) =
2 + 18=
20

Answer:

D) 20

Step-by-step explanation:

Hope It Helps!!!

PLEASE HELP ME, I BEG OF YOU TO HAVE MERCY ON MY POOR SOUL
1. Calculate the slope of the trend line. (Choose two points on the line and find vertical change over horizontal change.)

2. Using the slope and y-intercept, write the equation of the trend line (y = mx + b).

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4. Search for an item in a fast food menu having the same number of fat calories as the one you chose above. (If you cannot find the exact value, get as close as you can.) Compare the calculated value from step VI to this actual value. Explain why (or why not) you would have expected your prediction (calculated value) to be close to the actual value.

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The regression line is y = 10x + 300, and the value of calories is 90 and when x = 14 the value of y = 440 from the regression line, but the actual value is 330.

What is the line of best fit?

A mathematical notion called the line of the best fit connects points spread throughout a graph.

It's a kind of linear regression that uses scatter data to figure out the best way to define the dot's relationship.

From the data given, we can write the slope and y-intercept form:

y = mx + b

here, m = 10 and b = 300

y = 10x + 300

The number of fat grams in an item has that number of fat calories.

As we have the regression line:

y = 10x + 300

Put x = 1 in the regression line:

y = 10(1) + 300

y = 310 calories

For x = 14

y = 10(14) + 300 = 440

But the actual value from the graph is 330.

Thus, the regression line is y = 10x + 300, and the value of calories is 90 and when x = 14 the value of y = 440 from the regression line, but the actual value is 330.

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dentify the method that will be used in solving for x.

5 + x = three-fourths
distributive property
multiplication property of equality
division property of equality
subtraction property of equality

Answers

Answer:

I believe you're trying to say 5+x= 3/4


A ship is carrying gold bars and silver bars in the ratio 13:17. The ship's load
weighs 600 kg in total. If each bar weighs 5 kg, how many gold bars is the
ship carrying

Answers

Using proportions, considering the weight of each bar and the ratio, it is found that the ship is carrying 52 gold bars.

What is a proportion?

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

Each bar weighs 5 kg, and the total weight is of 600 kg, hence the number of bars is given by:

n = 600/5 = 120.

The proportion of gold bars is given by:

p = 13/(13 + 17) = 13/30

Hence, out of 120 bars, the number of gold bars is given by:

nG = 120 x 13/30 = 4 x 13 = 52.

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2
Select the correct answer.
What is the solution to the equation?
3+√3x5 = x
O A.
-2 and -7
OB.
2 and 7
O C.
-2
OD. 7

Answers

The solution to the equation is x = 7 , -2 , Option C and D is the right answer.

What is an Equation ?

An equation is a mathematical statement formed when two algebraic expression are equated by an equal sign.

It is given that the equation is

[tex]\rm 3 +\sqrt{3x - 5}= x[/tex]

Taking square on both sides

3x-5 = (x-3)²

3x-5 = x² +9 -6x

x² -9x -14 = 0

x² -7x +2x -14 = 0

x(x-7) +2(x-7) = 0

(x-7)(x+2) = 0

x =7 , x = -2

Therefore the solution to the equation is x = 7 , -2 , Option C and D is the right answer.

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A child’s building set contains a brick with dimensions 63 x 31 x 18mm . Assume this brick is a replica of a real brick that has a greatest side length of 23 cm, determine the surface area and volume of the real brick. (Please can someone help me )​

Answers

The surface area and volume of the real brick will be 983.2 cm²and 1738.11 cm³ respectively.

What is volume?

The term “volume” refers to the amount of three-dimensional space taken up by an item or a closed surface. It is denoted by V and its SI unit is in cubic cm.

The scale factor is ;

r = 630 cm /23

r = 27

L = 23 cm

b = 310 / 27 = 11.48 cm

h = 180/27 = 6.6 cm

The surface area of the brick;

A = 2(lb+bh+hl)

A = 2( 23 ×11.48+11.48×6.6+6.6×23)

A= 983.2 cm²

The volume of the brick is;

V= lbh

V=23 × 11.45 ×6.6

V=1738.11 cm³

Hence the surface area and volume of the real brick will be 983.2 cm² and 1738.11 cm³ respectively.

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PLEASE IM GONNA CRY MAY GOD BLESS YOU IF YOU WILL ANSWER DONT JOKE

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Good day my friendly person, I am sorry to inform you that I will not be able to provide an answer because the picture is simply too blurry.
U should make a new one if you want someone to help it’s way blurry sorry I couldn’t give u the answer! Have a great day or night

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Answer:

42.3cm

Step-by-step explanation:

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Answers

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Answer:

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Step-by-step explanation:

The solution is in the picture above...

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B.

Step-by-step explanation:

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C

Step-by-step explanation:

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What is the measure of the unknown angle?

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48°
49°
51°
53°

Answers

The answer would be 48 because a straight line has an angle of 180 so
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How many gold medals the team won?
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Answers

Answer:

The team won 144 gold medals

Step-by-step explanation:

A fraction tells us how many parts of a whole we have

144 / 360 translated into words is 144 out of 360

144 is the part and the 360 is the whole (total)

We want to identity the amount of gold medals the team won had 360 opportunity medals and have 144 of them.

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Who wants to solve a question.

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Answer:

Step-by-step explanation:

5(p-3)

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Bailey and julie go running during their lunch break. bailey ran x miles while julie ran 3x miles. what information can we gather about the relationship between the number of miles bailey and julie ran?

Answers

The information we can see from the given data is that the speed of Julie is three times the speed of Bailey.

What is speed?

Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance.

Given that:-

Bailey and Julie go running during their lunch break. bailey ran x miles while Julie ran 3x miles.

The speed of Bailey = x miles

The speed of the Julie = 3x miles

The ratio of the speeds will be given as:-

J / B = 3x / x

J / B = 3

J = 3 B

Therefore information we can see from the given data is that the speed of Julie is three times the speed of Bailey.

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The length of a rectangle is 8 cm more than four times the width. If the perimeter of the rectangle is 46 cm, what are the dimensions? ​

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Answer:

length = 20 cm

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Step-by-step explanation:

Yuki wants to make a reduced-size copy
of a drawing. The original drawing is
14 inches long. Yuki's copier can only
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hundredth of an inch.

Answers

the answer is about 4.43 because by taking 75 percent each time, you are multiplying the already reduced drawing by 25 percent or keeping 75 percent. therefore the equation is 14 * 0.75^4 which leads to 4.43. This is a model for exponential growth

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Group of answer choices

There will be no change to the graph because the exponential portion of the function remains the same.

The y-intercept is 22 spaces higher.

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All input values are moved 22 spaces to the right.

Answers

Answer:

The y-intercept is 22 spaces higher.

Step-by-step explanation:

A circle with the equation (x + 6)2 + (y + 3)2 = 16 is reflected over the line x = 2.

What is the equation of the image?

( x + 10) 2 + ( y + 3) 2 = 16
( x - 10) 2 + ( y + 3) 2 = 16
( x + 6) 2 + ( y + 7) 2 = 16
( x + 6) 2 + ( y - 7) 2 = 16

Answers

Answer: [tex](x-10)^{2}+(y+3)^{2}=16[/tex]

Step-by-step explanation:

We know the center of the original circle is (-6, -3). After reflecting this over the line x=2, the new center is now (10, -3).

Thus, the equation of the circle is [tex](x-10)^{2}+(y+3)^{2}=16[/tex].

Peter gave away 5/12 of his marbles and had 70 left how many marbles he had at first

Answers

Answer:

There were 120 marbles to start

Step-by-step explanation:

Let x be the number of marbles at the start

x* 5/12 = number of marbles given away

1 -5/12 = 7/12 = fraction of marbles left

x * 7/12 = number of marbles left

x * 7/12 = 70

Multiply each side by 12/7

x *7/12 * 12/7 = 70 * 12/7

x =120

There were 120 marbles to start

Where would 1.84 be on a number line?

Answers

Answer:

It is located to the right of the 0 on the line,

Step-by-step explanation:

the numbers are increasing going from left to right. 1.84 is located 1.84 from 0.

On a number line (which we will presume to be whole integers), 1.84 would be located definitely to the right of 0 because it is a positive decimal. In terms of full numbers, however, 1.84 would be located between integers 1 and 2, and it would be skewed closer to 2. Why? Well, 1.50 is representative of what would be considered halfway between 1 and 2. Because 1.84 is greater than 1.50, we know that 1.84 will be closer to 2 than it will be to 1. In terms of a widespread number line, between integers 1 - 10, 1.84 would be near the beginning, or further left side, of the number line because it is more than 1 but less than 2.

Your final answer: As far as a general number line, 1.84 will be located between 1 and 2, where it is skewed right more toward 2 than 1.

A car travels a distance of 300 miles along a straight road from point A to point B. The car maintains a speed of 30 miles pr
hour (mph) during the first 150 miles and a speed of 50 mph during the remaining 150 miles. What is the average speed of
car for the whole trip?
O20.0 mph
37.5 mph
40.0 mph
O45.0 mph
O80.0 mph
Click Save and Submit to save and submit. Click Save All Answers to save all answers.

Answers

Answer:

Definition: The average speed over the course of mobion can be calculated using the formula Total Distance Traveled Average Speed = Time of Travel A car fravels a distance of 300 miles along a straight road from point A to point B. The car maintains a speed of 30 miles per hour (mph) during the first 150 miles and a speed of 50 mph during the remaining 150 miles. What is the average speed of the car for the whole trip? 20.0 mph 37.5 mph 40.0 mph 45.0 mph 80.0 mph QUESTION 13 Wriat is the height h, of the equilateral triangle shown below? Aak Sareend Sabmit ro save and submit. Click Save AlAnseers to save all ansuers Save

Average speed of the whole trip is equals to 37.5 mph.

What is average speed?

" Average speed is defined as the ratio of the total distance travelled to the total time taken."

Formula used

Average speed = [tex]\frac{Total distance travelled }{Total time taken}[/tex]

According to the question,

Total distance travelled = 300miles

Speed for first 150 miles = 30 miles per hour

For,  30  miles = 1hour

    ⇒150 miles = 5 hours

Speed for remaining 150 miles = 50 miles per hour

For,  50  miles = 1hour

    ⇒150 miles = 3 hours

Substitute the value in the formula to get average speed,

Average speed = [tex]\frac{300miles}{(5 + 3)hours}[/tex]

                          [tex]=\frac{300}{8}\\ \\= 37.5 miles per hour[/tex]

Hence, average speed of the whole trip is equals to 37.5 mph.

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A sample has a sample proportion of 0.3 . Which sample size will produce the
widest 95% confidence interval when estimating the population parameter?

Answers

Answer: A 100

I did the text the other day

A sample size of 50 will produce the widest 95% confidence interval when estimating the population parameter.

What is Statistics?

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

To produce the widest confidence interval, we need to choose the smallest sample size.

This is because as the sample size decreases, the margin of error increases, leading to a wider confidence interval.

Among the given options, the smallest sample size is 50.

Therefore, selecting a sample size of 50 will produce the widest 95% confidence interval when estimating the population parameter.

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Help ASAP, with a explanation :)

Answers

C is due north I think not sure

rewrite to solve for y
12y+d=-19y+t

Answers

When we say to solve for something

 ⇒ essentially move everything to one side

    ⇒ and that 'something' to the other

In this case:

 ⇒ we need to move the y-variable by itself to one side

   ⇒ and everything else to the other

Let's apply that principle:

 [tex]12y+d=-19y+t\\12y+19y=t-d\\31y=t-d\\y=\frac{t-d}{31}[/tex]

   

Answer: (t-d) / 31

Hope that helps!

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Answer:

this right here

Step-by-step explanation:

31y=t-d

The total number of degrees in the center is 360°. if all five vertex angles meeting at the center are congruent, what is the measure of a base angle of one of the triangles? 54° 72° 108° 144°

Answers

Answer:

54°

Step-by-step explanation:

Since the 5 vertex angles are congruent, each vertex angle = 360/5 = 72°

The sum of the angles of each triangle is 180-72 = 108°

The base angles of each triangle are equal to each other so each base angle = 108/2 = 54°

I already worked on most of my question, although, I am just curious about how you would go about finding the fourth power of the square root of 50. Can someone please explain this in detail?

Answers

Answer:

(50^1/2)^4

Step-by-step explanation:

basically if I am comprehending your question correctly, the square root of 50 can also be written as 50^1/2

If you put 50^1/2 to the 4th power, it basically becomes (50^1/2)^4

(08.02)How many solutions are there for the system of equations of shown on the graph?
O No solution
O One solution
O Two solutions
O Infinitely many solutions

Answers

Answer: B. One solution

Step-by-step explanation: As you see, both of these lines intersect on the point (0, 3). The point where the lines intersect is the solution. Since these lines are perpendicular, they will only intersect one time. Therefore, there is only one solution, that being (0, 3).

I hope this helps!! Pls mark brainliest :)

+
Carla babysits and tutors to make extra money. She babysits for $5 an hour and tutors for $10 an hour.
She can only work at most 15 hours a week. She wants to go on a trip with her friend and needs to
make $95 dollars this week to cover the cost of the trip. Write a system of inequalities to represent this
situation.

Answers

The system of inequalities to represent this situation will be x + y ≤ 15 and 5x + 10y ≤ 95.

What is the linear system?

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

Carla babysits and tutors to make extra money.

She babysits for $5 an hour and tutors for $10 an hour.

She can only work at most 15 hours a week.

Likewise, she wants to go on a trip with her friend and needs to make 95 dollars this week to cover the cost of the trip.

Then the system of inequalities to represent this situation will be

Let x be the number of babysits hours and y be the number of tutor's hours.

     x + y ≤ 15

5x + 10y ≤ 95

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