We have proved that the Newton-Raphson iteration formula for solving the equation[tex]x^k e^x = 0[/tex] is given by [tex]x_{n+1} = (k - 1) x_n + x_n^2 / k + x_n.[/tex]
To prove that the Newton-Raphson method for solving the equation [tex]x^k e^x = 0[/tex], where k is a constant, is given by the formula
[tex]x_{n+1} = (k - 1) x_n + x_n^2 / k + x_n,[/tex]
we can start by considering the iterative process of the Newton-Raphson method.
Given an initial guess [tex]x_n[/tex], we want to find a better approximation [tex]x_{n+1}[/tex]that is closer to the root of the equation [tex]x^k e^x = 0.[/tex]
The Newton-Raphson method involves the following steps:
Calculate the function value [tex]f(x_n) = x_n^k e^x_n[/tex] and its derivative [tex]f'(x_n) = k x_n^(k-1) e^x_n.[/tex]
Find the next approximation x_{n+1} by using the formula:
[tex]x_{n+1} = x_n - f(x_n) / f'(x_n)[/tex]
Let's apply these steps to our equation [tex]x^k e^x = 0[/tex]:
Calculate the function value and its derivative:
[tex]f(x_n) = x_n^k e^x_n\\f'(x_n) = k x_n^(k-1) e^x_n[/tex]
Find the next approximation x_{n+1} using the formula:
[tex]x_{n+1} = x_n - f(x_n) / f'(x_n)[/tex]
Substituting the function value and its derivative:
[tex]x_{n+1} = x_n - (x_n^k e^x_n) / (k x_n^(k-1) e^x_n)\\= x_n - (x_n^k / k)[/tex]
Simplifying the expression by combining like terms:
[tex]x_{n+1} = x_n - (x_n^k / k)\\= x_n - x_n^k / k\\= (k - 1) x_n + x_n^2 / k + x_n[/tex]
Therefore, we have proved that the Newton-Raphson iteration formula for solving the equation[tex]x^k e^x = 0[/tex] is given by [tex]x_{n+1} = (k - 1) x_n + x_n^2 / k + x_n.[/tex]
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4 in.
3 in.
2 in.
2 in.
6 in.
Find the surface area.
square inches
(Hint: The rectangular faces
are different sizes.)
Answer:
The correct answer is 5in
Step-by-step explanation:
6+4=10÷2=5in
A circle's radius is 14 centimeters.
What is the circle's circumference (use 3.14 for pi and round to
nearest tenth)?
Answer:
seeee this is y i hate math too many numbers XD
What is MEAN ABSOLUTE DEVIATION and how do you find it?
Step-by-step explanation:
Step 1: Calculate the mean. Step 2: Calculate how far away each data point is from the mean using positive distances. These are called absolute deviations. Step 3: Add those deviations together. Step 4: Divide the sum by the number of data points.
Type the correct answer in each box.
50°
60°
709
х
50°
The value of xis
°, and the value of y is
Answer:
x = 60°
y = 50°
Step-by-step explanation:
✔️x + 50° + 70° = 180° (sum of a triangle)
x + 120° = 180°
Subtract 120° from each side
x = 180° - 120°
x = 60°
✔️50° + 60° = x + y (exterior angle theorem of a triangle)
110° = x + y
Plug in the value of x
110° = 60° + y
Subtract 60° from each side
110° - 60° = y
50° = y
y = 50°
kim works from 6 to 11 on friday and saturday evenings at ty’s diner. she gets $4.35 an hour plus tips. her tips were $37.35 on friday and $42.10 on saturday. how much did she earn for the 2 night’s work? _________ how much did she average per hour? ________
Answer:
Friday, total earning:
(11 - 6)*$4.35 + $37.35 = $59.10Saturday, total earning:
(11 - 6)*$4.35 + $42.10 = $63.85Total for the two nights is:
$59.10 + $63.85 = $122.95Average per hour is:
$122.95/(5 + 5) = $122.95 / 10 = $12.30 (rounded)Consider the following number line:
B
C
A+
11
=>
1
0
Drag the following cards to match each point to its value.
Point Value
А
1
5
B
0.8
3
5
Answer:
The pink A goes to the Green C on the number line. the green C goes to the pink A on the number line. The Blue B goes to the Blue B in the number line.
Step-by-step explanation:
hope it helped ;)
HELPPP!!! i need to know this asap!!
Answer:
The first option
(-10, -7)
Step-by-step explanation:
Also I really like your pfp <33
In APQR, what is the mZQ? Enter your answer in the box.
Answer:
∠Q = 105°
Step-by-step explanation:
(6x + 5) + (11x - 5) + x = 180°
combine like terms:
18x = 180°
x = 10°
∠Q = 11(10) -5 = 105°
how do you find how many pounds he used, and how many pounds did he use?
Answer:
I'm not too sure what you are referring too and I can't clearly see the image but I'll give you some tips!
One way to find out how many pounds he used is to add all the pounds you know he used (what is written down) or to multiply, divide, whatever is best for the situation
so yeah hope this helped!
Nicholas is currently in eighth grade and intends to attend a state college when he finishes high school. Nicholas’s parents currently have some money invested in mutual funds, but would like to invest this money in a more secure investment now to pay for college in 4 years. If they will need $25,000, how much do Nicholas’s parents have to invest now in a 48month CD that has a rate of 4.59% compounded monthly?
Answer: he has 10 monthly
Step-by-step explanation:
see from the question
What’s the volume of the rectangular prism of 2cm, 7/3 cm and 2cm?
Answer:
9 1/3 cm³
Step-by-step explanation:
First multiply two numbers.
2x2=4
Then multiply the product by the third number.
4x7/3
4 x 7
1 x 3
= 28/3 or 9 1/3
--
hope it helps
Rozlyn invested $2000 in an account that pays 4.25% annual simple interest. She will not make any additional deposits or withdrawals. How much interest will Rozlyn earn on her investment in 10 years?
Answer:
$850
Step-by-step explanation:
Interest = Principal x Rate x Time
I = 2000(.0425)(10)
I = 850
Cynthia says that when you evaluate the expression (21 3/4 + 4 1/2) - 5 3/12 you get a whole number. What whole number do you get?
Answer: 21
Step-by-step explanation:
First, convert the mixed fractions to improper fractions.
(87/4 + 9/2) - 21/4
Next, calculate within the parentheses:
87/4 + 9/2
Next, change the denominator of 9/2 to 4. To do that, multiply the denominator of 9/2 to get 4 to match the denominator of the first fraction. 9/2 * 2/2 = 18/4.
87/4 + 18/4 = 105/4
Then, 105/4 - 21/4 = 84/4
Finally, divide 84 by 4 and you get 21.
Show your work
2) Is(-3,-7) a solution to
4x – 8y < 24
Show your work
Answer: false, 44 is not less than 24
Step-by-step explanation:
Substitute-3 for x and -7 for y.
4(-3)-8(-7)<24
-12+56<24
44<24
WWW ie Www Anna baked 3 batches of cookies with c cookies in each batch. She then ate 8 cookies! How many cookies does Anna have left? Write your answer as an expression. TIME
Anna had 2 batches left also equal to 16 cookies
PLS HELPPPPPPP MEEEEE
Answer:
4.7 · 10^7
Step-by-step explanation:
What is the magnitude of -3 + 4i?
The magnitude of the complex number -3 + 4i is 5.
To find the magnitude of a complex number, we use the formula:
Magnitude = √(real^2 + imaginary^2)
In this case, the complex number is -3 + 4i.
The real part is -3, and the imaginary part is 4.
Using the formula, we can calculate the magnitude:
Magnitude = √((-3)^2 + 4^2)
= √(9 + 16)
= √25
= 5
Therefore, the magnitude of the complex number -3 + 4i is 5.
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Which of the following statements would be true about the product of 6 and 1 3/4?
Answer:
Where is the question
Step-by-step explanation:
:\
Answer:
[tex] \frac{21}{2} [/tex]
[tex]10 \times\frac{1}{2} [/tex]
Step-by-step explanation:
6/1 • 7/4= 42/4
The area of the trapezium is four times the area of the parallelogram. Work out the value of x
Answer:
2.5cm
Step-by-step explanation:
area of trapezium = 4 * area of parallelogram
1/2(a+b)*h=4* bh
1/2(5+11)*4= 4* 3.2x
8*4=4*3.2x
8/3.2=x
2.5cm=x
geometry 10 long 2.75 wide triangle what is the area?
ANSWER !!
ILL GIVE 40 POINTS !!
DONT SKIP :((
PLUS BRAINLIEST !
Answer:
The first one and the fourth one
Step-by-step explanation:
I’m pretty sure that is right
Answer:
A and C in my options below!
Step-by-step explanation:
3^2*3^-6 = 0.0123456790123
A. (3^-2)^2 = 0.0123456790123
B. 2^-12 = 0.000244140625
C. 1/3^4 = 0.0123456790123
D. (3^7)/3^3 = 81
What is the value of x in the equation −x = 6 − 3x + 8? (1 point) Question 10 options: 1) −14 2) −7 3) 14 4) 7
The answer is 4) 7
x=7
Answer:
7
Step-by-step explanation:
x = 7
A rectangular blanket is 2x + 1 feet wide and 4x - 3 feet longWhat is the area in terms of x?
Answer:
3/4
Step-by-step explanation:
So remembering the length times width formula:
Put it in an equation-
(2x+1)(4x-3)
Now start to solve for x:
Multiply using 'foil' method:
(2x+1)(4x-3)
8x -6x + 4x -3
8x -2x -3
Now, factrorize 8x^2 - 2x - 3: (Put a square since this is square measures)
8x^2 - 2x - 3 Sum = -2
Product = -24
Two numbers that give you the sum of -2 and product of -24:
-6 and 4
So now factor out like terms:
8x^2 -6x + 4x -3
2x(4x - 3) + 1(4x - 3)
(2x + 1) (4x-3) = 0
Solve for x in both:
2x + 1 = 0
x = -1/2
4x - 3 = 0
x = 3/4
The area cant be negative so the area in terms of x is:
x = 3/4
(Hope this helped)
Which numbers between 10 and 20 do not appear in the table at all?
And also why don’t they appear?
Answer:
11, 13, 17, 19,
Step-by-step explanation:
dunno
hi, I need to send you a screenshot
I NEED HELP WITH A PROPLEM
Answer:
A 121 m^2
Step-by-step explanation:
2) If you feel you have a "fixed mindset" right now, what would it
take for you to change it to a 'growth mindset"?
Please help
Answer:
Watch tv or play a game that's would help
Step-by-step explanation:
Answer:
Multiple steps and time.
Step-by-step explanation:
Looking at things in a positive way, even if it is a small daily thing will gradually help create a growth mindset.
24 ÷ v x k when v=2 and k=4
Answer:
48
Step-by-step explanation:
24 ÷ v x k
24 ÷ 2 x 4
(Since it's multiplication and division, you just go from left to right in order)
12 x 4
48
find the mode, 3,1,9,3,1,2,3
{math}
From the previous video: At age 40 you deposit $150 at the end of each month into an IRA that pays 4% interest
compounded monthly. In the previous question, we found that the value of the annuity at age 65 would be $77,119.43.
How much interest did you earn?
Round your answer to the nearest cent and do NOT include the dollar sign.
Do NOT round until you have calculated the final answer.
Answer: 32119.43
Step-by-step explanation:
Answer:
Step-by-step explanation:
74059.64