find the nth taylor polynomial for the function, centered at c. f(x) = ln(x), n = 4, c = 4
Answers
The nth Taylor polynomial for f(x) = ln(x), centered at c = 4 and n = 4 is: T₄(x) = 1.3863 + 0.25(x-4) - 0.03125(x-4)² + 0.00521(x-4)³ - 0.000244(x-4)⁴, for x > 0.
In order to find the nth Taylor polynomial for a function, centered at c, we need to follow these steps:
Firstly, we need to find the derivatives of f(x). Then, we need to evaluate these derivatives at c.
After that, we need to plug these values into the formula for the nth Taylor polynomial.
Finally, we simplify the expression to get the answer.
In the given problem, f(x) = ln(x), n = 4, c = 4.
The first four derivatives of f(x) are:
f(x) = ln(x)
f'(x) = 1/x
f''(x) = -1/x²
f'''(x) = 2/x³
f⁴(x) = -6/x⁴
To evaluate these derivatives at c = 4, we substitute 4 in place of x:
f(4) = ln(4)
= 1.3863
f'(4) = 1/4
= 0.25
f''(4) = -1/16
= -0.0625
f'''(4) = 2/64
= 0.03125
f⁴(4) = -6/256
= -0.02344
Now, we can plug these values into the formula for the nth Taylor polynomial:
Tₙ(x) = f(c) + f'(c)(x-c) + f''(c)(x-c)²/2! + ... + fⁿ(c)(x-c)ⁿ/n!
For n = 4, c = 4, we get:
T₄(x) = f(4) + f'(4)(x-4) + f''(4)(x-4)²/2! + f'''(4)(x-4)³/3! + f⁴(4)(x-4)⁴/4!
T₄(x) = 1.3863 + 0.25(x-4) - 0.0625(x-4)²/2 + 0.03125(x-4)³/6 - 0.02344(x-4)⁴/24
Therefore, the nth Taylor polynomial for f(x) = ln(x), centered at c = 4 and n = 4 is:
T₄(x) = 1.3863 + 0.25(x-4) - 0.03125(x-4)² + 0.00521(x-4)³ - 0.000244(x-4)⁴, for x > 0.
This polynomial approximates the function ln(x) to the fourth degree at x = 4.
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Related Questions
Corn is planted on a 49-acre field. The field is divided into one-acre subplots. A sample is taken from each subplot to estimate the harvest.What type of sampling is used?a. Cluster sampling is used since the field is divided into subplots, a number of subplots are selected, and every corn plant in the selected subplots is sampled.b. Stratified sampling is used since the field is divided into subplots and a random sample is taken from each subplot.c. Simple random sampling is used since each sample of corn plants of the same amount has the same chance of being selected.d. Convenience sampling is used since the corn plants closest to the barn are sampled.
Answers
The correct answer is (a) Cluster sampling is used since the field is divided into subplots, a number of subplots are selected, and every corn plant in the selected subplots is sampled.
In cluster sampling, the population is divided into groups or clusters, and a simple random sample of the clusters is selected. Then, all individuals in the selected clusters are included in the sample. In this case, the field is divided into subplots, and a sample is taken from each subplot. Therefore, the subplots are the clusters, and a sample of corn plants is taken from each selected subplot. This is cluster sampling since a number of subplots are selected, and all corn plants in the selected subplots are sampled.
Stratified sampling involves dividing the population into homogeneous groups or strata and then taking a random sample from each stratum. This is not the case here since the subplots may not be homogeneous in terms of soil type, crop history, etc.
Simple random sampling involves selecting individuals from the population randomly and independently, with each individual having an equal chance of being selected. This is not the case here since the sampling is done at the level of subplots, not individual corn plants.
Convenience sampling involves selecting individuals who are readily available and easy to sample, which is not the case here since the sampling is done from all subplots, not just the ones closest to the barn
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Round each decimal number to the nearest whole number. Then, select the best estimate for the addition equation 1.2 + 3.6 =
4.5
5
5.5
6
Answers
Answer:
4.5
Step-by-step explanation:
1.2 + 3.6 = 4.8 but when u do 4.8 -0.3 you will get 4.5
Answer:
It would be 5.5 or 5
17. Let f(x) = 2x2 + 5x + 6 and g(x) = 3x2 + 4x – 10.
a Find f(x) + g(x)
b. Find f(x) – g(x)
Answers
Step-by-step explanation:
f(x)+g(x)=(2x^2 + 5x +6) + (3x^2 +4x - 10)
Combine like terms
5x^2 + 9x -4
f(x)-g(x)=(2x^2 + 5x +6) - (3x^2 +4x - 10)
Distribute the negative
(2x^2 + 5x +6) + (-3x^2 -4x + 10)
Combine like terms
-x^2 +x +16
f(x)-g(x)= (2x^2+5x-6)-(3x^2+4x-10)= 2x^2+5x-6 (-3x^2 - 4x +10)= -x^2 +x+4
12-(3-5) to the 2 power divided by 10 divided by 5x2
Answers
Answer:
Step-by-step explanation:
let's start from the top
12-(3 - 5)^2
12 - ( 3-5)*(3-5)
12 - ( 9 - 30 +25)
remember! there's a negative sign that we must
multiply to the numbers inside the brackets
12 - 9 +30 - 25
3+30-25
8
the buttom
10/5.2
from the left side first
2*2 = 4
8/4 = 2 , and done!
Find the amount accumulated after investing a principal P for t years at an interest rate compounded k times per year. P = $3,500 r= 5% t = 10 k = 4
A = ?
Answers
Answer:
A = 5,752.60
Step-by-step explanation:
P = $3,500
r= 5%
t = 10
k = 4
A = P(1 + r/k)^kt
= 3,500(1 + 0.05/4)^4*10
= 3,500(1 + 0.0125)^40
= 3,500(1.0125)^40
= 3,500(1.6436)
= 5,752.6
A = 5,752.60
PLEASE HELP ME I AM BEING TIMED, I WILL MARK BRAINLIEST FOR WHOEVER GETS THIS RIGHT, WITH AN EXTRA 10 POINTS.
Answers
Answer:
43.98
Step-by-step explanation:
did some quick maths
c=2
\(c = 2 \times \pi \times r\)
which domain is most appropriate for a function that represents the number of items, placed into a laundry basket each day, x, for the month of january?
Answers
The domain which is the most appropriate for a function that represents the number of items, placed into a laundry basket each day is Whole numbers.
Although laundry cannot go negative in the real world, integers may. so no
Whole numbers are ideal because they are positive and don't include any laundry. so yep
Even if that isn't feasible, rational and irrational have decimal values that state that laundry can only be a certain percentage.
Whole numbers are defined as natural numbers plus zero (0). We are aware that the term "natural numbers" refers to a group of counting numbers beginning with 1, 2, 3, 4, and so forth.
Whole numbers are a collection of numbers that don't contain any fractions, decimals, or even negative integers. It is made up of zero and positive integers.
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Complete question:
Which domain is most appropriate for a function that represents
the number of items, f(x), placed into a laundry basket each day, x,
for the month of January?
(1) integers
(2) whole numbers
(3) rational numbers
(4) irrational numbers
What is the cop for y=7x
Answers
Answer:
The constant of Proportionality is 7
Step-by-step explanation:
In simpler terms, the C.O.P. is just the slope of a line as the slope is defined as the steepness of the line. Using the equation y = 7x, we can determine it is in Slope-intercept form (y = mx + b), in which 'm' is the slope. The 'b' value is actually the y-intercept which if there is no value in the 'b' location, we know the coordinates for the y-intercept are (0, 0). This deduces that the C.O.P. for y = 7x is 7.
a required question
A is the midpoint of BC. C is the midpoint of AD. E is the midpoint of CD. If CE =
3ft, how long is BD?
Answers
Answer:
18ft
Step-by-step explanation:
AC = CD = BA
CD = 2CE
BD = BA + AC + CD = 2CE + 2CE + 2CE
= 6CE
CE = 3
6 × 3 = 18
Please help :)))
1. How are rational exponents and radicals related? Explain how to rewrite an expression from rational exponent form into radical form.
2. Explain how equations involving rational exponents or radicals are solved using the rules of exponents.
3. How do extraneous solutions arise from radical equations?
i'll lichuarlly give you so many points
Answers
Every radical can be rewritten has an exponent .
Extraneous Solutions occur because squaring both sides of a square root equation results in 2 solutions (the positive and negative number).
1. Exponents that are written as fractions are referred to as rational exponents.
The top of the rational exponent is the new exponent on the radical, and the bottom of the rational exponent is the root, therefore a rational power can be reinterpreted as a radical in this fashion.
2. Separate the radical expression from the equal sign on one side. Put every every clause over there on the other side. Square both sides of the equation if the radical is a square root. Raise both sides of the equation to the third power if it is a cube root. Write an expression as a radical if the expression has a logical exponent. By examining the exponent's numerator, you may determine the power. By examining the exponent's denominator, you can get the root. Raise the radicand to the power while using the base as the radicand, and use the root as the index.
3. Extraneous Solutions appear because there are two solutions when you square the two sides of a square root equation (the positive and negative number). As a result, one of those figures will represent an extra solution, or a solution that is added but does not satisfy the initial equation.
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krytine has a weekend job advertising an upcoming play. she has two options for being paid. Option A is an hourly wage of $7.50 Option B is 5% commission on all money made at the play. she plans to work 7 hours each day on Saturday and Sunday. krystine estimates the play will make about $2,000 this weekend. Which option gives more earnings this weekend?
Answers
The Answer is: The hourly rate option of $112 is higher than the commission rate of $105.
Step-by-step explanation:
She will work 16 hours at $7.00 per hour:
16 * 7 = $112
Or she could take the 5% commission on $2,100:
2100 * .05 = $105.
The hourly rate is higher than the anticipated commission amount.
What would the height need to be for this curve to be a density curve?
startfraction 1 over 8 endfraction
startfraction 1 over 12 endfraction
startfraction 1 over 20 endfraction
1
Answers
The height needed for the curve start fraction 1 over 8 end fraction start fraction 1 over 12 end fraction start fraction 1 over 20 end fraction 1 to be a density curve is 1920.
In order for a curve to be a density curve, it must satisfy two conditions. First, the area under the curve must equal 1, representing the probability that an observation falls within the range of the variable. Second, the curve must be non-negative everywhere, representing the fact that probabilities cannot be negative.
To determine the height needed for the curve start fraction 1 over 8 end fraction start fraction 1 over 12 end fraction start fraction 1 over 20 end fraction 1 to be a density curve, we need to find the area under the curve. This can be done by integrating the function from negative infinity to infinity.
Integrating start fraction 1 over 8 end fraction start fraction 1 over 12 end fraction start fraction 1 over 20 end fraction 1 gives us:
∫ start fraction 1 over 8 end fraction start fraction 1 over 12 end fraction start fraction 1 over 20 end fraction 1 dx = (20/8) (12/8) (8/20) x = x/1920
To satisfy the first condition of a density curve, we need to set the area equal to 1:
∫ start fraction 1 over 8 end fraction start fraction 1 over 12 end fraction start fraction 1 over 20 end fraction 1 dx = 1
Therefore, we have:
1 = ∫ start fraction 1 over 8 end fraction start fraction 1 over 12 end fraction start fraction 1 over 20 end fraction 1 dx = x/1920
Solving for x gives us:
x = 1920
Thus, the height needed for the curve start fraction 1 over 8 end fraction start fraction 1 over 12 end fraction start fraction 1 over 20 end fraction 1 to be a density curve is 1920.
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Which of the following quantities is equal to the energy per second generated by fusion in the Sun's core? Select an answer and submit. For keyboard navigation, use the up/down arrow keys to select an answer. а the temperature at the Sun's photosphere. b the luminosity of the Sun's photosphere. с the temperature of the Sun's core. d the force of gravity holding the Sun together.
Answers
The quantity that is equal to the energy per second generated by fusion in the Sun's core is the temperature of the Sun's core. Therefore, the correct option is C.
The fusion reactions that occur in the core of the Sun release energy in the form of radiation and heat, and this energy is transported outwards towards the photosphere. The temperature of the core is directly related to the rate of fusion reactions and the amount of energy generated.
The luminosity of the photosphere (option b) and the force of gravity holding the Sun together (option d) are important factors in understanding the overall behavior of the Sun, but they are not directly related to the energy generated by fusion in the core. The temperature at the photosphere (option a) is also not directly related to the energy generated by fusion in the core, although it is a measure of the temperature of the outer layers of the Sun where visible light is emitted. Hence, the correct answer is option C.
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Find the equation of the straight line which passes through the point (-2,7) and Perpendicular to the line -4y+2x=-3.
Answers
Given: point (-2, 7)
The given line is perpendicular to the line we are to find.
For a line to be perpendicular to another, the slope of one will be the negative reciprocal of the other slope.
\(\begin{gathered} Equation\text{ of of the given line:} \\ -4y+2x=-3 \\ We\text{ need to write the equation in the form y = mx + b so as to get the slope} \\ -4y\text{ = -2x - 3} \\ \frac{-4y}{-4}\text{ = }\frac{-2x}{-4}-\frac{3}{-4} \\ y\text{ = }\frac{1}{2}x\text{ +}\frac{3}{4} \end{gathered}\)\(\begin{gathered} from\text{ the equation y = }\frac{1}{2}x\text{ + }\frac{3}{4} \\ m\text{ = }slope\text{ = 1/2} \\ b\text{ = }y-intercept\text{ = 3/4} \end{gathered}\)slope of the line perpendicular to the given line = negative reciprocal of the slope
slope = 1/2
reciprocal of the slope = 2/1 = 2
negative reciprocal = -2
2nd slope = -2
To get the equation of line with slope -2, we will use the point given:
\(\begin{gathered} \left(-2,\text{ 7}\right):\text{ x = -2, y = 7} \\ y\text{ = mx + b} \\ 7\text{ = -2}\left(-2\right)\text{ + b} \\ 7\text{ = 4 + b} \\ 7\text{ - 4 = b} \\ b\text{ = 3} \end{gathered}\)Th equation of line Perpendicular to the line -4y + 2x = -3 that passed through the point (-2, 7):
\(\begin{gathered} m\text{ = -2, b = 3} \\ y\text{ = mx + b} \\ \\ The\text{ equation:} \\ y\text{ = -2x + 3} \end{gathered}\)2) solve5 l9-5nl -7 =38
Answers
5 l9-5nl -7 =38
Add 7 to both sides of the equation:
5 l9-5nl -7 +7 = 38 +7
5 l 9 -5n l = 45
Divide both sides by 5
(5 l 9 -5n l ) /5 = 45/5
l 9 - 5n l = 9
Now, we have 2 solutions:
9-5n = 9
And
9-5n = -9
Solve each one
9-5n = 9
9-9 = 5n
0 = 5n
n= 0
9-5n = -9
-5n = -9-9
-5n= -18
n= -18/-5
n= 3.6
A caterer sets up a dining room for a reception with six chairs at each round table.
Which equation represents the relationship between the number of chairs,c, and the number of tables, t?
Answers
c = 6t this equation states that the number of chairs is equal to 6 times the number of tables.
What is an equation?An equation is a mathematical statement that shows that two expressions are equal. It usually contains one or more variables, which are represented by letters, and one or more constants, which are represented by numbers.
According to question:Based on the given information, we can see that the number of chairs is directly proportional to the number of tables.
When the number of tables increases, the number of chairs also increases, and vice versa.
The constant of proportionality is 6, since each table has 6 chairs. Therefore, the equation that represents the relationship between the number of chairs, c, and the number of tables, t, is:
c = 6t
This equation states that the number of chairs is equal to 6 times the number of tables.
For example, the equation 2x + 5 = 13 is an equation that contains the variable x, and states that the expression 2x + 5 is equal to 13. In this case, the goal is to find the value of x that makes the equation true, which is x = 4.
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Find the coordinates of d if e (-6,4) Is the midpoint of df and f has coordinates (-5,-3)
Answers
Answer:
Step-by-step explanation:
Let the coordinates of d be (x,y)
The midpoint of (x,y) and (-5,-3) is equal to ((-5+x)/2, (-3+y)/2)
this should be equal to the coordinates of e, (-6,4)
we have (-5/2+x/2, -3/2+y/2)
-5/2+x/2 = -6
-5 + x = -12
x = -7
-3/2+y/2 = 4
-3+y = 8
y = 11
Therefore the coordinates of d are (-7,11)
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. A circle has a diameter of 28 centimeters. Estimate the area of the circle. Use 3. 14 or 22/7 for π
Answers
The area of a circle with a diameter of 28 centimeters is equal to 615.44 square centimeters.
How to calculate the area of a circle?Mathematically, the area of a circle can be calculated by using this formula:
Area = πr²
Where:
r represents the radius of a circle.
Note: Radius = diameter/2 = 28/2 = 14 centimeters.
By substituting the radius into the formula for the area of a circle, we have the following;
Area of circle = 3.14 × 14²
Area of circle = 615.44 square centimeters.
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Stacy spent £20 on ingredients for bread.
She made 15 loaves and sold them for £1.80 each.
Calculate her percentage profit.
Answers
Answer:
35%
Step-by-step explanation:
Total made: (15)(1.80) = £27
\(\frac{27-20}{20} \times 100=35\%\)
What is the image of (-3, 4) after a dilation by a scale factor of 3 centered at the
origin?
Answers
After the dilation, the coordinates will become (- 9, 12).
What is image dilation?An enlargement or reduction of a figure that preserves shape but not size. All dilations are similar to the original figure. Dilations have a center and a scale factor.Given is the coordinate of point (- 3, 4).
The given coordinate is -
(-3, 4)
After the dilation, the coordinates will become -
(x, y) → (Kx, Ky)
The coordinates after the dilation will be -
(3 x - 3, 3 x 4)
(- 9, 12)
Therefore, after the dilation, the coordinates will become (- 9, 12).
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In the Summer Olympics in Sydney in 2000, the United States won gold silver, and bronze medals. The ratio of gold to silver medals was 5/3. The ratio of silver medals to bronze medals was 8/11. What were the total numbers of gold, silver, and bronze medals won by the United States?
Answers
Answer:
97
Step-by-step explanation:
Gold:silver
=5:3
=40:24
silver:bronze
=8:11
=24:33
total number=40+24+33=97
37=18q+1 show work pls
Answers
Answer:
37=18q+1
subtract 1 on both sides
then divide both sides by 18
q=2
Step-by-step explanation:
Answer:
q = 2Step-by-step explanation:
\(\sf 37=18q+1\)
\(\sf 18q+1=37\)
Subtract 1 from both sides:-
\(\sf 18q+1-1=37-1\)
Simplify:-
\(\sf 18q=36\)
Divide both sides by 18:-
\(\sf \cfrac{18q}{18}=\cfrac{36}{18}\)
\(\sf q=2\)
_____________________
Hope this helps!
Have a great day!
y=2x+1
answers anyone?
Answers
Answer: y= 2
Step by step: Multiply 2 and 1 to get 2
PLEASE ANSWER ASAP WILL GIVE BRAINLIST AND 29 POINTS!!!! Q: The group of points {(0, 1), (0, 5), (2, 6), (3, 3)} is not a function, but the group of points {(1, 4), (2, 7), (3, 1), (5, 7)} is a function. What do you notice about the two groups of points? What do you think it means to be a function?
Answers
Answer:
The first group of points is not a function due to repetition of elements in domain while second group of points is a function because no element of domain is repeated in any ordered pair.
Step-by-step explanation:
Why {(0, 1), (0, 5), (2, 6), (3, 3)} is not a function?
A relation is said to be a function if there is no repetition in the first elements of each ordered pair. In this group of points, 0 is repeated in two ordered pairs (0, 1), (0, 5) so it is not a function.
Why {(1, 4), (2, 7), (3, 1), (5, 7)} is a function?
The given group of points is a function because there is no repetition in first elements of each ordered pair i.e. there is not repetition in domain so it is a function
BRAINLIEST?
Answer:
The first group of points is not a function due to repetition of elements in domain while second group of points is a function because no element of domain is repeated in any ordered pair.
Step-by-step explanation:
(0, 1), (0, 5), (2, 6), (3, 3)} is not a function.
A relation is said to be a function if there is no repetition in the first elements of each ordered pair. In this group of points, 0 is repeated in two ordered pairs (0, 1), (0, 5) so it is not a function.
{(1, 4), (2, 7), (3, 1), (5, 7)} is a function.
The given group of points is a function because there is no repetition in first elements of each ordered pair i.e. there is not repetition in domain so it is a function
Carter buys 20 bottles of grapefruit juice at the corner store for a total
cost of $15. Assume each bottle of juice is the same price. If c
represents the total cost in dollars and cents of the juice for any
number, j, of bottles of juice, write a proportional equation for c in
terms of j that matches the context.
Answers
Answer:
c = 3/4 j your welcome hope this helps
convert 8.51 into a fraction
Answers
Answer:
46 or 0.46
Step-by-step explanation:
where is the the centroid of an octant of a solid sphere?
Answers
The centroid of an octant of a solid sphere is located at the point (r/3, r/3, r/3), where r is the radius of the sphere.
An octant is one-eighth of a solid sphere, so it is formed by cutting the sphere into eight equal parts along the x, y, and z axes. The centroid of a solid is the point at which the mass of the solid is evenly distributed, and for an octant of a sphere, this point is located at (r/3, r/3, r/3).
This can be determined by using the formula for the centroid of a solid, which is the average of the x, y, and z coordinates of all the points in the solid. For an octant of a sphere, the x, y, and z coordinates all range from 0 to r, so the average of these coordinates is r/3.
In conclusion, the point representing the centroid is (r/3, r/3, r/3).
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Solve. 4n - 6 (n + 1) > 12 (first blank is the inequality sign, second blank is the value) n
Answers
The solution to the inequality is: n < -9.
How to Solve an Inequality?Given the inequality statement, 4n - 6 (n + 1) > 12, to solve for the value of n, we would isolate the n to one side of the inequality as shown below:
4n - 6 (n + 1) > 12
Distribute
4n - 6n - 6 > 12
Combine like terms
-2n - 6 > 12
-2n - 6 + 6 > 12 + 6
-2n > 18
Divide both sides by -2
-2n/-2 < 18/-2
n < -9
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Solve the following system of equations by elimination. What is the value of y?
2x5y = 1
-3x+2y=-18
y = 3
y = -3
y = 1.5
y=-1.5
Answers
The value of the variable 'y' will be 3. Then the correct option is A.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The system of the linear equation is given below.
2x - 5y = 1 ...1
-3x + 2y = - 18 ...2
Multiply equation 1 by 2 and equation 2 by 5, then we have
4x - 10y = 2
-15x + 10y = - 90
Add both equations, then we have
4x - 15x = 2 - 90
11x = 88
x = 8
Then the value of the variable 'y' is calculated as,
-3 (8) + 2y = - 18
- 24 + 2y = - 18
2y = 24 - 18
2y = 6
y = 3
The worth of the variable 'y' will be 3. Then the right choice is A.
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Help me please
What is the area of the polygon
Answers
The area of the polygon in this problem is given as follows:
A = 123 mm².
How to obtain the area of a rectangle?To obtain the area of a rectangle, you need to multiply its length by its width. The formula for the area of a rectangle is:
Area = Length x Width.
The polygon in this problem is composed by two rectangles, with dimensions given as follows:
13 mm and 2 + 7 = 9 mm.13 - 10 = 3 mm and 2 mm.Hence the total area for the polygon is obtained as follows:
A = 13 x 9 + 3 x 2
A = 123 mm².
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