Consider the series [tex]\frac{1}{4} +\frac{1}{3} +\frac{4}{9} +\frac{16}{27} +\frac{64}{81}[/tex]
Does the series converge or diverge?
![Consider The Series [tex]\frac{1}{4} +\frac{1}{3} +\frac{4}{9} +\frac{16}{27} +\frac{64}{81}[/tex]Does](https://brainimage.s3.us-east-005.backblazeb2.com/contents/attachments/pQYNlFqWv9TESRO1qsgtlO54jCSSftDP.png)
Answers
Answer:
Diverge
Step-by-step explanation:
Each successive term is larger than the previous one, so the series will diverge.
The given series can be condensed to
[tex]\displaystyle \frac14 + \frac13 + \frac49 + \frac{16}{27} + \frac{64}{81} + \cdots = \frac14 \left(1 + \frac43 + \frac{4^2}{3^2} + \frac{4^3}{3^3} + \cdots\right) = \frac14 \sum_{n=0}^\infty \left(\frac43\right)^n[/tex]
which is a geometric series with ratio 4/3. Since this ratio is larger than 1, the sequence of partial sums of the series diverges, so the infinite series also diverges.
We can also just the n-th term test:
[tex]\displaystyle \lim_{n\to\infty} \frac14 \left(\frac43\right)^n = \frac14 \lim_{n\to\infty} \frac{4^n}{3^n} = \infty[/tex]
since 4ⁿ > 3ⁿ for all n > 0.
Related Questions
Solve this system of linear equations. Separate
the x- and y-values with a comma.
15x = -42 - 19y
3x = -54 - 19y
Answers
15x=-42-19y
15x+19y+42=0-(1)3x=-54-19y
3x+19y+54=0--(2)Subtract both
12x-12=012x=12x=1Put in second
3(1)+19y+54=019y+57=0y=-3So
(x,y)=(1,-3)Answer:
1, -3
Step-by-step explanation:
QuestionSolve the system of linear equations:
15x = -42 - 19y3x = -54 - 19y-------------------------------------------------------------------------------------
SolutionSubtract the equations to eliminate y:
15x = -42 - 19y
- 3x = -54 - 19y
----------------------
12x = 12
⇒ x = 12 ÷ 12
⇒ x = 1
Now substitute the found value of x into one of the equations and solve for y:
⇒ 15x = -42 - 19y
⇒ 15(1) = -42 - 19y
⇒ 15 = -42 - 19y
⇒ 19y = -42 - 15
⇒ 19y = -57
⇒ y = -57 ÷ 19
⇒ y = -3
Therefore, x = 1 and y = -3
help due today this might be confusing but try to answer
Answers
Answer:
56
Step-by-step explanation:
25 times 4 = 100
14 times 4 = 56
there are 75 students on the sapphire team and 1/5 of them are in the band . how many students are in band?
Answers
Answer:
15
Step-by-step explanation:
75/5 = 15
This spilts the 75 students into 5 different groups and each one has 15 which is 1/5 of the students
A map of your town has a scale of 1 inch to 0.25 miles. There are two roads that are 5 inches apart on the map. What is the actual distance between the two roads? CLEARCHECK The actual distance between the two roads is miles.
Answers
Answer:
Step-by-step explanation:
I'm not oversimplifying this answer.
If 1 inch is .25 miles then all you have to do is multiply .25 miles by 5 inches and u get 1.25 miles.
[tex]\begin{array}{ccll} \stackrel{in}{model}&\stackrel{mi}{actual}\\ \cline{1-2} 1 & 0.25\\ 5& x \end{array} \implies \cfrac{1}{5}=\cfrac{0.25}{x}\implies x=(5)(0.25)\implies x=1.25[/tex]
Convert the angle \frac{11\pi}{12} 12 11π radians to degrees
Answers
The angle 11π/12 radian after converting it to degree it become 165 degree.
What is an angle?The measurement between the two lines is called an "Angle" when the two lines or rays converge at a common location.
We have given:
An angle 11π/12
Let's denote it with β
[tex]\rm \beta = \dfrac{11\pi}{12}[/tex]
To convert it to degree, replace π with 180°, we get:
[tex]\rm \beta = \dfrac{11\times180}{12}[/tex]
β = 165°
Thus, the angle 11π/12 radian after converting it to degree it become 165 degree.
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i need hep with my ready i really need it
Answers
Answer:
Figure JK is shown in the drawing.
Step-by-step explanation:
Auden rolled two number cubes and recorded the results. What is the experimental probability that the sum of the next two numbers rolled is greater than 5? Enter your answer as a simplified fraction.
Roll #1 Roll #2 Roll #3 Roll #4 Roll #5 Roll #6 Roll #7
5, 5 5, 6 6, 5 1, 2 2, 4 6, 5 1, 2
Answers
1 and 2 is 3 (2)
1 and 3 is 4 (3)
1 and 4 is 5 (4)
2 and 1 is 3 (5)
2 and 2 is 4 (6)
2 and 3 is 5 (7)
3 and 1 is 4 (8)
3 and 2 is 5 (9)
4 and 1 is 5 (10)
you have 36 different ways you can role and 10 of them are 5 or less so you have a 26/36 chance of rolling greater than 5
Please help ASAP
A horizontal stretch by a factor of k uses the rule: (x,y) → (kx, y) Use this rule to perform a
horizontal stretch on the figure by a scale of 3/2 on the pentagon ABCDE.
New
Original
A(-4,2)
B(-1,5)
C(3,3)
D(2,-2)
P(-2,-1)
Is the new figure similar or congruent to the original? Explain how you know
Answers
A' = (-6, 2), B' = (-3/2, 4), C' = (9/2, 3), D' = (3, -2) and E' = (-3, -1). The new figure is similar to the original figure
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
A horizontal stretch by a factor of k uses the rule: (x,y) → (kx, y). Pentagon ABCDE is stretched horizontally by a factor of 3/2, hence:
A' = (-6, 2), B' = (-3/2, 4), C' = (9/2, 3), D' = (3, -2) and E' = (-3, -1)
The new figure is similar to the original figure
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Newton Street and Oakland Avenue intersect. If the diagonal distance across the intersection is 17 meters and Newton Street is 15 meters wide, how wide is Oakland Avenue?
Answers
The graph of a quadratic equation is shown here, and the intercepts with the axes are marked. Explain how you can use the graph to write the polynomial as a product of linear factors C(x - x1)(x - x2). Be sure to state the values of x1 and x2.
Answers
The graph is a quadratic function, and the equation of the function is C(x) = (x + 4)(x - 3)
How to determine the equation of the graph?From the graph the x-intercepts are:
x = -4 and x = 3
Rewrite as:
x + 4 = 0 and x - 3 = 0
Evaluate the product of both equations
(x + 4) * (x - 3) = 0* 0
This gives
(x + 4)(x - 3) = 0
Express as a function
C(x) = (x + 4)(x - 3)
Hence, the equation of the function is C(x) = (x + 4)(x - 3)
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AB is a straight line.
Work out the size of angle x.
Not drawn accurately
132%
х
ܬ
B
Answers
Answer:
x would be 48
Step-by-step explanation:
180 (because its a straight line) take away 132 and it gives you 48
ANOTHER BIG QUESTION, 100 POINTS
Write reciprocals, opposites, the same, or negative reciprocals in each blank.
The slopes of parallel lines are _.
The slopes of perpendicular lines are _.
Find the slopes of lines AB and CD. Show your work.
Line AB goes through points A(3, 4) and B(7, 7).
Line CD goes through points C(0, 0) and D(-6, 8).
Use Parts I and II to determine if AB and CD are parallel, perpendicular, or neither. Explain your answer.
Graph and on the grid to support your answer from Part III.
Answers
Answer:
The slopes of parallel lines are the same
The slopes of perpendicular lines are negative reciprocals
Line AB
[tex]\textsf{let}\:(x_1,y_1)=(3,4)[/tex]
[tex]\textsf{let}\:(x_2,y_2)=(7,7)[/tex]
[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{7-4}{7-3}=\dfrac{3}{4}[/tex]
Line CD
[tex]\textsf{let}\:(x_1,y_1)=(0,0)[/tex]
[tex]\textsf{let}\:(x_2,y_2)=(-6,8)[/tex]
[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{8-0}{-6-0}=-\dfrac{4}{3}[/tex]
As the slopes of AB and CD are negative reciprocals of each other, lines AB and CD are perpendicular.
Select the correct answer from each drop-down menu.
The number of people who visited a state park over the last nine years is recorded in the table.
Year
2
3
4
5
6
7
8
9
Visitors
452
360
348
302
198
124
204
308 398
Answers
The visitor data is best modelled by a quadratic function
Based on the model, the state park management should plan for more than 400 visitors next year
Graphing functionsFrom the question, we are to determine the type of function that best describes the visitors data.
From the graph, we deduce that the type of function that best describes the visitors data is a quadratic function
Also, from the graph, we can say that the state park management should plan for more than 400 visitors next year
Hence, the visitor data is best modelled by a quadratic function
Based on the model, the state park management should plan for more than 400 visitors next year
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Answer:
The correct answers are Quadratic and More.
Step-by-step explanation:
I got it right on the Edmentum test.
-5 x + y = -1
-5x + y = 10
Answers
Answer:
No solution
Step-by-step explanation:
As the coefficient of x is the same, and the constant terms are different, the lines will lie parallel to each other and never intersect.
Hence, this system of equations has no solution.
Answer:
no solution
Step-by-step explanation:
the equation has no solution
Which linear inequality is represented by the graph?
Answers
Answer:
y≤2/3x+1/5
or the very first one
Step-by-step explanation:
what’s the area and perimeter for this problem?
Answers
Answer:
area:1.9×0.75÷2
perimeter:2+0.75+2.25
Use the layout of the parking lot to answer the questions. what is the total area available for cars to park? m2. if the parking spaces are compact, they have an area of 12.5 m2. how many compact parking spaces will fit in the lot? . if the parking spaces are not compact, they will be 3 meters by 5.5 meters. how many noncompact parking spaces will fit in the lot? .
Answers
The true statements are:
The total area available is 858 square metersThe number of compact parking space is 68 The number of non-compact parking space is 52The total area available for cars to parkFrom the complete question, we have the dimensions of the parking lot to be: 78 meters by 19 meters
Also, the dimension of the aisle is: 8 meters by 78 meters
The total parking area is the difference between the parking lot area and the aisle area
This gives
Parking Area = 78 * 19 - 8 * 78
Parking Area = 858
The total area available for cars to park is 858 square meters
The number of parking spaceThe number of parking lot is the quotient of the total parking area and the area of each compact
So, we have:
n = 858/12.5
n = 68.64
Remove the decimal
n = 68
Hence, the number of parking space is 68
The number of parking space for non-compact parking spaceThe number of parking lot is the quotient of the total parking area and the area of each non-compact space
So, we have:
n = 858/(5.5 * 3)
n = 52
Hence, the number of parking space is 52
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Find the value of x that will make A||B.
A
B.
14x
2x
X =
= [?]
Answers
Answer:
x = 30
Step-by-step explanation:
if A||B, then 4x + 2x must equals to 180 (interior angles of 2 parallel lines)
6x = 180
x = 30
What is the value of x?
Input Output
1 5
2 7
3 9
Х 17
Answers
to get the equation of any straight line, we simply need two points off of it, so let's use the points in the picture below.
[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{9}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{9}-\stackrel{y1}{5}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{1}}}\implies \cfrac{4}{2}\implies 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{2}(x-\stackrel{x_1}{1})[/tex]
now, if we use the last point from the table, namely (x , 17), we can see that x = x and y = 17, so let's plug those in the equation
[tex](17)-5=2(x-1)\implies 12=2x-2\implies 14=2x\implies \cfrac{14}{2}=x\implies 7=x \\\\[-0.35em] ~\dotfill\\\\ ~\hfill (7~~,~~17)~\hfill[/tex]
ANSWER FOR 25 POINTS
Answers
Answer:
2058
Step-by-step explanation:
every 5 years is 0.53 so you times that by 11 to get 7.61 and then half of .53 is .265 and round that up you get three more years so 2058 is the answer.
HELP ME WITH THIS PLEASEEE
Answers
Answer:
0.125%
Step-by-step explanation:
area of square
10*10=100
area of triangle
(5*5)/2=12.5
[tex]\frac{12.5}{100}[/tex]=0.125
A doctor observes a graph that shows the electrical activity (in volts) of the heart of a patient over a period of time (in seconds). Each spike corresponds to one heart beat. The doctor needs to calculate the heart rate of the patient in beats per minute.
What is the heart rate of this patient?
Answers
To calculate a patient's heart rate, the doctor must take into account a segment of time, such as a minute, and count the number of times the heart beats in that segment.
What is heart rate?Heart rate is a term that refers to the number of heart contractions or beats per unit of time.
Heart rate is usually measured at various points, but most commonly it is measured at the wrist, neck, or chest.
According to the above, the most common way for the doctor to establish the patient's heart rate is to count the heart beats in a segment of time such as one minute.
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60 beats per minute
I got it right on the Kahn Academy Unit Test, trust me <3
Circle A has center of (0,4) and a radius of 6, and circle B has a center of (-3,5) and a radius of 24. What steps will help show that circle A is similar to circle B?
Translate circle A using the rule (x + 3y - 1). Rotate circle A 180° about the center
Dilate circle A by a scale factor of 4
Reflect circle A over the line y = x
Answers
Answer: Translate circle A using the rule (x + 3y - 1), Dilate circle A by a scale factor of 4
Step-by-step explanation:
You need to first map the centers onto each other, then make the radii equal using a dilation.
The triangle on the right is a scaled copy of the triangle on the left. Identify the scale factor. Express your answer as a whole number or fraction in simplest form.
Answers
Step-by-step explanation:
let x=8 for a small triangle
y=10 for a big triangle
She is serving hot coffee and cold coffee in two rectangular-shaped tanks, each with dimensions width 8.75 inches, length 8.75 inches, height 23 inches.
The hot coffee has a density of 5.8 oz/in3 and the cold coffee has a density of 3.5 oz/ in3
(A) What is the volume of the coffee in each tank?
Show all math work needed to complete this problem.
(B) What is the mass of the coffee in each the tank?
Show all math work needed to complete this problem.
(C) How many tanks can be placed on a table which can support a maximum weight of 800 lb?
Explain why or why not.
Show all math work needed to complete this problem.
Answers
The volume of the coffee in each tank will be 1760. in³. The mass of cold coffee and hot coffee will be 6163.29 oz and 10213.45 oz. Then the number of the tank placed on a table is one only.
How to find the density and volume?She is serving hot coffee and cold coffee in two rectangular-shaped tanks, each with dimensions width of 8.75 inches, a length of 8.75 inches, and a height of 23 inches.
The hot coffee has a density of 5.8 oz/in³ and the cold coffee has a density of 3.5 oz/ in³.
Then the volume of the coffee in each tank will be
We know that the dimension of both tanks is equal. Then the volume will remains equal.
Volume = L × B × H
Volume = 8.75 × 8.75 × 23
Volume = 1760.9375 ≅ 1760.94 in³
Then the mass of the coffee in each the tank will be
The mass of hot coffee will be
Mass = Density × Volume
Mass = 5.8 × 1760.94
Mass = 10213.45 oz
The mass of cold coffee will be
Mass = Density × Volume
Mass = 3.5 × 1760.94
Mass = 6163.29 oz
Then the number of the tank placed on a table is one only.
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What are the dimensions of the rectangular prisms you identified in parts a and b? list dimensions for all your decompositions (sets of shapes).
Answers
The dimensions of the rectangular prisms are the side lengths of the rectangular prism
How to determine the dimensions?
A rectangular prism has the following dimensions
Length, width and height
This means that the dimensions of the rectangular prisms are the length, width and height of the prism
To determine the dimension, we simply take the value of the above terms i.e. length, width and height
Note that the question is incomplete, so I gave a general explanation
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Estimate the answers after rounding to the indicated place value
748-154 (tens)
a:610
b:600
c:500
d:590
e:900
Answers
The value of the expression after rounding to the nearest tens is 600
How to estimate the expression?The expression is given as:
748 - 154
When rounded to the nearest tens, we have:
750 - 150
Evaluate the difference
600
Hence, the value of the expression after rounding to the nearest tens is 600
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A 90 ° angle is divided into 2 angles. Find the size of the angles. 3x+15 and 2x+25
Answers
The two angles are 45 degrees.
Step-by-step explanation:
You are just halfing the 90 degree angle, so all you have to do is divide 90 by two, and you have 45.
On a coordinate plane, a triangle is shown. It has points (1, 4), (5, negative 2), and (negative 3, negative 2).
Mary thinks the triangle is equilateral. How would you support or dispute her conjecture?
Calculate the slope of all three sides, and check whether the slopes are equal.
Calculate the slope of all three sides, and check whether any slopes are reciprocals.
Use the distance formula to calculate the length of all three sides, and check whether all sides are congruent.
Use the distance formula to calculate the length of all three sides, and check whether any two sides are congruent.
Answers
Answer: C
Step-by-step explanation:
To determine if a triangle is equilateral, you need to see if all the sides have the same length.
Answer:
C
Step-by-step explanation:
Ben
The product of a number y and 3 is 6.
Answers
Answer:
y=2
Step-by-step explanation:
y*3=6
divide both sides by 3
y=2