Answers
You're using Newton's method to find the roots to
f(x) = g(x) → x ⁶ = cos(x)
Recast this as finding the roots to
h(x) = f(x) - g(x) = x ⁶ - cos(x)
First, get the tangent line approximation L(x) to h(x) at an arbitrary starting point x = x₀ ; in a small neighborhood of x₀, we have
h(x) ≈ L(x) = h(x₀) + h'(x₀) (x - x₀)
Find the root to the tangent line function:
0 = h(x₀) + h'(x₀) (x - x₀) → x = x₁ = x₀ - h(x₀)/h'(x₀)
x₁ is the first approximation of a root to h(x). Repeat the process - that is, take the tangent line to h(x) at x₁ to find the next approximation x₂, and so on - until you meet the required condition.
For the smaller root, take x₀ = -π/2 :
x₀ ≈ -1.5708
x₁ = x₀ - h(x₀)/h'(x₀) ≈ -1.31348
x₂ = x₁ - h(x₁)/h'(x₁) ≈ -1.11366
x₃ = x₂ - h(x₂)/h'(x₂) ≈ -0.982446
x₄ = x₃ - h(x₃)/h'(x₃) ≈ -0.928013
x₅ = x₄ - h(x₄)/h'(x₄) ≈ -0.920039
x₆ = x₅ - h(x₅)/h'(x₅) ≈ -0.919887
Stop at x₆ because |x₆ - x₅| ≤ 0.001.
For the larger root, you can start the process over with a different seed for x₀, such as π/2. But since h(x) is an even function and symmetric about the y-axis, the larger root will just be the same root with positive sign, 0.919887.
Related Questions
Katya went to a craft store to buy beads. The table shows her choices.
Bead Packages
Number per Package
Cost
25
$1.25
70
$2.50
100
$2.95
180
$3.60
Which should Katya choose if she wants to buy the package of beads with the lowest unit cost?
O A. 25 beads for $1.25
B. 70 beads for $2.50
O C. 100 beads for $2.95
D. 180 beads for $3.60
Answers
Answer:
100 beads for $2.95
Step-by-step explanation:
This is because the unit cost per item if you buy 100 beads for $2.95 would be $0.03
Kendall worked 25.5 hours one week.
If he earns $12.50 per hour, how
much did he earn that week? How did
you know where to put the decimal
point?
Answers
multiply 25.5 by 12.5 which equals 318.75.
to know where to put the decimal, you count the numbers to the right of the decimal point. in this equation youre multiplying 25.5 and 12.5. there are 2 numbers to the right of the equation so in your answer, there should be 2 numbers to the right of the decimal.
Please answer this thanks
Answers
2) adjacent (they are next to each other)
[tex]1) \longrightarrow\boxed{ \bf \: Vertical \: angles} \: ( \sf \: they \: share \: the \: same \: vertex) \\ 2) \longrightarrow\boxed{\bf \: Adjacent \: angles} \: ( \sf \: they \: are \: located \: next \: to \: each \: other)[/tex]
15. Find the area of the circle. Use 3.14 as pie. Round to the nearest tenth. Include units. The radius is 4 inches.
Answers
*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆
Answer: 50.24
Explanation:
3.14(4)^2 = 50.24
I hope this helped!
<!> Brainliest is appreciated! <!>
- Zack Slocum
*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆
Answer: A=50.2
Step-by-step explanation:
using 3.14 as pie...
A=3.14[tex]r^{2}[/tex]
A=3.14x[tex]4^{2}[/tex]
A=3.14x16
A=50.24
rounding to nearest tenth..
A=50.2
A woman bought some large frames for $13 each and some small frames for $6 each at a closeout sale. If she bought 18 frames for $136, find how many of each type
she bought
She bought large frames
vie
Answers
Answer:
she bought 4 large frames and 14 small frames!
Step-by-step explanation:
This is a system of equation problem!
let's say that x= large frames and y=small frames.
since there's 18 total, we already have our first equation set.
x+y=18
(number of large frames) + (number of small frames)= 18
13x would represent the large frames because each one is 13 dollars.
6y would represent the small frames because each one is 6 dollars.
Since she paid 136 dollars total, we can already tell that
13x+6y=136
(price of large frames*number of large frames) + (price of small frames*number of small frames)=136.
Now, time for the math!
Attached below is how you would work it out using substitution.
Hope this helps!
x=4 and y=14
Meaning that she bought 4 large frames and 14 small frames!
Esther estimates that she will need about $8,600 for the first year of tuition at college. Her grandparents contribution will cover 65% of the tuition expenses, and Esther will need to save to pay for the rest. If Esther has 2 years to save, what is the minimum amount that she should save each month?
Answers
Answer:
$125.42
Step-by-step explanation:
Her grandparents will cover 65% of $8600, which is 8600 * 0.65 = $5590. Therefore, she needs to pay for the part they're not covering, which is $8600 - $5590 = $3010.
2 years = 24 months, so assuming she wants to save the same amount each month, we need to divide $3010 by 24 to get the amount per month. This gets us $125.42
The minimum amount that she should save each month for two years is $125.42.
What is the minimum amount she would have to save each month?Percentage can be described as a fraction out of an amount that is usually expressed as a number out of hundred.
Amount given by her grandparents = 65% x 8600= $5590
Amount she would have to save each month for two years = (8600 - $5590) / 24 = $125.42
To learn more about percentages, please check: https://brainly.com/question/25764815
Helppppp pleaseeeeee asapppp
Answers
(12)(4)+(2)(8)+(13)(7)
48+16+91
155
What is the answer? Please tell me soon.
Answers
Answer:
61
Step-by-step explanation:
it's only 1 number difference
1. The graph of f(x) = x^2 was transformed to create the graph of g(x) = f(x) + 11. Which statement about the graphs is true?
A. The y-intercept of the graph of g is 11 units above the y-intercept of the graph of f
B. The vertex of the graph of g is 11 units to the right of the vertex of the graph of f
C. The graph of g is a reflection of the graph of f across the y-axis
D. The of g is a reflection of the graph of f across the x-axis
2. The graph of g (x) = x^2 was transformed to create the graph of h (x) = 3x^2. Which of these describes the transformation from the graph of g to the graph of h?
A. A vertical stretch by a factor of 3
B. A vertical compression by a factor of 3
C. A reflection over the x-axis
D. A vertical shift up 3 units
3. The graph of f (x) = x^2 was transformed to create the graph of g (x) = 1/4x^2. Which of these describes this transformation?
A. The graph shows a vertical compression
B. The graph is a reflection across the x-axis
C. The graph shows a shift up
D. The graph shows a vertical stretch
Answers
2 B
3 D
these are the answers
Seventy-five college students are taking part in a study initiated by a large computer manufacturer. The company is designing a new type of laptop computer and has created prototypes of it with two different keyboard designs. They are also including the current design of the laptop in the experiment. Each of the students was randomly assigned to one of the three types of computers. The students are asked to spend 15 minutes on one of the computers performing several tasks (typing words, numbers, making corrections, etc.). The ease of use of the keyboard was then rated on a five-point scale by having the students fill out a short questionnaire. Which of the following was not used in this experiment?
a. control
b. replication
c. blocking
d. randomization
Answers
Answer:
c
Step-by-step explanation:
blocking is not used in this experiment
The triangle shown below has an area of 16 units^2
Answers
Answer:
8
Step-by-step explanation:
base x height / 2 = the area
4 x h / 2 = 16
h = 8
so x is 8
Answer:
8
Step-by-step explanation:
i just took the quiz
Can someone please help me out?
Answers
Answer:
x | f(x)0 | 02 | 25 | 39 | 110 | 0Step-by-step explanation:
On the left side of the chart, is the x values. The x values are listed on the x axis which is the horizontal line.
The right side of the chart are the y values. The y values are listed on the y axis which is the vertical line.
Knowing this, we can start
First, for all the answer that we know the x value, we need to find the number that matches on the x axis. Once we find that number, we go up or down on the y axis until we find the line.
If we know the y value, we need to find the number that matches on the y axis. Then we will go right until we find the line.
Remember - There CAN NOT be two y values for the same x value but THERE CAN BE two x values for the same y value
Please help me ASAP Please
Answers
Answer:
31x=217 x=7
Step-by-step explanation:
begin with what you know. You know that you will have 31 days to complete the goal and that the goal is 217 miles. This gives you your y (217) and your m (31). Then set up into y=mx+b form. This gives 31x=217. Then to solve divide 217 by 31. This gives the needed the needed answer of 7 miles per day
a contractor was paving a driveway he mixed 4/7 ton lf sand and 1/3 ton of concrete how much did the mixture weigh
Answers
Answer: 19/21
Step-by-step explanation: find the same multiple for both so you can combine them
The table below lists the number of layers of centimeter cubes, along with the number
of cubes in each layer, in each of four rectangular prisms.
LAYERS OF CUBES IN RECTANGULAR PRISMS
Prism
Number of
Layers
Number of Cubes
in Each Layer
R
3
8
S
5
5
T
6
5
U
7
4
Which rectangular prism has the greatest volume?
A Prism R
B Prism S
C Prism T
D Prism U
Answers
Answer:
The answer would be C: Prism T
Step-by-step explanation:
R=3x8=24 cubes
S=5x5=25 cubes
T=6x5=30 cubes
U=7x4=28
Therefore, T is biggest
Which box plot matches the date set 34,36,41,45,49,50,51,52,56,59
Answers
Answer:
D
Step-by-step explanation:
The box has to go from the first to the third quartile and that one does and c isn't correct because the line isn't at the median.
Find the value of x
Answers
Answer:
v=53
Step-by-step explanation:
90-37=53
Yo please help I’ll mark you brainliest
Answers
Answer:
1116units²
Step-by-step explanation:
area of trapezium= (a+b)h all over 2
a=38
b=55
h=24
area= (38+55)*24 allover 2
area= 1116units²
which of the following is the equivalent to the radical expression below when x> 0
square foot 12x^3 + Square root 6x
Answers
Answer:
i think it is b
Step-by-step explanation:
The equivalent to the radical expression will be x√2. Then the correct option is C.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The expression is given below.
⇒ √(12x³) ÷ √(6x)
Simplify the expression, then we have
⇒ √(12x³) ÷ √(6x)
⇒ √(12x³ ÷ 6x)
⇒ √(2x²)
⇒ x√2
The comparable to the extreme articulation will be x√2. Then the right choice is C.
More about the Algebra link is given below.
https://brainly.com/question/953809
#SPJ2
Find the slope of the
(4,5), (6,2)
Answers
Answer:
Answer and steps are in picture.
what is the area of the figure?
Answers
Area r= 1 2/3
Area total = 5 1/3
name types of angles in geometric figures
Answers
Answer:
obtuse angle,acute angle,right angle,straight angle hope it helps
Right --> 90 degrees
obtuse --> more than 90 degrees but less than 180
straight --> 180 degrees
reflex --> greater than 180 degrees
full rotation --> 360 degrees
A store owner has 12 pounds of pasta worth 70¢ a pound. She wants to mix it with
pasta worth 45¢ a pound so that the total mixture can be sold for 55¢ a pound
(without any gain or loss). How much of the 45¢ pasta must she use?
Answers
Answer:
The store owner must use 18 pounds of the 45 ¢ pasta.
Step-by-step explanation:
Given that a store owner has 12 pounds of pasta worth 70 ¢ a pound, and she wants to mix it with pasta worth 45 ¢ a pound so that the total mixture can be sold for 55 ¢ a pound, to determine how much of the 45 ¢ pasta must she use, the following calculation must be performed:
100 x 0.7 + 0 x 0.45 = 70
90 x 0.7 + 10 x 0.45 = 67.5
50 x 0.7 + 50 x 0.45 = 57.5
40 x 0.7 + 60 x 0.45 = 55
40 = 12
60 = X
60 x 12/40 = X
720/40 = X
18 = X
Thus, the store owner must use 18 pounds of the 45 ¢ pasta.
You spin a spinner that is equally divided into 5 parts, and then you spin it again. 1 part is pink, 2 parts are blue, and 2 parts are black. What is the probability of the spinner dropping on a blue section on the first spin and then a blue section of the second spin?
Answers
Answer:
There is a 16% chance of the spinner dropping on a blue section on the first spin and then a blue section of the second spin.
Step-by-step explanation:
Given that I spin a spinner that is equally divided into 5 parts, and then I spin it again, knowing that 1 part is pink, 2 parts are blue, and 2 parts are black, to determine what is the probability of the spinner dropping on a blue section on the first spin and then a blue section of the second spin the following calculation must be performed:
Blue parts: 2
Total Parts: 5
2/5 = 0.4 = 40%
0.40 x 0.40 = 0.16
Thus, there is a 16% chance of the spinner dropping on a blue section on the first spin and then a blue section of the second spin.
A teacher buys packs of notebooks to give to his students. The ratio of gold notebooks to red notebooks is represented in the tape diagram.
Answers
Answer:
40 gold notebooks
Step-by-step explanation:
5:3 gold notebooks to red notebooks so using this we can set up a proportion
5 x
-- = ---
3 24
cross multiplying
3x = 120
x= 40
so there are 40 gold notebooks if there are 24 red notebooks
Answer: Answer above is right. Kudo's to him
Step-by-step explanation:
Mr. Turner bought x boxes of pencils. Each box holds 25 pencils. He left 3 boxes of pencils at home and took the rest to school. Write a function rule that represents the total number of pencils he took to school.
Answers
Answer:12
Step-by-step explanation:I divided 3 by 120 and got 0.12 take the zesty out and the demical
Write 4.5 as a mixed number.
Answers
Answer:
9/2
Step-by-step explanation:
4.5 = 4 1/2 = 9/2
A college student has two different jobs. Her combined work schedules consist of no more
than 48 hours in one week.
Which graph best represents the solution set for all possible combinations of x, the number of
hours she worked at her first job, and y, the number of hours she worked at her second job,
in one week?
Work Schedule
Work Schedule
54
42
36
30
с
Number of Hours Worked
54
48
842
36
30
24
18
12
6
24
18
12
6
0
6 12 18 24 30 36 42 48 54
Number of Hours Worked
at First Job
6 12 18 24 30 36 42 48 5x
Number of Hours Worked
at First Job
Work Schedule
Work Schedule
В
B
Number of Houn worked
48
42
36
30
24
18
12
6
D
Number of Hours Worked
Second Job
54
48
42
36
30
$24
18
12
6
0
6 12 18 24 30 36 42 48 54
Number of Hours Worked
at First Job
6 12 18 24 30 36 42 48 54
Number of Hours Worked
at First Job
Answers
Answer:
A
Step-by-step explanation:
I just did it and it was the correct answer !
A bag contains 7 blue, 4 yellow, 4 green, and 5 red marbles. Find the probability of choosing a green marble without looking. Mark only one oval. Dood
Answers
Answer:
1/4
Step-by-step explanation:
total balls=7+4+4+5=20
probability of green marble=?
green marbles are 5 so,
Probability=number of favourable outcomes / number of all possible outcomes
total outcomes=20
green ball chances=5
=5/20
=1/4
Coin Calculation plz help
Answers
Answer:
You didnt add a question, file or possible answer choices