Can someone help me out with this math problem and weather it converges or diverges?
Answers
The given infinite series is divergent.
Given,
[tex]\sum \limits^\infty_{n=1 }{(-1)^{n+1}\frac{3n^2+n+1}{2n^2-1}}[/tex]
it is in the form,
[tex]\sum \limits^\infty_{n=1 }{(-1)^{n+1}\ a_n[/tex]
If the series is convergent then it satisfies,
i)[tex]b_{n+1}\ \leq\ b_n\ for\ all\ n[/tex]
ii)[tex]\lim_{n \to \infty} a_n =0[/tex]
if any of the above condition dissatisfies then the series is divergent
First check the 2nd condition,
[tex]\lim_{n \to \infty}\frac{3n^2+n+1}{2n^2-1}}\\\\= \lim_{n \to \infty}\frac{n^2(3+\frac{1}{n}+\frac{1}{n^2})}{n^2(2-\frac{1}{n^2})}}\\\\=\frac{3+0+0}{2-0}\\\\=\frac{3}{2}[/tex]
Here, [tex]\lim_{n \to \infty} a_n \neq 0[/tex]
Thus, the given series is divergent.
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Related Questions
14 11/12 + 3 1/6 need help
Answers
Answer:
18.0833333333
Step-by-step explanation:
online calculator
Evaluate the exponential functions
Answers
I hope this helps. Have a great rest of your day!
The number of computer security breaches is expected to increase at a yearly rate of 86%
Use the exponential growth model to determine the equivalent monthly rate.
Enter the rate, to the nearest tenth of a percent, in the box.
____%
Answers
Answer:
The population is expected to grow at a rate of 1.36% each year. What is the population of the town in 2006? Round your answer to the nearest whole number.
Step-by-step explanation:
Factor of 14a–35? Pls Ty
Answers
Consider the equation and the following ordered pairs: (6,y) and (x,1).
y=−2x+5
Answers
The values of x and y are 2 and -7 respectively, this forms an ordered pair of (6,-7) and (2,1).
What are the the values of x and y to complete the given ordered pair?Given the equation and ordered pair the question;
y = -2x + 5Point: (6,y) Point; (x,1)To determine, the y-value, plug the x-value into the equation and solve for y.
y = -2x + 5
Plug in x = 6
y = -2( 6 ) + 5
y = -12 + 5
y = -7
Determine the x-value by plunging in the y-value into the equation and solve for x.
y = -2x + 5
Plug in y = 1
1 = -2x + 5
1 + 2x = 5
2x = 5 - 1
2x = 4
x = 4/2
x = 2.
Therefore, the ordered pair are (6,-7) and (2,1).
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Help!
WILL MARK BRAINLYIST!
Graph the function f(x) = [x + 3]
over the interval -2 ≤ x ≤ 2
Answers
Answer:
The graph of a function f is the set of points which satisfy the equation y = f(x). ... However, of these two answers, only x = −2 fits in the domain.
Step-by-step explanation:
(6, y) and (-8, 4); slope: 1/7
Answers
For the given points (6, y) and (-8, 4) having slope = 1/7 the value of y = 10.
What is the slope of a line?
A line's slope, also known as its gradient, is defined as the value of a line's steepness or direction in a coordinate plane. Slope can be calculated using various methods given a line equation or the coordinates of points on a straight line.
If P(a, b) and Q(c, d) are two given points on a coordinate plane, then the slope of line PQ can be computed using the formula
[tex]Slope(m)=\frac{d - b}{ c - a}[/tex]
The given points are (6, y) and (-8, 4).
and the slope of the line is given as m = 7.
By using the slope of a line formula, we get
[tex]m = \frac{8-y}{-8-7}\\\\ \frac{1}{7}= \frac{8-y}{-8-7}\\\\\frac{1}{7}= \frac{8-y}{-14}\\\\\\8-y=-2\\y=8+2\\y=10[/tex]
Hence, the value of y is 10.
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A driveway is being surfaced with concrete pavers in the shape of regular hexagons. If the driveway is 24-ft by 26-ft rectangle, and the pavers measure 6 inches across the flats, how many pavers are needed?To surface a driveway about _ pavers are needed
Answers
The number of pavers required is 961.
The area is the region defined by an object's shape. The area of a shape is the space covered by a figure or any two-dimensional geometric shape in a plane.
Given data
A driveway is being surfaced with concrete pavers in the shape of regular hexagons. If the driveway is a 24-by-26-foot rectangle with pavers 6 inches wide across the flats.
We have to determine how many pavers are needed
We know that area of a regular hexagon
A = (3√3)/2 a^2
= (3√3)/2 〖(6)〗^2
= (3 x 1.732)/2 x 36
= 93.528 sq.inches
Now area of rectangle
= l x w
= 24 x 26 x (12)2 (1feet = 12 inches)
= 89856 sq.inches
Now pavers required
= 89856/93.528
= 960.73
= 961
Therefore the number of pavers required is 961.
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Need help solving this problem, please and thank you
Answers
6x35=210
What is the first step to find the quotient of a long division problem?
Divide the terms with the highest degree
Multiply terms by the divisor
Subtract the product from the dividend
Place the result in the quotient
Answers
The first step to find the quotient of a long division problem is to Divide the terms with highest degreee
What is quotient of a long division?A quotient is a quantity produced by the division of two numbers. For example 16/4 ,the number that is being divided (in this case, 16) is called the dividend, and the number that it is being divided by (in this case, 4) is called the divisor. The result of the division(5) is the quotient.
The step that is needed to find a quotient of a division are
1.Divide the terms with the highest degree
2.Multiply terms by the divisor
3.Place the result in the quotient
4. Subtract the product from the dividend
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Find the circumference and the area of a circle with diameter 7 cm.
Answers
The circumference of the circle is 21.98cm and the area of the circle is 38.465 square cm.
Circumference of the circle:
The Circumference (also known as) perimeter of circle = 2πR
where,
R is the radius of the circle
π is the mathematical constant with an approximate value is 3.14.
Area of circle:
The formula to find the area of the circle is;
A = πr²
Where r represents the radius of the circle.
Given,
The diameter of the circle is 7 cm.
Here we need to find the circumference and the area of a circle.
Here we have the value of diameter, in order to find the circumference we have to find the value of radius that can be derived by dividing the diameter by 2.
So, the radius is
=> 7/2 = 3.5
Now the circumference of the circle is calculated as,
C = 2 x π x 3.5
When the value of π = 3.14
Therefore, the circumference of the given circle is,
=> C = 2 x 3.14 x 3.5
=> C = 21.98
Now, the area of the circle is,
=> A = π x (3.5)²
=> A = 3.14 x 12.25
=> 38.465
Therefore, the area of the circle is 38.465 square cm.
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48 - (3 c+4)=4(c+5)+3 c=???
Answers
Answer in multiple forms depending on what needed
Answer:
c = 3
Step-by-step explanation:
48- (3c+4)=4(c+5)+3
48-3c-4=4(c+5)+3 Distributed the - sign
48 -3c -4= 4c+20 +3 Distributed the 4
44-3c =4c+23 Combined like terms
21-3c=4c Subtract 23 from both sides
21=7c Add 3c to both sides
3=c
What is the first step needed to solve 4 over 7 multiplied by x minus 5 equals negative 13 ? (1 point)
Group of answer choices
Add 5 to both sides
Multiply both sides by 4
Subtract 13 from both sides
Divide both sides by 7
Answers
Answer:add 5 to both sides
Step-by-step explanation:
A submarine was 400 meters below sea level it then moved to 583 meters below sea level. How many meters did the submarine descend? how did you get the answer?
Answers
Answer:
Step-by-step explanation:
You subtract 583 from 400 (400-583)
Then you get 183
According to the graph provided, the weight for someone who is 1.4 meters tall is predicted to be close to kilograms
Answers
According to the scatterplot (graph) provided, the weight for someone who is 1.4 meters tall is predicted to be 34.8 kilograms.
What is a scatterplot?A scatterplot is also referred to as scatter diagram, scattergram, or scatter chart and it can be defined as a type of graph which is used for the graphical representation of the values of two (2) variables, with the resulting points showing any association between the data set.
For this exercise, the height (M) was plotted on the x-axis of the scatterplot (graph) while the weight (in kg) would be plotted on the y-axis of the scatterplot (graph).
From the scatterplot which models the relationship between the height (M) and weight (in kg) of a person, an equation for the line of best fit is given by:
Weight, kg = -114.3 + 106.5M
When M = 1.4 meters, we have the following weight:
Weight, kg = -114.3 + 106.5(1.4)
Weight, kg = -114.3 + 149.1
Weight, kg = 34.8 kg.
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Complete Question:
According to the graph provided, the weight for someone who is 1.5 meters tall is predicted to be close to ____ kilograms.
what did i do wrong? how do i do y-int?
Answers
The laundry room at a hotel sent 160 bath
towels and 64 washcloths to the most rooms
they could so that each room received the
same number of each type of towel. How
many bath towels and how many washcloths
went to each room?
Answers
Answer:
5 bath towels
2 washcloths
Step-by-step explanation:
160 = 2⁵ × 5
64 = 2⁶
HCF= 2⁵ = 32
160 ÷ 32 = 5
64 ÷ 32 = 2
Colton made a scale drawing of a city park. In real life, the soccer field is 90 meters long.
It is 18 millimeters long in the drawing. What scale did Colton use?
Answers
By using unitary method it is obtained that -
Scale used my Colton = 1 : 500
What is unitary method?
Unitary method is the process in which the value of single unit can be calculated from the value of multiple unit and the value of multiple unit can be calculated from the value of single unit. Sometimes Value of single unit can be less than the value of multiple unit. For example - The relation between the cost of a commodity and the quantity of the commodity
Sometimes Value of single unit can be more than the value of multiple unit. For example - The relation between the number of men and the number of days taken by those men to do a certain job.
Here unitary method is used
18 mm long field in the drawing is equivalent to 9000 mm long field in real
1 mm long field in the drawing is equivalent to [tex]\frac{9000}{18}[/tex] mm long field in real
1 mm long field in the drawing is equivalent to 500 mm long field in real
Scale used by Colton 1 : 500
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PLEASE HELP ME ASAP!!!
The stem-and-leaf plot displays the distances that a heavy ball was thrown in feet.
2 0, 1, 4
3 1, 2, 6
4 1, 3, 7
5 1, 1
6 5
Key: 3|2 means 3.2
What is the mean, and what does it tell you in terms of the problem?
Answers
The mean of the data is 3.85 using the stem-and-leaf plot.
It means the average feet that the heavy ball was thrown is 3.85 feet, which is the typical number.
How to calculate the Mean of a Data?To find the mean of a data set that is represented by a stem-and-leaf plot, first, list out all the data values that are represented on the stem-and-leaf plot, add all the values, and divide by the number of values that were represented on the stem-and-leaf plot.
Given the stem-and-leaf plot, using the key, the data points represented are:
2.0, 2.1, 2.4, 3.1, 3.2, 3.6, 4.1, 4.3, 4.7, 5.1, 5.1, 6.5
Mean = [2.0 + 2.1 + 2.4 + 3.1 + 3.2 + 3.6 + 4.1 + 4.3 + 4.7 + 5.1 + 5.1 + 6.5]/12
Mean = 46.2/12
Mean = 3.85 feet
The mean of 3.85 feet means that the average distance that the heavy ball was thrown in feet is 3.85.
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4. Enrique collected 152 recyclable bottles, and
Latasha collected brecyclable bottles. Write
an expression for the number of bottles they
collected altogether.
Answers
The required expression is Total = 152+x .
What is expression ?
Mathematical statements called expressions must contain a minimum of two terms with either numbers, variables, or both, joined by an operator. The four different types of mathematical operators are addition, subtraction, multiplication, and division. For instance, the expression x + y is an expression where x and y are terms with an addition operator between them. Mathematical expressions can be divided into two categories: algebraic expressions, which include both numbers and variables, and numerical expressions, which solely contain numbers.
Here,
The number of bottles Enrique collected = 152
Let us take number of bottles collected by Latasha as x. Then,
Total number of bottles collected by the is ,
=> Total = Number of bottles collected + Number of bottle collected
by Enrique By Latasha.
=> Total = 152+x
Hence the required expression is Total = 152+x.
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pls help! thanks in advance :)
Answers
Equation of the perpendicular line in slope intercept form is [tex]y = \frac{5}{2}x + 2[/tex]
Option A is correct
What is equation of line in slope intercept form?
The most general form of equation of line in slope intercept form is given by y = mx + c
Where m is the slope of the line and c is the y intercept of the line.
Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.
If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by
m = [tex]tan\theta[/tex]
The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.
The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.
Here, the given line is
2x + 5y = 10
5y = -2x + 10
[tex]y = -\frac{2}{5}x + \frac{10}{5}\\y = -\frac{2}{5}x + 2[/tex]
Slope of the given line is [tex]-\frac{2}{5}[/tex]
Slope of the line perpendicular to this given line is [tex]\frac{5}{2}[/tex]
The line passes through (-2, -3)
Equation of the required line
[tex]y - (-3) = \frac{5}{2}(x - (-2))\\y + 3 = \frac{5}{2}(x + 2)\\2y + 6 = 5x + 10\\2y = 5x + 10 - 6\\2y = 5x + 4\\y = \frac{5}{2}x + \frac{4}{2}\\y = \frac{5}{2}x + 2[/tex]
Equation of the perpendicular line in slope intercept form is [tex]y = \frac{5}{2}x + 2[/tex]
Option A is correct
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Question 2b answer please
and working out
Answers
Answer:
20 mph
Step-by-step explanation:
If it took the car originally 12 minutes to travel the road with an average speed of 60 mph. Than you would just divide the average speed by three because it is taking 3 times the amount of time than it would originally.
36/12=3
60/3=20
20 mph
in exercises 10-11, find the value of x so that the function has the given value.
10. m(x) = -3/5x - 4; m(x) = 2
11. w(x) = 5/6x - 3; w(x) = -18
Answers
The value of x so the the the function has the given value is as follows:
m(x) = 2; x = - 10w(x) = - 18; x = - 18How to find the value of the input of a function?A function relates an input to an output.
In other words, a function is a special relationship among the inputs and their outputs codomain) where each input has exactly one output value.
Therefore, let's find the value of x so that the function has the given values.
m(x) = -3/5x - 4; m(x) = 2
let's find the value of x when m(x) = 2
2 = - 3/5x - 4
2 + 4 = - 3/5x
6 = - 3/5 x
cross multiply
-3x = 30
x = 30 / - 3
Hence,
x = - 10
w(x) = 5/6x - 3; w(x) = -18
let's find the value of x when w(x) = -18
- 18 = 5/6x - 3
- 18 + 3 = 5 / 6 x
- 15 = 5 / 6 x
5x = - 90
x = -90 / 5
Hence,
x = - 18
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At Happy Tails Animal Boarding, cat food and dog food is purchased weekly, Last week, Karen purchased 6 bags of cat food and 9 bags of dog food for a total of 117$. This week, she purchased 4 bags of cat food and 7 bags of dog food for a total of 87$.
Assuming the prices for cat and dog food have not changed over the past two weeks, find and solve the system of equations which can be used to determine the cost of a bag of cat food, c, and the cost of a bag of dog food, d.
c=cost of a bag of cat food
d=cost of a bag of dog food
Write Two Equation
?
?
Answers
One bag of cat food costs $6 and one bag of dog food costs $9.
What is system of equations?
A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.
The problem states that c equals the cost of bag of cat food and d equals the cost of bag of dog food.
Last week she paid $117 for 6 bags of cat food and 9 bags of dog food.
Therefore, the equation becomes,
6c + 9d = 117 ..(1)
This week she paid $87 for 4 bags of cat food and 7 bags of dog food.
Therefore, the equation becomes,
4c + 7d = 87 ..(2)
Now to solve the system of equations
To solve the first equation for c.
6c + 9d = 117
6c = 117 - 9d
[tex]c = \frac{117}{6}-\frac{9d}{6}[/tex]
Plug value of c in equation (2).
[tex]4(\frac{117}{6}-\frac{9d}{6}) +7d = 87\\78 - 6d + 7d = 87\\d = 87-78\\d = 9[/tex]
Plug d = 9 in equation (1)
6c + 9(d) = 117
6c + 9(9) = 117
6c + 81 = 117
6c = 117 - 81
6c = 36
c = 6
Hence, one bag of cat food costs $6 and one bag of dog food costs $9.
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I NEED HEEEEELP!!
There are 5 cockroaches crawling on each square meter of the front of this building. How many cockroaches are crawling on the front of the building?
Please, show your work and explain. TYSM!! ^^
Answers
There are 855 cockroaches crawling on the front of the building
What is an equation?An equation is an expression showing the relationship between two or more numbers and variables.
The population density is given as:
Population density = total animals / area occupied
Given that, the population density of the cockroaches is 5 cockroaches per square meter.
The area of the building = area of triangle + area of square
Area of building = (1/2) * (24 - 9)(12) + (9 * 9) = 90 + 81 = 171 m²
Population density = total animals / area occupied
5 cockroaches per square meter = Total cockroaches / 171 m²
Total cockroaches = 855
There are 855 cockroaches
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The money used in Switzerland is called
the Franc. The exchange rate is $5 for 6
Francs. Find how many dollars you would
receive if you exchanged 18 Francs.
Answers
put them in form of fractions where
$5/6 francs = x(unknown $)/18 francs
then cross multiply numbers
6 times x = 6x
5(18)=90
divde both by 6
90/6=15
6x/6=x
x=15
furthermore to prove it 15/18 can be reduced to 5/6
Critical thinking questions:
Write a system of equations with the solution (4, -3).
Answers
Answer: (4,-3)
Step-by-step explanation:
4x+5y=1 (1)
3x-2y=18 (2)
Multiply both parts of equation (1) by 2 and both parts of equation (2) by 5:
8x+10y=2
15x-10y=90
Sum these equations:
23x=92
Divide both parts of the equation by 23:
x=4
Substitute the value of x=4 into equation (1):
4(4)+5y=1
16+5y=1
16+5y-16=1-16
5y=-15
Divide both parts of the equation by 5:
y=-3
Thus, (4,-3)
Hello, please answer this correctly and you will get 5 stars and 20 points.
Answers
Answer:
Step-by-step explanation:
90
Oliver saves 10% of his weekly earnings for living expenses. He usually makes $520 each week. This week he made 10% more. Oliver incorrectly claims that he has $520 left for spending money this week.
Answers
Answer:
10% of $520
=$52
Money made this week :
$520+$52=$572
Saving:
10% of $572
=$57.2
Money left:
$572-$57.2=$514.8
Please mark as brainliest
Answer: We have been given that,
Oliver's weekly earnings = $520
His earnings this week = 10% of $520 +$520
= $520+$52= $572
As he saves 10% of his weekly earnings so he would have been left with
= 10% of $572
= $57.2
So, he only has $52.7 left for spending money this week
Step-by-step explanation:
Which of the quotients is equivalent to -5/8? Select all that apply.
Answers
The equivalent quotient to -5/8 are; -5/8 and .5/-8.
The correct answer options are options A and C
How to find equivalent quotient?A quotient is the number resulting from the division of one number by another. For instance, the quotient of 12 divided by 4 is 3.
A divisor number or expression that another is to be divided by. For instance, in "42 ÷ 3" the divisor is the 3.
Dividend is a number or expression that is to be divided by another. For instance, In "42 ÷ 3" the dividend is the 42.
Complete question:
Given options:
A. -5/8
True
B. 5/8
False
C.5/-8
True
D. -(5/-8)
False
E. -5/-8
False
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