The nth taylor polynomial for the given function is
P₄(x) = ln5 + 1/5 (x-5) - 1/25*2! (x-5)² + 2/125*3! (x-5)³ - 6/625*4! (x - 5)⁴
Given:
f(x) = ln(x)
n = 4
c = 3
nth Taylor polynomial for the function, centered at c
The Taylor series for f(x) = ln x centered at 5 is:
[tex]P_{n}(x)=f(c)+\frac{f^{'} (c)}{1!}(x-c)+ \frac{f^{''} (c)}{2!}(x-c)^{2} +\frac{f^{'''} (c)}{3!}(x-c)^{3}+.....+\frac{f^{n} (c)}{n!}(x-c)^{n}[/tex]
Since, c = 5 so,
[tex]P_{4}(x)=f(5)+\frac{f^{'} (5)}{1!}(x-5)+ \frac{f^{''} (5)}{2!}(x-5)^{2} +\frac{f^{'''} (5)}{3!}(x-5)^{3}+.....+\frac{f^{n} (5)}{n!}(x-5)^{n}[/tex]
Now
f(5) = ln 5
f'(x) = 1/x ⇒ f'(5) = 1/5
f''(x) = -1/x² ⇒ f''(5) = -1/5² = -1/25
f'''(x) = 2/x³ ⇒ f'''(5) = 2/5³ = 2/125
f''''(x) = -6/x⁴ ⇒ f (5) = -6/5⁴ = -6/625
So Taylor polynomial for n = 4 is:
P₄(x) = ln5 + 1/5 (x-5) - 1/25*2! (x-5)² + 2/125*3! (x-5)³ - 6/625*4! (x - 5)⁴
Hence,
The nth taylor polynomial for the given function is
P₄(x) = ln5 + 1/5 (x-5) - 1/25*2! (x-5)² + 2/125*3! (x-5)³ - 6/625*4! (x - 5)⁴
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For a standard normal curve, find the z-score that separates the bottom 70% from the top 30%.
Using the normal distribution, the z-score that separates the bottom 70% from the top 30% is z = 0.525.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The z-score that separates the bottom 70% from the top 30% is z with a p-value of 0.7, hence z = 0.525.
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What are the domain and range of g of x equals negative 3 times the square root of the quantity x minus 1? d: (1, [infinity]) and r: (0, [infinity]) d: [–3, [infinity]) and r: [0, [infinity]) d: (–3, [infinity]) and r: (–[infinity], 0) d: [1, [infinity]) and r: (–[infinity], 0]
Answer:
d: d [1, infinity) and r (-infinity, 0)
Step-by-step explanation:
right on the test :3 good luck dear!!
If amelia wants to make the maximum amount of money working only 22 hours per week, which company should she work for? explain your answer.
C) Company B: Using linear regression models from both data sets, she determines that it pays about $10 more.
What is linear regression?
Linear regression analysis is used to predict the value of a variable based on the value of another variable.
The variable you want to predict is called the dependent variable.
The variable you are using to predict the other variable's value is called the independent variable.
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Amelia should work for (C) company B: using linear regression models from both data sets, she determines that it pays about $10 more.
What is a linear model?The word linear model is used differently in statistics depending on the context. The most common usage is in relation to regression models, and the phrase is frequently used interchangeably with linear regression models. However, the phrase is also used with a different connotation in time series analysis.Linear regression analysis predicts the value of one variable depending on the value of another.The variable you wish to forecast is referred to as the dependent variable.The variable you are using to forecast the value of the other variable is known as the independent variable.Therefore, Amelia should work for (C) company B: using linear regression models from both data sets, she determines that it pays about $10 more.
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The complete question is given below:
If Amelia wants to make the maximum amount of money working only 22 hours per week, which company should she work for? explain your answer.
A) Company A: Using linear regression models from both data sets, she determines that it pays about $14 more.
B) Company A: Using quadratic regression models from both data sets, she determines that it pays about $5 more.
C) Company B: Using linear regression models from both data sets, she determines that it pays about $10 more.
D) Company B: Using exponential regression models from both data sets, she determines that it pays about $8 more.
The motion of an object was recorded by measuring the velocity of the object in meters per second at various times, as shown in the table.
The scatterplot below was graphed from the data in the table, where t represents the time, and v represents the velocity. Based on the scatterplot, which equation BEST represents the relationship between velocity and time?
The equation BEST represents the relationship between velocity and time is y = 2.2x + 6.
According to the statement
we have given some data in the form of graph according to the velocity per time and we have to find the relationship between the velocity and time.
So, for this purpose,
we know that the best method show the relationship is a slope intercept form.
So,
The slope intercept form is a the equation of a straight line in the form y = mx + b where m is the slope of the line and b is its y-intercept.
And
Using the coordinate points on the plane (0, 6) and (10, 28)
now we Determine the slope
Slope = 28-6/10-0
Slope = 22/10
Slope = 2.2
And then Determine the y-intercept
6 = 2.2(0) + b
b = 6
And now we have to put in the general form of the slope intercept form which is y = mx + b
Then the equation become
y = 2.2x + 6
So, The equation BEST represents the relationship between velocity and time is y = 2.2x + 6.
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Build Your Math Skills 2C, Round decimals to the nearest hundredth (0.01): 2.364
Answer:2.36
Step-by-step explanation:
Factorize: p(x)=x^2+9x^2+23x+15
Answer:
(x+1),(x+3),(x+5)
Step-by-step explanation:
may be this answer helps to solve the problems
7
of the trains are arriving late due to a train strike.
Write down the ratio of on-time trains to late trains.
15
Answer:
15:7
Step-by-step explanation:
you put the numbers in order first the number of on time trains to off time trains
subtract the sum of -5/6 and -1 3/5 from the sum of 2 2/3 and -6 2/5
- 1.3 is the number we get when we subtract the sum of -5/6 and -1 3/5 from the sum of 2 2/3 and -6 2/5. This can be obtained by finding sum separately and then subtracting them.
What is the required number:Here in the question it is given that,
subtract the sum of -5/6 and -1 3/5 from the sum of 2 2/3 and -6 2/5
By separating them as two parts
sum of -5/6 and -1 3/5 sum of 2 2/3 and -6 2/5⇒ sum of -5/6 and -1 3/5
- 5/6 + - 1 3/5 = - 5/6 + - 8/5 (∵ a b/c = (ac+b)/c(5+3)/5 = 8/5)
= (- 25 - 48)/30 (LCM = 30)
= - 73/30
⇒ sum of 2 2/3 and -6 2/5
2 2/3 + -6 2/5 = 8/3 + -32/5
= (40 - 96)/15 (LCM = 15)
= - 56/15
subtract the sum of -5/6 and -1 3/5 from the sum of 2 2/3 and -6 2/5
= (sum of 2 2/3 and -6 2/5) - (sum of -5/6 and -1 3/5)
= (- 56/15) - (- 73/30 )
= - 56/15 + 73/30
= - 112/30 + 73/30 (LCM = 30)
= - 39/30
= - 13/10
= - 1.3
Hence - 1.3 is the number we get when we subtract the sum of -5/6 and -1 3/5 from the sum of 2 2/3 and -6 2/5.
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The graph shows the amount of money that the journalism club raised for a scholarship fund over a 5-week period. If x represents the number of weeks, which function is the BEST fit for the information in this graph?
The line of best fit for the information in this graph is:
f(x) = 200x + 100.
How to find the equation of linear regression using a calculator?To find the equation, we need to insert the points (x,y) in the calculator.
For this problem, the points (t,v) are given as follows:
(2, 500), (3, 700), (4, 900), (5, 110)
Hence, inserting these points into a calculator, the equation is given by:
f(x) = 200x + 100.
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Solve the system of equations.
y equals x plus 8
y equals 3 x plus 2
Answer:
The answer is (3,11) or x = 3, y = 11
Step-by-step explanation:
:)
Answer:
(3, 11 )
Step-by-step explanation:
y = x + 8 → (1)
y = 3x + 2 → (2)
substitute y = 3x + 2 into (1)
3x + 2 = x + 8 ( subtract x from both sides )
2x + 2 = 8 ( subtract 2 from both sides )
2x = 6 ( divide both sides by 2 )
x = 3
substitute x = 3 into either of the 2 equations and solve for y
substituting into (1)
y = 3 + 8 = 11
solution is (3, 11 )
Sierra found that 15 meters is equivalent to 49.2 feet. Which of the following is an equivalent ratio?
3 to 8.84
5 to 18.22
7 to 22.96
9 to 25.32
Answer:
7 to 22.96
Step-by-step explanation:
Hello!
We can represent each ratio as a fraction:
Original: 15 to 49.2 = [tex]\frac{15}{49.2}[/tex]3 to 8.84 = [tex]\frac{3}{8.84}[/tex]5 to 18.22 = [tex]\frac{5}{18.22}[/tex]7 to 22.96 = [tex]\frac{7}{22.96}[/tex]9 to 25.32 = [tex]\frac{9}{25.32}[/tex]To find equivalent values, we can convert each fraction into a decimal by dividing them.
ConvertOriginal: [tex]\frac{15}{49.2} = 0.304878048780488[/tex][tex]\frac{3}{8.84} = 0.339366515837104[/tex][tex]\frac{5}{18.22} = 0.274423710208562[/tex][tex]\frac{7}{22.96} = 0.304878048780488[/tex][tex]\frac{9}{25.32} = 0.355450236966825[/tex]The ratio of 7 to 22.96 is equivalent to the ratio of 15 to 49.2.
Help please!
A collection of numbers M consists of all positive integers less than 20. If a collection of numbers N is a collection created by randomly choosing five numbers from M. Which of the following must be true about M?
i. The range must be at least 4
ii. The median must be at least 3
iii. The mean can be above 17
a. i only
b. ii only
c. i and ii only
d. i and iii only
The answer choice which represents statements which are correct regarding the datasets described in the task content is; Choice C; i and ii only.
Which of the answer choices represents statements which are true about the dataset described?It follows from the task content that the universal set M is described to contain all positive integers less than 20 while the collection of numbers N is created randomly by choosing five numbers from it.
Consequently, it follows that since 5 number are to be chosen, the range must be at least 4 as this follows from the extreme case scenario of selecting consecutive numbers. Hence, statement i is correct.
Also, the median must be at least three as the extreme case scenario in which numbers 1,2,3,4 and 5 are chosen still renders the median to be 3.
The mean of the five numbers cannot be above 17 because, when when numbers, 15,16,17,18 and 19 are chosen, the mean is 17 and does not exceed 17. Hence, statement iii is incorrect.
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Sketch a graph of the following rational function: h(x)= x²-1/ x³-2x²-x+2
Note that
[tex]\frac{x^2-1}{x^3 - 2x^2 -x+2}=\frac{x^2 -1}{x^2 (x-2)-(x-2)}=\frac{x^2 -1}{(x^2 -1)(x-2)}[/tex]
So, for all [tex]x \neq \pm 1[/tex], [tex]f(x)=\frac{1}{x-2}[/tex].
So, the graph looks like something like as following in the image.
solve this if u can pls!
using the numbers 5, 7, and 8 only once each, fill in the boxes to make the statement true.
Answer:
its log 5 7/8
Step-by-step explanation:
A rectangle on a coordinate plane is translated 5 units up and 3 units to the left. Which rule describes the
translation?
(x + 5, y-3)
(x + 5, y + 3)
(x, y)(x-3, y + 5)
(x, y) (x + 3, y + 5)
(x, y)
O(x, y)
Mark this and return
Save and Exit
lext
Submit
Answer:
(x+5, y-3)
Step-by-step explanation:
I would say this because when a plane is translated up it would be positive and when it's translated to the left it would be negative,
Helppp!! pleasee i put a ss!
Answer:
-20
Step-by-step explanation:
He went back 20 and not forward 20. Everyone would want a penalty if you got to go forward.
What's the total surface area of a covered box with a length of 4 ft, a width of 3 ft, and a height of 6 ft?
Answer: 108 square feet
===============================================
Work Shown:
L = 4 = length
W = 3 = width
H = 6 = height
SA = surface area of the box
SA = 2*(LW + LH + WH)
SA = 2*(4*3 + 4*6 + 3*6)
SA = 108
PLEASE HELP ITS MATH PLEASE
Answer:
y=3x-5
Step-by-step explanation:
they are parallel meaning that only the constant is changing
-2 = 3(1) - (something)
-2 = 3 - (something)
something = 5. - > that was 3+2
so y=3x+(-5)
If f(5) = 12, f ' is continuous, and 7 f '(x) dx 5 = 16, what is the value of f(7)? f(7) =
The value of function f(x) at x = 7 is f(7) = 28
For given question,
we have been given the value of function f(x) at x = 5.
f(5) = 12
We have been given that f'(x) is continuous on 5 and 7
Also, [tex]\int\limits^7_5 {f(x)} \, dx =16[/tex]
We need to find the value of f(7)
Since ∀x, f'(x) = f'(x), f is a primitive function of f' .
And f ' is continuous
[tex]\Rightarrow \int\limits^7_5 {f(x)} \, dx =16\\\\\Rightarrow [f(x)]_5^7=16[/tex]
⇒ [f(7) - f(5)] = 16
⇒ f(7) - 12 = 16
⇒ f(7) = 16 + 12
⇒ f(7) = 28
Therefore, the value of function f(x) at x = 7 is f(7) = 28
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(d) The perimeter of the figure below is equal to 150 cm.
X
x+6
x+5
x+1
x+8
X+4
What is the length of the longest side of the polygon?
Use mathematics to explain how you determined your answer.
Use words, symbols, or both in your explanation.
Based on the given perimeter of the polygon and the length of each side; the length of the longest side of the polygon is 29 cm
Perimeter of a polygonPerimeter = 150 cmPerimeter of the polygon = x + (x + 6) + (x + 5) + (x + 1) + (x + 8) + (x + 4)
150 = x + x + 6 + x + 5 + x + 1 + x + 8 + x + 4
150 = 6x + 24
150 - 24 = 6x
126 = 6x
x = 126/6
x = 21
The longest side of the polygon is (x + 8)
= 21 + 8
= 29 cm
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1. If R = 32 - 11 (OC+2y). then find R when: x=2 and y=4
The correct equation says to find R = 32 - 11 (X+2y). This gives us the value of -78.
How to solve for the equation belowWe have this
R = 32 - 11 (X+2y)
we have the following values for x and y as 2 and 4 respectively.
What we have to do would be to find the value of R after we have put in these values in the equation.
To do this, we would then have:
R = 32 - 11(2 + 2*4)
R = 32 -11(2+8)
R = 32 - 11 * 10
R = 32 - 110
This would give us the value that says
R = -78
Hence the value of R is given as -78
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please help
the line ABC is tangent to a circle at B centre O with diameter EB the angle DAB = 28
(a) ABE=
(b) EDB=
(c) AOB=
(d) BOD=
(e) OBD=
(f)DBC=
Answer:
A 90°
B 90°
C 62°
D 118°
Hopefully this helps u
tan 45- cos ~ 60° = x. Sin 45. ta
The trigonometric values we require :
[tex]\begin{tabular}{c | l}trigonometric value & numerical value \\\cline{1-2}tan 45^{o}& 1 \\cos 60^{o} & 0.5 \\sin 45^{o} & 1 \div \sqrt{2}\end{tabular}[/tex]
Now, let's solve for x.
tan 45° - cos 60° = x (sin 45°)
[tex]\mathrm {1 - \frac{1}{2} = x (\frac{1}{\sqrt{2}})}[/tex]
[tex]\mathrm {\frac{1}{2} = \frac{x}{\sqrt{2}}}[/tex]
[tex]\mathrm {x = \frac{\sqrt{2}}{2}}[/tex]
[tex]\mathrm {x = \frac{1}{\sqrt{2}}}[/tex]
The value of x is 1/√2.
I hope it helped you solve the problem
Good luck on your studies!
Rose and Tyler divided their 1.5kg of pizza
dough in the ratio 2:3.
How much did Rose receive?
Answer:
0.6kg
Step-by-step explanation:
first roses share becomes 2:5
then you change the kilograms into grams for an easier working
then you multiply 2:5 by 1500g to get roses share
While playing baseball, sofia takes note of the extreme vectors for which she bats. what is the angle between her two extreme bats? extreme 1: <-8, 12> extreme: 2: <13, 15>
The angle between the two extreme vectors of Sofia bats is 74.60 degrees.
In this question,
The angle between two vectors will be deferred by a single point, which is called as the shortest angle at which we have to turn around one of the vectors to the position of co-directional with another vector.
The extreme vectors of Sofia bats are [tex]\vec u = < -8, 12 >[/tex] and [tex]\vec v = < -8, 12 >[/tex]
The angle between the vectors is
[tex]\theta = cos^{-1} \frac{\vec u.\vec v}{||\vec u|| ||\vec v||}[/tex]
The dot product is calculated as
[tex]\vec u. \vec v = (-8)(13)+(12)(15)[/tex]
⇒ [tex]-104+180[/tex]
⇒ 76
The magnitude can be calculated as
[tex]||\vec u|| = \sqrt{(-8 )^{2} +(12)^{2} }[/tex]
⇒ [tex]\sqrt{64+144}[/tex]
⇒ [tex]\sqrt{208}[/tex]
[tex]||\vec v|| = \sqrt{(13 )^{2} +(15)^{2} }[/tex]
⇒ [tex]\sqrt{169+225}[/tex]
⇒ [tex]\sqrt{394}[/tex]
Thus the angle between the vectors is
[tex]\theta = cos^{-1} \frac{76}{(\sqrt{208} )(\sqrt{394} )}[/tex]
⇒ [tex]\theta = cos^{-1} \frac{76}{\sqrt{81952} }[/tex]
⇒ [tex]\theta = cos^{-1} \frac{76}{286.27 }[/tex]
⇒ [tex]\theta = cos^{-1} (0.2654)[/tex]
⇒ [tex]\theta=74.60[/tex]
Hence we can conclude that the angle between the two extreme vectors of Sofia bats is 74.60 degrees.
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Are the two triangles similar?
Answer:
Yes
Step-by-step explanation:
The missing angle in triangle DER is 42 (as angles in a triangle add up to 180) and the missing angle in TVA (LOKI lol ) is 110 (as angles in a triangle add up to 180) .
Since all angles are equal the triangles must be similar .
Hope this helped and have a good day
what value ofx is in the solution set of 3(x-4)>5x +2?
[tex]\boldsymbol{\sf{3(x-4) > 5x +2 }}[/tex]
Use the distributive property to multiply 3 by x−4.
[tex]\boldsymbol{\sf{3x-12 > 5x+2 }}[/tex]
Subtract 5x on both sides.
[tex]\boldsymbol{\sf{3x-12-5x > 2 } }[/tex]
Combine 3x and −5x to get −2x.
[tex]\boldsymbol{\sf{-2x-12 > 2 }}[/tex]
Add 12 to both sides.
[tex]\boldsymbol{\sf{-2x > 2+12 \ \longmapsto \ \ [Add \ 2 +12]}}[/tex]
[tex]\boldsymbol{\sf{-2x > 14}}[/tex]
Divide both sides by −2. Since −2 is < 0, the inequality direction is changed.
[tex]\boldsymbol{\sf{x < \dfrac{14}{-2} \ \ \longmapsto \ \ \ [Split]}}[/tex]
[tex]\boxed{\boldsymbol{\sf{x < -7 }}}[/tex]
So in the inequality 3(x-4)>5x +2, the value of x is -7.
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https://brainly.com/question/17070130Troy travels 100 miles in 2 hours. Find the unit rate of speed by filling in the missing number.
100 miles/ 2hours = ? miles/ 1 hour = ? miles/hour
Answer:
50 miles/1 hour = 50 miles/hour
Step-by-step explanation:
The fraction is reduced by dividing numerator and denominator by their common factor of 2.
100 miles / (2 hours) = 50 miles/ (1 hour) = 50 miles/hour
Which statements are true for the functions g(x) = x2 and h(x) = –x2 ? Check all that apply.
For any value of x, g(x) will always be greater than h(x).
For any value of x, h(x) will always be greater than g(x).
g(x) > h(x) for x = -1.
g(x) < h(x) for x = 3.
For positive values of x, g(x) > h(x).
For negative values of x, g(x) > h(x).
The answer choice which is correct regarding the two functions is; For any value of x, g(x) will always be greater than h(x).
Which statement is true for the functions?It follows from the task content that the functions given are; g(x) = x² and h(x) = –x².
On this note, since all values of x return a positive value for g(x) due to the square, it follows that the corresponding value of h(x) is always lesser.
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Choose the most appropriate translation of the english sentence. the amount of time spent spent driving is 5 hours
The most appropriate translation of the English sentence. the amount of time spent driving (which depends on the speed of the car) is 5 hours. is time(speed) = 5, making option C the right choice.
The time spent by a body covering a certain distance at a certain speed is given as time = distance/speed.
In the question, we are asked to translate the English sentence, :"the amount of time spent driving (which depends on the speed of the car) is 5 hours".
In the given sentence, the time spent driving is given to be 5 hours, depending on the speed of the car.
Thus, the time can be shown as a function of speed with a value of 5.
Thus, the translation can be, time(speed) = 5.
Thus, the most appropriate translation of the English sentence. the amount of time spent driving (which depends on the speed of the car) is 5 hours. is time(speed) = 5, making option C the right choice.
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The provided question is incomplete. The complete question is:
"Choose the most appropriate translation of the English sentence. the amount of time spent driving (which depends on the speed of the car) is 5 hours.
a. speed(time) = 5
b. time(5) = 50 mph
c. time(speed) = 5
d. time(speed) > 0"