Find the coefficient of x 4 in the taylor series expansion centered at the origin for the function f(x) = 8 ln(9 + 3x 2 ).
Answers
Note, that it is the full solution, it is possible to make it shorter.
The coefficient of x4 in the Taylor series expansion of the given function is 0.
Explanation:To find the coefficient of x4 in the Taylor series expansion of the function f(x) = 8 ln(9 + 3x2), we need to compute the fourth derivative of f(x) and evaluate it at x = 0.
The Taylor series expansion for a function centered at the origin is given by:
f(x) = f(0) + f'(0)x + f''(0)x2/2! + f'''(0)x3/3! + f''''(0)x4/4! + ...
In this case, we have:
f'''(x) = 48x/(9 + 3x2)
Evaluating f'''(x) at x = 0 gives:
f'''(0) = 0/9 = 0
Therefore, the coefficient of x4 in the Taylor series expansion centered at the origin for the function f(x) = 8 ln(9 + 3x2) is 0.
Related Questions
During a two week period, Norm worked 85.6 hours. His hourly wage is $6.92. How much did he earn? (Round the answer to the nearest cent)
Answers
Karla is mowing her lawn. She knows 2/5 of the lawn before stopping for a snack. She resumes mowing after her snack and mows another 1/3 of her lawn before stopping. What total fraction of the lawn does Karla mow before lunch?
Answers
2/5+1/3=6/15+5/15=11/15 she mows before lunch
Karla mows a total of 11/15 of her lawn before lunch after adding the fractions 2/5 and 1/3 with a common denominator of 15.
The student's question has two parts where Karla mows her lawn in fractions, first 2/5 and then another 1/3. To find the total fraction of the lawn that she mows before lunch, these two fractions need to be added. However, since they do not have the same denominator, we first need to find a common denominator to combine these fractions properly.
The least common denominator (LCD) for 5 and 3 is 15. We convert the fractions to have this common denominator:
(2/5) becomes (6/15) after multiplying both the numerator and denominator by 3.(1/3) becomes (5/15) after multiplying both the numerator and denominator by 5.Now we add the fractions:
(6/15) + (5/15) = (11/15)
Thus, Karla mows a total of 11/15 of her lawn before lunch.
A plumbing contractor receives proceeds of $4,713.54 on a 12.5% simple discount note with a face value of $5,000. Find the time of the note in days. (Assume a 360-day year.) Do not round intermediate calculations!
Answers
t = I/(Pr)
.. = (5000 -4713.54)/(5000*0.125)
.. = 165/360
The time period of the note is 165 days.
The time of the note in days is calculated using the simple discount formula, and by substituting the values of proceeds, face value, and discount rate, the result is 164.99856 days.
The question involves finding the time in days for which a simple discount note is held, given the proceeds, face value, and discount rate. The note's face value is $5,000 and the proceeds received are $4,713.54. The simple discount rate is 12.5%. Assuming a 360-day year, we need to calculate the time period for the note.
Firstly, we need to determine the amount of the discount, which is the difference between the face value and the proceeds: $5,000 - $4,713.54 = $286.46. The discount, given the simple discount formula, is equal to the face value multiplied by the discount rate and the time (in years). The simple discount formula can be expressed as: Discount = Face Value × Discount Rate × Time. Rearranging this formula to solve for time, we get: Time = Discount ÷ (Face Value × Discount Rate).
Substituting the known values we have: Time = $286.46 ÷ ($5,000 × 0.125) = $286.46 ÷ $625 = 0.458336 years. To convert years to days, we multiply the time in years by the number of days in a year (assuming a 360-day year): 0.458336 years × 360 days/year = 164.99856 days. Since we're instructed not to round intermediate calculations, the time of the note is 164.99856 days.
Calculate.
(10.4)2 =
20.16
100.16
108.16
20.8
Answers
[tex]\boxed{ \frac{2^4*13^2}{5^2} = 108.16000} \\ \\ \\ \\ we \ first \ simplify \ 52/2 \\ \\ \boxed{\boxed{(52)^2 = (2^2*13)^2 = 2^4 *13^2}} \\ \\ this \ would \ all \ sum \ up \ to \ be . . . . \\ \\ (108.16)[/tex]
Your answer would be the: (third option)
An apple juice producer buys all his apples from a conglomerate of apple growers in one northwest state. the amount of juice squeezed from each of these apples is approximately normally distributed with a mean of 2.25 ounces and a standard deviation of 0.15 ounce.what is the probability that a randomly selected apple will contain between 2.00 and 2.15 ounces?
Answers
A class has 50 students. use the third row of digits in the random number table below to select a simple random sample of three students. if the students are numbered 01 to 50, what are the numbers of the three students selected
Answers
To select a simple random sample of three students from a class of 50 students using the third row of digits in the random number table, you would use the digits in the third row to determine the numbers of the selected students.
Explanation:To select a simple random sample of three students from a class of 50 students using the third row of digits in the random number table, you would start by numbering the students from 01 to 50.
Then, you would use the digits in the third row of the random number table to select the students.
For example, if the digits in the third row are 579362814, you would select the students with the corresponding numbers: 05, 79, and 36.
Learn more about Selecting a simple random sample of students here:https://brainly.com/question/14526207
#SPJ12
What is the truth value of p ∨ q?
Answers
Answer:
T T T F
Step-by-step explanation:
suppose that p is true and q is true then the truth value of p∨q is true .
when p is true and q is false then the truth values of p∨q is true
when we take p is false and q is true then the truth value is p∨q is true
when we take p is false and q is false then the truth value is p∨q is false .
if any value of p or q is true then truth value of p∨q is true and if both are false then the truth value of p∨q is false .
Write a mixed number for p so that 3 1/4 x p is more than 3 1/4
Answers
The value of p just needs to be greater than 1. It could be 43 million (and 2/7, since you want a mixed number).
Ethan is conducting an experiment to determine whether a new medication is effective in reducing sneezing. He finds 1,500 volunteers with sneezing issues and divides them into 2 groups. The control group does not receive any medication; the treatment group receives the medication. The patients in the treatment group show reduced signs of sneezing. What can Ethan conclude from this experiment?
Answers
Based on results from that hypothesis testing Ethan can decide if there is a significant decrease of sneezing in the patients of treatment group or not.
However, before performing any such testing, Ethan can also observe the data and conclude on basis of his observations i.e. if considerable number of patients in treatment group show reduced signs of sneezing then the new medicine is effective in reducing sneezing.
Find the volume of a frustum of a right circular cone with height 25, lower base radius 32 and top radius 15.
Answers
There are 50 dimes in a roll of dimes, 40 nickels in a roll of nickels, and 40 quarters in a roll of quarters. Rob has 12 rolls of coins with a total value of $70.00. He has 3 more rolls of nickels than dimes. How many rolls of each coin does he have?
Answers
If your expenses are more than your income, then you have a positive net cash flow. Please select the best answer from the choices provided T F
Answers
Answer:
No, it is not a positive net cash flow. Because they are spending more than they even have which is creating debt.
Step-by-step explanation:
If your expenses are more than your income, then you have a positive net cash flow, which is false.
What is cash flow?The cash balance of liquid assets coming into and going out of a business is referred to as cash flow. Money spent and money received reflect inflows and outflows, respectively.
The cash flow is the difference between outflow and inflow.
Cash flow = out flow - inflow
If the value of the cash flow is negative that means the expense is more.
If the value of the cash flow is positive that means the income is more.
If your expenses are more than your income, then you have a positive net cash flow, which is false.
More about the cash flow link is given below.
https://brainly.com/question/10714011
#SPJ5
A coyote 43 mph while rabbit can man up to 35 mph right to equivalent expressions in then find how many more miles a coyote can run in six hours then a rabbit these rates
Answers
r = 58.3333 mpm
6c - 6r =
Answer:
(6x43)+(6x35)
6•43+6•35
48 miles
Step-by-step explanation:
Lou Harris is guaranteed a minimum of $275 weekly salary plus 5 1/4% of hs total sales. What are his total sales for a week in which his gross pay was $700
Answers
We can set up an equation for this. Let x be the amount of sales. 5.25% = 5.25/100 = 0.0525.
275+0.0525x=700
Subtract 275 from both sides:
275+0.0525x-275 = 700-275
0.0525x=425
Divide both sides by 0.0525:
0.0525x/0.0525 = 425/0.0525
x = 8095.24
Looking at the waves on an ocean beach, a girl notices that the waves reach the shore at the same time apart. She also notices that the distance between waves looks the same. In science, what do we call the distance between waves? A) amplitude B) frequency C) period D) wavelength
Answers
Answer:
D) Wavelength
Step-by-step explanation:
The correct answer is wavelength. Wavelength is defined as the distance between two identical points on the waves.
Amplitude is the maximum/minimum height reached by the wave. Frequency is defined as the number of waves passing through a point in 1 sec. Period or Time period is the reciprocal of Frequency and it represents time taken for the wave to complete its one cycle.
Therefore, from the given options, Wavelength is the best possible answer.
Answer: THE ANSWER IS D)WAVELENGTH
Step-by-step explanation:
4n less than or equal to 12
Answers
Mark’s father drove the family car 32,143 miles last year. He drove the car 29,675 miles this year.
How many fewer miles did Mark’s father drive the car this year?
A. 2,468 mi
B. 2,578 mi
C. 3,468 mi
D. 3,478 mi
Answers
Calculate the effective rate of interest (to the nearest hundredth percent) of the following Treasury bill. Given: $10,000 Treasury bill, 3.85% for 13 weeks.
Answers
.. (effective rate) = r/(1 -rt)
If we assume a 52-week year, the t = (13 weeks)/(52 weeks) = 1/4.
.. (effective rate) = 0.0385/(1 -0.0385/4) ≈ 0.038874 ≈ 3.89%
The center of a circle is located at (5, −5) . The radius of the circle is 3.
What is the equation of the circle in general form?
x2+y2−10x+10y+41=0
x2+y2+10x−10y+47=0
x2+y2+10x−10y+41=0
x2+y2−10x+10y+47=0
Answers
[tex](x - xo) {}^{2} + (y - yo) {}^{2} = r {}^{2} [/tex]
(x-5)²+(y+5)²=3²
x²-10x+25+y²+10y+25=9
x²+y²-10x+10y+41=0
Answer:
I did this twice to help anyone who might have missed from the same question I answered earlier. Have a nice day! Stay safe! And this is really good for k12 students!
Step-by-step explanation:
A woman has 7 keys. only one of them will open her door. when seh arrives at the door there is no sufficient light for her to find the correct key. if she tries one key at a time and discards the keys that don't work, what is the probability that she will open the door with the first key she picks? what is the probability that it will take exactly three attempts to open the door? suppose that the first three attempts to open the door have been unsuccessful. what is the probability that she will pick the right key the fourth time?
Answers
[tex] \frac{1}{7} [/tex]
if it takes three attempts to open the door,the probability is
[tex] \frac{1}{3} [/tex]
if the three attempts would not work
then the probability that the fourth attempt will open the door is
[tex] \frac{1}{4} [/tex]
hope this helps
The chance of the woman opening the door with the first key she picks is 1/7, or approximately 14.29%. The probability that it takes exactly three tries to find the correct key is also 1/7 or 14.29%. If the first three tries are unsuccessful, the probability that the fourth key is the correct key is 1/4, or 25%.
The probability that the woman will open the door with the first key she picks is 1 out of 7 keys, or about 14.29%. This is because each key has an equal chance of being the correct one, and there is only one correct key among the seven.
For the probability that it will take exactly three attempts to open the door, we need to consider the sequence of events: She picks a wrong key first (6 out of 7 chances), and then picks another wrong key from the remaining six (5 out of 6 chances), and then finally picks the correct key from the remaining five (1 out of 5 chances). We multiply these probabilities: (6/7) * (5/6) * (1/5) = 1/7 or about 14.29%.
If the first three attempts have been unsuccessful, we are now left with four keys, one of which is the correct one. Therefore, the probability that she will pick the right key on the fourth attempt is 1 out of 4, or 25%.
A new sidewalk will be 4 ft wide, 280 ft long, and filled to a depth of 9 inches (0.75 ft) with concrete. How many cubic yards of concrete are needed?
Answers
Answer:
Volume of the pit is [tex]31.11[/tex] cubic yards.
Step-by-step explanation:
First lets change all the values to yards.
1 yard = 3 foot
Width in yards = [tex]\frac{4}{3}[/tex] yards
Length in yards = [tex]\frac{280}{3}[/tex] yards
Depth in yards = [tex]\frac{0.75}{3}[/tex] yards
Volume of the pit = Length * Width * Depth
=[tex]\frac{4}{3} *\frac{280}{3} *\frac{0.75}{3}[/tex]
=[tex]\frac{4*280*0.75}{3*3*3}[/tex]
=[tex]\frac{840}{27}[/tex]
=[tex]31.11[/tex] cubic yards.
Volume of the pit is [tex]31.11[/tex] cubic yards.
the width of a large, rectangular-shaped tree farm is 1.9 kilometers. The length of the farm is 4.4 kilometers. What is the best estimate of the area of the farm ?
Answers
Answer:- The best estimate of the area of the farm is 8 kilometers.
Explanation:-
Given:- Width of the rectangular shaped tree farm= 1.9 kilometers
⇒Estimated width of the farm=2 kilometers [2 is the nearest integer to 1.9]
Length of the rectangular shaped tree farm=4.4 kilometers
⇒Estimated length of the farm=4 kilometers [4 is the nearest integer to 4..4]
To make estimates, we usually round the numbers the nearest integer.
Now, Estimated Area of the Farm= estimated width × estimated length
= 2×4 kilometers = 8 kilometers.
∴the best estimate of the area of the farm =8 kilometers.
Marlena is making fruit salad she will choose from 6 of the 11 different fruits offered at a fruit stand. How many different fruit salads can she make
Answers
The Correct answer is 462
uka and Anja each measured the height of their friend three times. Their friend is 59 inches tall. They recorded their measurements as shown. Luka: 59 in., 58, in., 58 in. Anja: 59.3 in., 59.6 in., 58.2 in. Which statement is true? Luka’s measurements are more precise and more accurate. Anja’s measurements are more precise and more accurate. Luka’s measurements are more precise, but Anja’s measurements are more accurate. Luka’s measurements are more accurate, but Anja’s measurements are more precise.
Answers
Your correct answer would be the (last option, option d). The reason to why Luka’s measurements are more accurate, but Anja’s measurements are more precise would be because if you have noticed, Luka's is rounded to the answer, which would make this accurate, because it's rounded. But when it is very precise, that would be different, because this would not be accurate, because it would contain a direct number in this situation.
I hope this helps you!
Luka’s measurements are more precise, but Anja’s measurements are more accurate.
What is measurement?In the study of science and mathematics, measurement is a fundamental concept. The characteristics of an object or event that we can compare to other things or events are quantified by measurement. When discussing the division of a quantity, the term "measurement" is the one that is used the most frequently. Also, when it takes a certain number of things to complete a certain task. We frequently encounter various length, weight, and time measurement types in our daily lives.
Given actual height of their friend is 59 inches
Luka recording 59 in, 58 in, 58in
Anja recording 59.3 in, 59.6 in, 58.2 in,
Accuracy is how close a measured value is to the actual value.
Precision is how close the measured values are to each other.
Accuracy:
Luka: ( 59 + 58 + 58 ) / 3 = 58.33
Anja: ( 59.3 + 59.6 + 58.2 ) / 3 = 59.03 ( closer to 59 )
Precision:
Luka : 59 - 58 = 1 ( subtract the lowest from the highest result )
Anja: 59.6 - 58.2 = 1.4
Luka's measurements are more precise, but Anja's measurements are more accurate.
Hence option C is correct.
Learn more about measurement;
https://brainly.com/question/4725561
#SPJ2
How do I solve the y= x/11- 11x
d/dx ( x/11- 11/x)
Answers
A merchant can place 8 large boxes or 10 small boxes into a carton for shipping. In one shipment, he sent a total of 96 boxes. If there are more large boxes than small boxes, how many cartons did he ship?
Answers
If I had 10 small boxes, there would need to be 86 large boxes. 86 is not evenly divisible by 8 so that doesn't work.
If I had 20 small boxes, there would be 76 large boxes. 76 is not evenly divisible by 8.
If I had 30 small boxes, there would be 66 large boxes. 66 is not evenly divisible by 8.
If I had 40 small boxes, there would be 56 large boxes. 56 is every divisible by 8.
4 cartons of 10 small boxes and 7 cartons of 8 large boxes would be needed. This is a total of 11 cartons.
a collection of dimes and nickels is worth $4.70 there are 60 coins in all how many of each are there?
Answers
Answer:
26 nickels34 dimesStep-by-step explanation:
If all were nickels, the value would be 60×$0.05 = $3.00. Their $4.70 value is $1.70 more than that. For each nickel replaced by a dime, the value goes up by $0.05, so there must be 1.70/0.05 = 34 replacements. That is, ...
... there are 34 dimes and 60-34 = 26 nickels.
_____
Using an equation
In mixture problems, it often works well to let the variable represent the quantity of the largest contributor. Here, we can let "d" represent the number of dimes, the coin with the greatest value. Then 60-d will be the number of nickels, and the total value of the coins (in dollars) is ...
... (60 -d)×0.05 + d×0.10 = 4.70
... 0.05d + 0.05×60 = 4.70 . . .simplify
... 0.05d = 4.70 -3.00 . . . . . . . subtract 3.00
... d = 1.70/0.05 = 34 . . . . . . . . divide by the coefficient of d
There are 34 dimes and 26 nickels.
The sequence of math steps should look a lot like the sequence of steps described in words, above.
_____
As a mixture problem
The average coin value is 4.70/60 = 0.07833... = 7 5/6¢. Then the proportion that are dimes is given by ...
... (7 5/6 - 5)/(10 - 5) = (2 5/6)/5 = 17/30 . . . . . 10 and 5 are the cents values of the coins in the mix
Multiplying by the 60 coins, we find (17/30)×60 = 34 are dimes. The remaining 26 are nickels.
- - -
The formula used above is ...
... proportion of highest contributor = ...
... ((mix value) - (least contributor)) / ((greatest contributor) - (least contributor))
This is the generic solution for any mixture problem.
What is 5(7h+3m) equal to?
Answers
5(7h)=35h
5(3m)=15m
you should then have 35h+15m and since you cannot combine the variables that should be your final answer
5(7h) + 5(3m)
35h + 15m
Charlene has nine different necklaces, and she wears four at a time. How many different ways can Charlene wear four necklaces?
Answers
What is the range of f(x) = (3/4)x – 4?
{y | y > –4}
{y | y > 3/4}
{y | y < –4}
{y | y < 3/4}
Answers
Answer:
A- {y | y > -4}
Step-by-step explanation:
Since the range is x - 4 the range will only go down to - 4. It will not go past the - 4 mark. Therefore the range should be anything greater then -4 to infinity.
SO-
A- {y | y > -4}