(a) Use Newton's method with x1 = 1 to find the root of the equation
x3 − x = 4
correct to six decimal places.
x =
(b) Solve the equation in part (a) using x1 = 0.6 as the initial approximation.
x =
(c) Solve the equation in part (a) using x1 = 0.57. (You definitely need a programmable calculator for this part.)
x =
(d) Graph
f(x) = x3 − x − 4
and its tangent lines at
x1 = 1,
0.6, and 0.57.
WebAssign Plot WebAssign Plot
WebAssign Plot WebAssign Plot
Answers
9514 1404 393
Answer:
x ≈ 1.796322 . . . in all cases
Step-by-step explanation:
For Newton's method iteration, we like to use a function such that we are finding a zero of the function. Here, this means we want to rearrange the equation to ...
f(x) = x^3 -x -4
so that we are finding x for f(x) = 0.
The iterator is ...
next x = x - f(x)/f'(x) . . . . . where f'(x) is the first derivative
Many graphing calculators can accept the notation f'(x), so we do not actually have to determine the derivative algebraically. In the first attachment, we have used the function f1(x) to compute the next iteration value ("next x").
__
a) In the first attachment, we have used a math package to define the function, the iterator, and an accumulator of iteration values. The N[ ] function causes the display of 7 significant digits. Computations are performed to 30 significant digits. Starting values are the third argument from the right end of the expression doing the computation. They are 1, 6/10, 57/100.
It shows that it takes 6 iterations starting from x=1 to get to 6 decimal places of accuracy. The 7th iteration is computed so that we can compare the first 6 decimal places. The final iteration gives a value of x of 1.796322.
We know that Newton's method converges quadratically (from a close-enough starting point), so 4 good decimal digits in the 5th iteration can be expected to become 8 good decimal digits in the 6th iteration. That is, if two iterations agree in the first 3 decimal digits, then the second of those can generally be considered accurate to at least 6 decimal digits.
__
b) Starting from x=0.6, more iterations are required. The attachment shows that 6-decimal place accuracy is achieved in 13 iterations. More iterations are required because the starting point is closer to the function turning point, so initial iterations tend to diverge from the root.
__
c) Starting from x=0.57, 20 iterations are required. This starting point is on the wrong side of the turning point of the function, so the initial iteration sends the computation a significant distance in the wrong direction.
__
d) The graph and tangent lines are shown in the second attachment. Successively smaller starting values have tangents with successively smaller slopes.
Related Questions
Tell whether the angles are adjacent or vertical. Then find the value of x.
Answers
Answer:
Vertical/ x = 25.
Step-by-step explanation:
Vertical angles are self-explanatory; vertical angles are angles that are vertical from each other.
Vertical angles are also congruent (equal), meaning that both angles equal 75°.
4x - 25 = 75.
To solve this expression, we must first add 25 to 75. This is because there is a subtraction sign in front of 25, so we must do the opposite.
25 + 75 = 100
Lastly, divide 100 from 4.
4x = 100
100 / 4 = 25
x = 25
In the interval 0≤x<360°
0
≤
x
<
360
°
, how many values of x
x
satisfy the equation sin2x=14
sin
2
x
=
1
4
?
Answers
Answer:
Step-by-step explanation:
since -1≤sin2x≤1 no x values would satisfy the equation
The dot plots show the age of different players on two different local soccer teams.
Team A
Team B
+
+
+
4
20
+
29
23
20
24
21
25
26
27
28
29
30
21
22
23
24
28
30
26
28
27
Age (years)
Age (years)
Which statement is best supported by the information in the table?
A.
The range of the data for Team A is equal to the range of the data for Team B
B.
The mode of the data for Team B is greater than the mode of the data for Team A
C.
The distributions of the data for Team A and Team B are approximately
symmetrical
D.
The median of the data for Team B is less than the median of the data for Team A
Answers
Answer:
answer is b...............
Write a question that represents the following equation.
5 · n = 35
Answers
Answer:
Hey, dude what grade are you in and I use ignitia
Step-by-step explanation:
g During winter, red foxes hunt small rodents by jumping into thick snow cover, without any visual clue. Researchers examined the compass direction of hundreds of such jumps. They found that 73% of jumps in the northeast direction were successful, compared with 60% of jumps in the southwest direction and only 18% of jumps in all other directions. True or False: Jumping direction and jump outcome are independent.
Answers
Answer: False
Step-by-step explanation:
Events can be classed as being dependent or independent depending on whether the outcome of a certain event affects the outcome of another. In the scenario above, the success rate of jumps in the Northeast direction is higher than in the southwest direction and even much than in other directions. With these uneven rate of success, the probability that a fox will have a successful jump will depend on the direction in which the fox is jumping. With an high expected success probability in the Northeast and southwest than in other directions
It's Friday afternoon and six fraternity brothers at UNC havejust attended their last class of the semester. To unwind beforethe final exam Monday morning, they decide to spend the weekend atthe beach. After a weekend of immature, irresponsible behavior,they oversleep Monday morning and miss the final exam. Later thatday they go to their professor (who received her Ph.D. from NCState) and explain that they went to the beach and were on the wayback for the final exam but their car (a BMW of course) had a flattire. The professor says that they can come back the next morningand she will give them a make-up final exam consisting of oneshort-answer question! The students are ecstatic and high-five eachother all the way back to the frat house. The next morning theprofessor puts each student in a different room and hands themtheir one-question test. The question: Whichtire?
Aside: Clickhere for interesting related site.
What is the probability that all 6 students will say that thesame tire was flat? (Use 5 decimal places.)Hint: the answer is NOT(1/4)^6.
Answers
I NEED HELP PLEASE RIGHT NOW
Answers
Answer:
Average is 2 hours
The population of largemouth bass in a pond is decreasing at the rate of 10% per year. If the population of largemouth bass is 5,000 this year, what will the population be in 16 years?
Answers
Answer:
Population after 16 year = 927 people (Approx.)
Step-by-step explanation:
Given:
Decrease rate = 10% per year
Current population = 5,000
Find:
Population after 16 year
Computation:
A = P[1-r]ⁿ
A = 5,000[1-0.1]¹⁶
A = 5,000[0.9]¹⁶
A = 5,000[0.1853]
A = 926.51
Population after 16 year = 927 people (Approx.)
A baker has determined that four every
4 pounds of flour, she can make 6
loaves of bread.
Answers
ms.vellejo has these cans of soup in her cabinet 1 can of tomato soup 4 cans of chicken soup 3 cans of cheese soup 2 cans of beef soup ms.velljo will randomly choose one can of soup what is the probililty that she will choose a can of beef or chicken soup
Answers
Answer:
There is a 40% chance that she will choose a can of beef soup, a 20% chance that she will choose a can of chicken soup, and a combined 60% chance that she will choose a can of beef or chicken soup.
Step-by-step explanation:
Since Ms. Vellejo has 1 can of tomato soup, 4 cans of chicken soup, 3 cans of cheese soup and 2 cans of beef soup in her cabinet, and she will randomly choose one can of soup, to determine what is the probililty that she will choose a can of beef or chicken soup, the following calculation must be performed:
1 + 4 + 3 + 2 = 10
Beef soup = 2 cans = 2/10 = 0.2 = 20%
Chicken soup = 4 cans = 4/10 = 0.4 = 40%
20 + 40 = 60
Thus, there is a 40% chance that she will choose a can of beef soup, a 20% chance that she will choose a can of chicken soup, and a combined 60% chance that she will choose a can of beef or chicken soup.
Billy wants to buy these tickets for a show: 4 adult tickets at £15 each and 2 child tickets at £10 each. A 10% booking fee is added to the ticket price. 3% is then added for paying by credit card. Work out the total charge for these tickets when paying by credit card.
Answers
Answer:
The total charge for these tickets when paying by credit card is £ 90.64.
Step-by-step explanation:
Since Billy wants to buy 4 adult tickets at £ 15 each and 2 child tickets at £ 10 each for a show, and a 10% booking fee is added to the ticket price, and 3% is then added for paying by credit card, for work out the total charge for these tickets when paying by credit card the following calculation must be performed:
((4 x 15 + 2 x 10) x 1.10) x 1.03 = X
((60 + 20) x 1.10) x 1.03 = X
(80 x 1.10) x 1.03 = X
88 x 1.03 = X
90.64 = X
Thus, the total charge for these tickets when paying by credit card is £ 90.64.
Question 1
mp4
A dartboard has a radius of 9 inches, with a bullseye that has a radius of 2 inches. Find the probability of throwing a dart into
the bullseye. Round to the nearest hundredth, if necessary
check.mp4
in
Check
Probability =
Next
Pause test
Next
6:33 PM
Answers
Answer:
P=0.05
Step-by-step explanation:
You need to find the ratio of the areas, and they vary in function of the square of the radius, so you have P=2²/9²=4/81≈0.05
Please help will give brainliest
Answers
Is the following relation a function?
Answers
Explanation: The relation is not a function because there is more than one output (y) for a single input (x).
Answer:
No this is not a function since 2 of the domain values have the same range.
Step-by-step explanation:
Well in simpler terms, if one or more range values (right side) have more then 1 arrow pointing to them, its automatically not a function. If each one has one arrow pointing towards them, its a function.
John will rent a car for the weekend. He can choose one of two plans. The first plan has an Initial fee of $51 and costs an additional $0.12 per mile driven. The second plan has an initial fee of $46 and costs an additional $0.14 per mile driven. For what amount of driving do the two plans cost the same? miles What is the cost when the two plans cost the same?
Answers
Answer:
The first plan has an initial fee.
The first plan has an initial fee of $51 and costs an idditional $0.11 per mile driven.
Step-by-step explanation:
In the late 2000's sales of SUVs decreased due to higher gas prices and improved alternative vehicles. A car dealer is interested whether it takes more days to sell SUV's vs. small cars. He gathers data from a sample of the most recent couple of months of sales and calculates that the he sold 18 SUV's with an average number of days to sale of 95 and a standard deviation of 32 days. For small cars, he sold 38 of them in an average of 48 days with a standard deviation of 24 days. The dealer wants to estimate how much longer it takes to sell an SUV vs. a small car by constructing a 95% confidence interval. 1. The facts of this problem are:
Answers
Answer:
1. The facts are;
[tex]\overline x _1[/tex] = 95 days
s₁ = 32 days
n₁ = 18 SUV's
[tex]\overline x _2[/tex] = 48 days
n₂ = 38 small cars
s₂ = 24 days
The confidence level = 95%
The confidence interval is (29.55, 64.45)
Step-by-step explanation:
The facts of the problem are;
The number of SUV's he sold, n₁ = 18 SUV's
The average number it took to sell the 18 SUV's, [tex]\overline x _1[/tex] = 95 days
The standard deviation of the time it took to sell the 18 SUV's, s₁ = 32 days
The number of small cars he sold, n₂ = 38 small cars
The average number it took to sell the 38 small cars, [tex]\overline x _2[/tex] = 48 days
The standard deviation of the time it took to sell the 38 small cars, s₂ = 24 days
The 95% confidence interval is given as follows;
Using a graphing calculator, we get, the critical-t, [tex]t_c[/tex] = 2.055529
[tex]\left (\bar{x}_1-\bar{x}_{2} \right ) \pm t_{c} \cdot\sqrt{\dfrac{s _{1}^{2}}{n_{1}}+\dfrac{s _{2}^{2}}{n_{2}}}[/tex]
[tex]\left (95-48 \right ) \pm 2.055529 \times \sqrt{\dfrac{32^{2}}{18}+\dfrac{24^{2}}{38}}[/tex]
We get C.I. = 29.55259 < μ₁ - μ₂ < 64.44741
∴ C.I. ≈ 29.55 < μ₁ - μ₂ < 64.45
What is the range of the data set?
Answers
Answer:
Range = 19
Step-by-step explanation:
Range = maximum value - minimum value
Maximum value is indicated by the whisker to our far right on a box plot = 25
Minimum value is at the whisker to our far left = 6
Range = 25 - 6 = 19
Which expression is equivalent to (29P+4)??
PLSSS HURRY
Answers
Answer:
[tex]4g^{6} + 16g^{3}+16[/tex]
Step-by-step explanation:
[tex]2(2g^{3}+4)*g^{3}+4(2g^{3}+4)[/tex]
Answer:
(2g³+4)²
using formula of (a+b)²=a²+2ab+b²
(2g³)²+2×2g³×4+4²
2g^5+16g³+16 Is your answer
A triangular prism has base edges 2 cm, 6 cm, and 7 cm long. Its lateral area is 330 cm2. What is the height of the prism? cm. The height of the prism is (Simplify your answer.)
Answers
9514 1404 393
Answer:
22 cm
Step-by-step explanation:
The lateral area is the product of the perimeter and the height. The perimeter is the sum of side lengths.
P = a+b+c = (2 +6 +7) cm = 15 cm
LA = Ph
330 cm^2 = (15 cm)h . . . fill in the known values
h = (330 cm^2)/(15 cm) = 22 cm
The height of the prism is 22 cm.
Pls help me I’m so stuck
Answers
Answer:
1/9
Step-by-step explanation:
We know that the variable multiplied is just the reciprical which is 1/9
By the way, can you follow me on Brainly?
Thanks!
A circle has a radius of 4 cm and an arc of length 6 cm. What is the measure of the angle at the center?
Answers
HELP ASAPPPP!!!BRAINLEST WILL BE GIVEN!!!
Answers
Answer:
30 days
Step-by-step explanation:
The common multiples of 15 and 6 are 30, 60, 90 etc and because it increases by 30 each time we can find out that he will play both football and basketball together in thirty days!
Answer: 30 days i think
Step-by-step explanation:
hope this helps you bud
If you invest 3,500 in a savings account that pays 4% simple interest how much will the new balance be after including interest?
Answers
Answer:
New balance = 3640
Step-by-step explanation:
Given the following data;
Interest rate = 4% = 4/100 = 0.04
Principal = 3500
To find the new balance;
First of all, we would find the amount at the interest rate;
New amount = interest rate * principal
New amount = 0.04 * 3500
New amount = 140
Now, to find the new balance;
New balance = principal + new amount
New balance = 3500 + 140
New balance = 3640
Please take a look at the question. Please explain and type your explaination. Please make it quick as possible. Thankyou!
Answers
Answer:
Yes, it's true
Step-by-step explanation:
A fraction is a part of a whole number for example 1/2. 1/2 is a half of one whole piece and if you multiply it into any whole number whether it's 2,4,6,8,10...... basically, if you multiply a fraction less than one with a non-zero whole number, it will always be less than the whole number it's being cut into smaller pieces. However, if the fraction is greater than 1, we would technically have an answer greater than the whole number product, just something to remember.
In which number does the digit 2 have a value that is ten times as great as the value of the digit 2 in the number 135,284?
Answers
= 10 × 200
= 2000
What is the perimeter of a parallelogram with a base of 28 cm, side
length 50 cm, and a height of 30 cm?
Answers
[tex] \sf{Formulas \: we \: use}[/tex]
Perimeter of parallelogram2×(Base+Height)Now lets start.2×28+30
2×58
116
The perimeter is 116 cm²Which table of values goes with this equation?
y = x/5
Answers
In triangle IJK, the measure of angle K is 90, IK= 39, JI = 89 and KJ= 80. What ratio represents the sine of angle I?
Answers
Answer:
80 / 89
Step-by-step explanation:
Please see attached photo for explanation.
In the attached photo, the following data were obtained:
<I = θ
Hypothenus = 89
Opposite = 80
Sine <I =?
Sine ratio of <I can be obtained as follow:
Sine θ = Opposite / Hypothenus
Sine <I = 80 / 89
Thus, the ratio of sine <I is 80 / 89
16. A rock weighs 6 and 1/2 tons. How many pounds does the rock weigh?
2,000 lb = 1 T
Answers
Answer:
13000
Step-by-step explanation:
1 = 2,000 pounds
0.5 tons = 1000 pounds
Answer: 13,000 lb
Step-by-step explanation:
6 x 2,000 = 12,000
1/2 * 2,000 = 1,000
12,000 + 1,000 = 13,000
The building below is shown to scale; for every 1 inch of drawing, it is 5 feet in actual distance. The exterior surface area of the building is 250,000 square feet. What is the exterior surface area of the model?
Answers
Answer:
50,000 square inches
Step-by-step explanation:
1:5 ratio so 250,000/5=50,000