Part A: The common difference is 4.
Part B: The 4th term is 17 and the 5th term is 21 of this sequence.
What do you mean by arithmetic sequence?
The difference between each term in an arithmetic sequence is a constant. To put it another way, we just add the same value repeatedly, indefinitely.
According to the given question,
We have the given information:
The arithmetic sequence:
5, 9, 13,...
Now, we need to find the common difference and we will find it in this way,
The common difference is the difference between two consecutive terms in a sequence. To find it, we just need to do simple subtraction.
d = t2 - t1
= 9-5 = 4
So, the common difference is 4.
Then, we need to find the 4th and 5th terms of this sequence,
t4 = t3 + d
= 13+4
= 17
t5 = t4 + d
=17 + 4
=21
Therefore, the 4th term is 17 and the 5th term is 21.
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The common difference of this arithmetic sequence is 4 and 4th, 5th term of this arithmetic sequence is 17 and 21.
What in mathematics is an arithmetic sequence?Each phrase in an arithmetic sequence increases by adding or subtracting a specific constant, k. Each word in a geometric sequence is raised by either multiplying by or dividing by a certain constant, k.
Briefing:Part A:
The constant difference between consecutive terms of an arithmetic sequence is called the common difference and its is denoted by d.
Therefore, the common difference (d) is equal to 9 - 5 = 4.
The 4th and 5th terms of this sequence are
Part B:
Using Arithmetic progression formula,
aₙ = a + (n- 1)d
where
n = nth term
a (first term = 5
d = common difference = 4
4th term of the sequence
a₄ = a + (n- 1)d
a₄ = 5 + (4 - 1)4
a₄ = 17
5th term of the sequence
a₅ = a + (n- 1)d
a₅ = 5 + (5 - 1)4
a₅ = 21
Hence the 4th and 5th term of this arithmetic sequence is 17 and 21.
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Which entence i correct?
A. -3 > 2
B. -3 < -6
C. -3 > - 8
D. -3 > -2
The correct sentence is C, "-3 > -8."
Here's how you can determine which sentence is correct:
In sentence A, -3 is not greater than 2, so sentence A is incorrect.
In sentence B, -3 is not less than -6, so sentence B is incorrect.
In sentence C, -3 is indeed greater than -8, so sentence C is correct.
In sentence D, -3 is not greater than -2, so sentence D is incorrect.
Remember that when comparing two negative numbers, the one with the smaller absolute value is the larger negative number. For example, -8 is a larger negative number than -3 because -8 is closer to 0 (which is the smallest possible number). Similarly, -2 is a larger negative number than -3 because -2 is closer to 0.
Hence, The correct sentence is C, "-3 > -8."
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Find the curl and the divergence of the vector field.F(x, y, z) = ‹ex, exy, exyz›
The curl and the divergence of the vector field is illustrated below.
The term vector in math contains both position and magnitude.
Here we need to find the curl and the divergence of the vector field.
While we looking into the given question, we have the function
=> F(x, y, z) = <ex, exy, exyz>
AS per the concept of convergence, here we have consider that F=⟨P,Q,R⟩ is a vector field in R3 and Px, Qy, and Rz all exist here then the divergence of F is defined by as,
=> div F = Px + Qy + Rz
=> div F = ∂P/∂x + ∂Q/∂y + ∂R/∂z.
The term curl in vector field is defined as a vector operator that describes the infinitesimal circulation of a vector field in three-dimensional Euclidean space
And the curl of the vector field is calculated as,
=> curl F = (Ry−Qz)i + (Pz−Rx)j + (Qx−Py)k
=> curl F = (∂R/∂y−∂Q/∂z)i + (∂P/∂z−∂R/∂x)j + (∂Q/∂x−∂P/∂y)k.
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A group of friends wants to go to the amusement park. They have no more than $160 to spend on parking and admission. Parking is $10.50, and tickets cost $32.50 per person, including tax. Write and solve an inequality which can be used to determine x, the number of people who can go to the amusement park.
Answer:
x=4.6 answer is at most 4 people can go
Step-by-step explanation:
32.50x+10.50=160.00
- 10.50 -10.50
149.50
32.50x = 149.50
Divide 32.50 and 149.50 to find x.
x = 4.6 round down because you cant have a fraction of a person. so 4 people can go.
a linear function has an x-intercept of −8 − 8 and a y-intercept of 4 4 . which of these is an equation of the linear function?
So, y = (1/2)(x + 8) is the equation of the linear function.
To write the equation of a linear function with a given x-intercept and y-intercept, we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
In this case, we are given that the x-intercept is (-8, 0) and the y-intercept is (0, 4). We can use the coordinates of the x-intercept as (x1, y1) and the slope of the line as m to write the equation:
y - 0 = m(x - (-8))
y = m(x + 8)
We can then substitute the y-intercept into this equation to find the value of m:
4 = m(0 + 8)
4 = 8m
m = 1/2
Substituting the value of m back into the equation, we get:
y = (1/2)(x + 8)
This is the equation of the linear function.
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y - y1 = m(x - x1)
y - 0 = m(x - (-8))
y = m(x + 8)
We can then substitute the y-intercept into this equation to find the value of m:
4 = m(0 + 8)
4 = 8m
m = 1/2
Substituting the value of m back into the equation, we get:
y = (1/2)(x + 8)
How do you identify a quadrilateral?
We can identify quadrilateral because a regular polygon must have four equal sides in order to be called a quadrilateral.
Describe the quadrilateral.
Having four sides, four vertices, and four angles, a closed quadrilateral is a type of polygon. It consists of four connected non-collinear points. Quadrilaterals' internal angles always add up to 360 degrees.
According to the given question:
In a quadrilateral -
Four vertices make up each of them.Four sides comprise each side.All interior angles add up to 360 degrees.There are 2 diagonals.Both regular and irregular quadrilaterals exist.In order to be considered a quadrilateral, it must have four sides, four angles.
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I don't really understand this page, can anyone help me?
The unit conversion from celsius to fahrenheit is given by the formula
F = (9/5)C + 32.
What is unit conversion?The same attribute is expressed using a unit conversion but in a different unit of measurement. For instance, time can be expressed in minutes rather than hours, and distance can be expressed in kilometers, feet, or any other measurement unit instead of miles.
We know we can convert temperatures from celsius to fahrenheite or from fahrenheite to celsius.
The conversion of celsius to fahrenheit is given by the formula,
C = (5/9)(F - 32).
Now, we have to solve for F.
C = (5/9)F - (160/9).
Now to get rid of the fraction we'll multiply 9 to each term.
9C = 5F - 160.
5F = 9C + 160.
Solving for F we have,
F = (9/5)C + 32.
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Why binomial theorem is used?
Binomial theorem is used to calculate the roots of the equations with highest degree in advance mathematical calculation in any subject.
Binomial theorem is represented by :
( a + b )ⁿ = ⁿC₀aⁿb⁰ + ⁿC₁aⁿ⁻¹b¹ + ⁿC₂aⁿ⁻²b² +..............+ ⁿCₙa⁰bⁿ
When the value of n is higher it helps us to calculate the value of the given expression easily and accurately.I t helps us to calculate the roots of the equation with higher degree in advance mathematics.It also help us to prove many mathematical and Physics equations.It help us to determine the Weather forecast , in architecture calculations , and cost estimation in many engineering projects.Therefore, the binomial theorem help us to calculate the roots of the equations with highest degree in advance mathematical calculations in many subjects.
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-8/19+(-2)/57 solve.
[tex] \frac{ - 8}{19} + \frac{ - 2}{57} \\ \\ [/tex]
LCM of 19 and 57 is 57
so,
[tex] \frac{ - 8 \times 3}{19 \times 3} \\ + \\ \frac{ - 2 \times 1}{57 \times 1} [/tex]
[tex] \frac{ - 24}{57} + \frac{ - 2}{57} \\ [/tex]
as negative negative cancel out each other.
[tex] \frac{24}{57} + \frac{2}{57} \\ [/tex]
now simply add this
[tex] \frac{24 + 2}{57} = \\ \frac{26}{57} [/tex]
Now the answer is :: 26/57
Please help me with this
(a) When r = 12, then the value of M would be M = 504.
(b) When M = 224, then the value of r would be r = 64.
What is a direct variation?
The relationship between two values where their ratio equals a constant number is known as a direct proportion or direct variation.
In the given question, M is directly proportional to r²
M ∝ r²
M = kr²
Now When r = 2, M = 14,
k = 14/(2)²
k = 7/2
(a) When r = 12,
M = (7/2)(12)² = (7/2)*144 = 72 * 7
M = 504
(b)When M = 224,
224 = (7/2)r² = (224*2)/7 = 32 * 2
M = 64
Hence,
(a) When r = 12, then the value of M would be M = 504.
(b) When M = 224, then the value of r would be r = 64.
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Sakhi old a watch at a profit of 15%. Had he bought it at 10% le and old for R. 28 le, he would have gained 20%. Find the cot of the watch
Based on the calculation, we get that the cost of the watch is Rs 22.50.
Cost is the amount of resources, time, money, or effort that must be expended to achieve a goal or achieve something. It can refer to the financial or monetary expense of something, but it can also refer to other types of resources or effort that must be invested.
Let C be the cost of the watch.
The profit that Sakhi made on the watch was 15% of C. We can express this as:
Profit = (15/100) * C
If Sakhi had bought the watch at 10% less than the price at which he sold it and sold it for Rs. 28 le, he would have gained 20% on the sale. We can express this as:
Profit = (20/100) * (C - (10/100) * C)
We can set these two expressions for profit equal to each other and solve for C:
(15/100) * C = (20/100) * (C - (10/100) * C)
This simplifies to:
15/100 = 20/100 - (10/100)^2
Which simplifies to:
15 = 20 - (10/100)
Solving for C, we find that the cost of the watch is:
C = Rs. 22.50
Therefore, the cost of the watch is Rs. 22.50.
The missing part in the question is shown below.
Sakhi sold a watch at a profit of 15%. Had he bought it at 10% le and sold for Rs. 28 le, he would have gained 20%. Find the cost of the watch
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Find an equivalent ratio in simplest terms:
22:36
Answer:
11:18.
Step-by-step explanation:
22:36
We divide each number by their Greatest Common Factor.
The GCF of 22 and 36 is 2.
So, in simplest terms
22:36 = 11:18.
Mr. Harrell has 64 feet of fencing that he will use to build a rectangular enclosement for chickens and he will use his barn as one of of the sides of the rectangle as seen in the image. Write a function A (x) relating the area of the enclosement A and the width of the rectangle x. Then, find the width that maximizes the area. Then state the maximum area.
Answer:
A = x(64 -x)/2x = 32 ft512 ft²Step-by-step explanation:
Given 64 feet of fencing that can be used for three sides of a rectangular enclosure next to a barn wall, you want a function for area in terms of enclosure width, the width that maximizes area, and the maximum area.
(a) FunctionIf we define the width (x) as the dimension parallel to the barn wall, then the fence available for the "height" (out from the barn wall) is (64-x) in length. Half that is used on either end of the enclosure, so the area is ...
A = WH
A(x) = x(64 -x)/2
(b) Best widthWe notice this function describes a parabola that opens downward, with zeros at x=0 and x=64. The vertex (maximum) is on the line of symmetry, halfway between the zeros:
x = (0 +64)/2 = 32
The width that maximizes area is x = 32 ft.
(c) Maximum areaUsing x=32 in the area formula, we find the maximum area to be ...
A(32) = 32(64 -32)/2 = 1024/2 = 512 . . . . square feet
The maximum area is 512 square feet.
__
Additional comment
Perhaps you can see that the best width is half the length of the available fence. The other half of the fence is used for the ends of the enclosure. This is the generic solution to this kind of problem.
Why is it called line graph?
It is formed by simply drawing lines connecting the data points. Also called linear chart.
A line chart is a graphical representation of changes that occur over a period of time. A line chart has a horizontal axis called the x-axis and a vertical axis called the y-axis. The x-axis usually has a period of time over which we want to measure the quantity of a particular thing or item on the y-axis. Line charts are useful for analyzing trends, whether the quantity on the y-axis is increasing or decreasing over time. A line chart clearly shows an uptrend or a downtrend.
The line chart above represents bike sales by bike company from January to June, with the x-axis representing the time interval and the y-axis representing the number of bikes sold per month. Black dots in the graph indicate data points. A data point in a line chart represents the magnitude or number corresponding to a specific time on the x-axis. In this example, 50 bikes were sold in January. 30 bikes were also sold in February. This data can be interpreted by month using data points. Line segments connecting these individual data points show whether bike sales are trending upwards or downwards.
The key points of line charts are:
A line chart is a chart used to show changes over time as a series of data points connected by straight line segments on two axes.Line charts are also called linear chartsThis helps determine the relationship between two value sets where one data set always depends on the other.Helps show information about factors and patterns. Line charts can create expectations about outcomes for information that has not yet been obtained.In this case, the slope of the line is the most important observation. Slope indicates the slope of the line. Useful for comparing the magnitude of change between two consecutive points on the graph. For example, the steeper the slope, the greater the change in size between two consecutive points.Learn more about Linear chart:
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SON
Omar works at Walmart. Last
week he earned $500 for
working a total of 50 hours.
How much did Omar earn per
hour?
Answer:
10$
Step-by-step explanation:
Because if you divide you get 10$ per hour so if you divide 50 by 5 = 10 so your answer is 10$.
Hope this helps :D
Is 7 is a polynomial?
7 is a constant value and it is a polynomial of degree 0.
7 is a polynomial.
What is a polynomial?Polynomial is an equation written as the sum of terms of the form kx^n.
where k and n are positive integers.
We have,
7
This can be assumed as 0x³ + 0x² + 0x + 7.
This is a polynomial.
Thus,
7 is a polynomial.
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Sam recorded how many pound he gained each month for four month and recorded the reult a: one-eighth, 0. 75,two-fifth, tart fraction 5 over 6 end fraction. Lit the amount he gained each month in order from leat to greatet. A. One-eighth, two-fifth, 0. 75, tart fraction 5 over 6 end fraction B. Tart fraction 5 over 6 end fraction, one-eighth, 0. 75, two-fifth C. One-eighth, 0. 75, two-fifth, tart fraction 5 over 6 end fraction D. Two-fifth, tart fraction 5 over 6 end fraction, one-eighth, 0. 75
C. The amount he gained each month in order from least to greatest is One-eighth, 0. 75, two-fifth, tart fraction 5 over 6 end fraction.
Sam recorded how many pounds he gained each month for four months and recorded. First, we need to convert the fractions into decimals. One-eighth is equal to 0.125, two-fifth is equal to 0.4, and the tart fraction 5 over 6 end fraction is equal to 0.833.
Therefore, the amounts gained each month in order from least to greatest are 0.125, 0.75, 0.4, and 0.833.4. The correct answer is C. One-eighth, 0. 75, two-fifth, tart fraction 5 over 6 end fraction.
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Determine the range of the following graph:
Answer:
[-9,0]
Step-by-step explanation:
Look along the y inercept and find where the lines end
plus they are solid circles so it'd be closed
Answer: see below
Step-by-step explanation:
The range is the set of possible output values shown on the y-axis.
This graph's maximum y value, or the highest y value, is 0. The lowest y value is -9
R:yE[-9,0]
What is a linear graph formula?
Linear graph equations are one-degree equations. It is a straight-line equation. A linear equation with parameters a and b equal to zero has the conventional form ax + by + c = 0.
How do one express the standard form of a linear equation?
A linear equation has the following standard form: ax + by + c = 0.
Here, variables x and y and constants a, b, and c are used.
Also, a ≠ 0, and b ≠ 0.
For linear equations, the slope-intercept formula is: y=mx+b
Where m stands for the line's slope and b represents the y-intercept.
The three types of linear equations are point-slope, slope-intercept, and standard form.
When an algebraic equation is graphed, it always produces a straight line since each term has an exponent of 1 or 0. This type of equation is known as a linear equation.
Steps of drawing linear graphs are described below:
Step 1: Using the provided linear equation, determine the value of y with respect to x.
Step 2: Arrange these data in a table format.
Step 3: Create a graph using the points from the database.
Step 4: Connect the points to form a straight line.
So, ax + by + c = 0 is a linear graph formula.
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In the figure below OZ perpendicular OX and OY perpendicular OW. If a= 50, what is the value of C? A.50 B.45 C.40 D.35 E.30
Answer:
A. 50
Step-by-step explanation:
a + b = 90
b = 90-50 = 40
b + c = 90
c = 90-40 = 50
What score is 3 standard deviations above the mean?
The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
A score that is 3 standard deviations above the mean is consider as a very high score relative to the rest of the scores in the population.
What is standard deviation?The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
What is mean?The sum of all values divided by the total number of values determines the mean of a dataset.
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What are 2 digit multiples of 27?
The first 20 multiples of 27 are as follows:
27, 54, 81, 108, 135, 162, 189, 216, 243, 270, 297, 324, 351, 378, 405, 432, 459, 486, 513, and 540.
What are multiples?A multiple in mathematics is created by multiplying any number by an integer.
In other words, if b = na for some integer n, known as the multiplier, it can be said that b is a multiple of a given two numbers, a and b.
This is equivalent to stating that b/a is an integer if an is not zero.
A is known as a divisor of b when a and b are both integers and b is a multiple of a.
First 20 multiples of 27:
27, 54, 81, 108, 135, 162, 189, 216, 243, 270, 297, 324, 351, 378, 405, 432, 459, 486, 513, and 540.
Therefore, the first 20 multiples of 27 are as follows:
27, 54, 81, 108, 135, 162, 189, 216, 243, 270, 297, 324, 351, 378, 405, 432, 459, 486, 513, and 540.
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Correct question:
What are the first 20 multiples of 27?
2x + 3y = 12
what is the slope
answer : slope is -2/3
line should look like
y = mx + b
slope is m or the number next to x
slope refers to the rate or speed of something
make 2x + 3y = 12 look like y = mx + b
2x + 3y = 12
3y = -2x + 12
y = (-2x + 12)/3
y = -2/3x + 12/3
y = -2/3x + 4
slope is -2/3
b is called the y intercept
b is +4 which is where the line passes thru in the y axis at (0,4)
when x is 0 but y is not then that means the graph is not proportional
Simplify the expression a^2(m-7a^3)-m(a^2-10)
Answer:
the answer it's-7a^5+10m
10
Select all correct combinations of partial quotients that can be used to find 84 ÷ 4.
20,1
10, 10, 1
10, 5, 5, 1
O20, 4
20, 10, 1
The combinations of partial quotients that can be used to find the quotient of 84÷4 are given as follows:
10,10,120,1What is the partial quotient method?
when a division is done applying the partial quotient method, consecutive subtractions are done with n groups of the divisor. Each partial quotient is the number of groups of each term and the final quotient is the sum of the partial quotients.
The final quotient of 84÷4 as follows:
84÷4 =21
hence the sum of quotients is 21.
The possible combinations are only two.
20,10 10,10,1The other combinations are incorrect.
The circumference of a circle is 13π cm. What is the area, in square centimeters? Express your answer in terms of \piπ.
Answer:
The circumference of a circle is given by the formula $C = 2\pi r$, where $r$ is the radius of the circle. In this case, the circumference of the circle is $13\pi$ cm, so we can set up the equation $13\pi = 2\pi r$ to solve for the radius. Dividing both sides by $2\pi$, we get $r = \frac{13\pi}{2\pi} = \frac{13}{2}$ cm. The area of a circle is given by the formula $A = \pi r^2$, so the area of this circle is $A = \pi \left(\frac{13}{2}\right)^2 = \frac{169}{4}\pi$ square cm. Therefore, the area of the circle is $\frac{169}{4}\pi$ square cm.
Step-by-step explanation:
What is SSS rule in maths?
According to the SSS rule, two triangles are said to be congruent if all three sides of one triangle are equal to the corresponding three sides of the second triangle.
What is the SSS condition?According to the SSS rule, two triangles are considered to be congruent if the corresponding three sides of each triangle are equal to each other.
The triangles are congruent if all three sets of comparable sides are present.
The side-side-side shortcut is a congruence technique (SSS).
Side-angle-side (SAS), which uses two sets of sides and an angle between them that is known to be congruent, is another shortcut.
Therefore, according to the SSS rule, two triangles are said to be congruent if all three sides of one triangle are equal to the corresponding three sides of the second triangle.
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please help draw line segment AB and find its axis of symmetry
The figure is attached.
What is axis of symmetry?The axis of symmetry is a straight line that makes the shape of the object symmetrical. The axis of symmetry creates the exact reflections on each of its sides.
Given that, draw line segment AB and find its axis of symmetry
Let's first draw a line segment of length 7.3 cm.
1) Draw a line l, mark point A on it.
2) Since length is 7.3 cm, we measure 7.3 cm using ruler and compass.
3) Now, keeping compass opened the same length, we keep pointed end at point A and draw an arc on line l.
So, the required line segment is AB = 7.3 cm.
Now, we need to find its axis of symmetry.
1) Given a line segment AB.
2) Now with A as centre, and radius more than half AB, draw an arc on top and bottom of AB.
3) Now with B as centre, and same radius, draw an arc on top and bottom of AB.
4) Where the two arcs intersect above AB is point C and where the two arcs intersect below AB is point D.
Join CD.
CD is the line of symmetry of line segment AB.
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Identify the graph of f(x)=2|x+3|.
Answer:
The graph f(x)=2×+3 will have y-intercepts of (0,3) and a slope of 2.
What is the volume of a pyramid that has the same base and height if a prism has a volume of 45 m cube?
The volume of a pyramid that has the same base and height if a prism has a volume of 45 m cube is 15 cu. m.
In this question we have been given the volume of a prism which is of 45 m cube.
we need to find the volume of a pyramid that has the same base and height.
We know that the formula of the volume of prism is:
V = base area * height of prism
From given, V = 45 m^3
But as we know prism and pyramid have same base area and height.
We know that the formula for the volume of pyramid.
volume of pyramid = 1/3 * base area * height
volume of pyramid = 1/3 * V
volume of pyramid = 1/3 * 45
volume of pyramid = 15 cubic meter
Therefore, the volume of pyramid is 15 m^3
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Determine whether the following series converges or diverges. In the case of convergence, state whether the convergence is conditional or absolute. sigma^infinity_k = 0 9(-1)^k/k^4 + 2 Which test should be used to test whether the given series converges? The Test with a_k = Find lim_k rightarrow infinity a_k. lim_k rightarrow infinity a_k = Are the terms of the series nonincreasing in magnitude for k greater than some index N? A. Yes. because there is an exponent in the denominator and whenever there is an exponent in the denominator, the terms of a series are nonincreasing in magnitude. B. No. only the first two terms of the series are nonincreasing in magnitude, and the rest of the terms increase. C. No. only the first five terms of the series are nonincreasing in magnitude, and the rest of the terms increase. D. Yes. all the terms of the series are nonincreasing in magnitude. Does the series converge or diverge? A. The series diverges. B. The series converges. In the case of convergence, state whether the convergence is conditional or absolute. Choose the correct answer below. A. From the Limit Comparison Test, the series converges conditionally. B. From the Integral Test, the series converges absolutely. C. From the Limit Comparison Test, the series converges absolutely. D. From the Integral Test, the series converges conditionally. E. The series diverges.
A. From the Limit Comparison Test, the series converges conditionally.
The Limit Comparison Test can be used to determine whether a given series converges or diverges. In this case, the given series is sigma^infinity_k = 0 9(-1)^k/k^4 + 2.
To use the Limit Comparison Test, we need to compare the given series to a known series. For example, we can compare it to the series sigma^infinity_k = 1/k^4.
We can then calculate the ratio of the two series:
sigma^infinity_k = 0 9(-1)^k/k^4 + 2
sigma^infinity_k = 1/k^4
Ratio: sigma^infinity_k = 0 9(-1)^k / (1/k^4)
Since the limit of the ratio of two series is a finite number, the given series converges. However, since the ratio is not 1, it converges conditionally, not absolutely.
Therefore, the answer is A - From the Limit Comparison Test, the series converges conditionally.
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