Determine whether the series converges absolutely or conditionally, or diverges. 00 sint(2n - 1)/2] (– ] n n=1 a)converges conditionally
b) converges absolutely c)diverges
Answers
The given series is\($ \sum_{n=1}^{\infty} \frac{\sin(t(2n-1))}{2n} $.\)We have to determine whether the given series converges absolutely or conditionally or diverges.The given series is of the form\($\sum_{n=1}^{\infty}a_n$ where $a_n = \frac{\sin(t(2n-1))}{2n}$As $a_n$\) contains $\sin$ term we can't directly apply Alternating series test, Integral test, or Comparison test.
So, we have to use the Absolute convergence test and the Dirichlet test.The Absolute Convergence Test states that if the series obtained by taking the absolute value of the terms of a given series is convergent, then the original series is said to be absolutely convergent. If the series obtained by taking the absolute value of the terms of a given series is divergent or conditionally convergent, then the original series is said to be conditionally convergent.
The Dirichlet Test states that if the sequence of partial sums of a given series is bounded, and the sequence of its terms is monotonic and tends to zero, then the series is convergent.
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Related Questions
solve fast pls i am mark you
Answers
Answer:
\( \bold{ x = - \frac{5}{6} }\)
Step-by-step explanation:
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⠀⠀⠀⠀■ Question\( \large \sf{ \frac{4x + 9}{3x + 11} = \frac{4x + 3}{3x + 2} }\)
Solve for x.
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⠀
⠀⠀⠀⠀□ Solution⠀
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We will cross multiply the above equation⠀
\( \sf (4x + 9)(3x + 2) = (4x + 3)(3x + 11) \\ \\ \sf 4x(3x + 2) + 9(3x + 2) = 4x(3x + 11) + 3(3x + 11) \\ \\ \sf 12 {x}^{2} + 8x + 27x + 18 = 12 {x}^{2} + 44x + 9x + 33 \\ \\ \sf 12 {x}^{2} + 35x + 18 = 12 {x}^{2} + 53x + 33\)
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⠀
Now we will take the values of RHS(right hand side) to LHS(left hand side) of the equation. During this, the values of RHS will get opposite sign while going to LHS.⠀
\( \sf 0 = 12 {x}^{2} + 53x + 33 - 12 {x}^{2} - 35x - 18 \\ \\ \sf 0 = 18x + 15\)
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⠀
Taking 15 to LHS⠀
\( \sf - 15 = 18x\)
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⠀
Dividing both RHS and LHS of the equation by 18⠀
\( \large{ \sf \frac{ - \cancel{15} \tiny {5}}{ \cancel {18} \tiny6 } = x} \\ \\ \boxed{ x = - \frac{5}{6} }\)
Answer:
\(\textsf{$x=-\dfrac{5}{6}$}\)
Step-by-step explanation:
Given: \(\textsf{$\dfrac{4x+9}{3x+11}=\dfrac{4x+3}{3x+2}$}\)
1. Cross-multiply
(4x + 9)(3x + 2) = (4x + 3)(3x + 11)
2. Distribute
⟶ (4x + 9)(3x + 2) = (4x + 3)(3x + 11)
⟶ 4x(3x) + 4x(2) + 9(3x) + 9(2) = 4x(3x) + 4x(11) + 3(3x) + 3(11)
⟶ 12x² + 8x + 27x + 18 = 12x² + 44x + 9x + 33
3. Combine like terms
⟶ 12x² + 8x + 27x + 18 = 12x² + 44x + 9x + 33
⟶ 12x² + 35x + 18 = 12x² + 53x + 33
4. Subtract 12x² from both sides
⟶ 12x² - 12x² + 35x + 18 = 12x² - 12x² + 53x +33
⟶ 35x + 18 = 53x + 33
5. Subtract 35x from both sides
⟶ 35x - 35x + 18 = 53x - 35x + 33
⟶ 18 = 18x + 33
6. Subtract 33 from both sides
⟶ 18 = 18x + 33
⟶ 18 - 33 = 18x + 33 - 33
⟶ -15 = 18x
7. Divide both sides by 18 to isolate the variable
\(\longrightarrow\textsf{$\dfrac{-15}{18}=\dfrac{18x}{18}$}\\\\\\\longrightarrow\textsf{$\dfrac{-15}{18}=x$}\\\\\)
8. Reduce
\(\longrightarrow\textsf{$\dfrac{-15\div 3}{18\div 3}=x$}\\\\\\\longrightarrow\textsf{$-\dfrac{5}{6}=x$}\)
I need help solving this question. A large company is considering installing charging stations for electric cars in their company parking lots. Suppose that 1.5% of employees at the main office have electric cars and 2% of employees at the branch office have electric cars.
Answers
Answer:
C; right answer on Khan Academy
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
help ! question 6 . I’ll give brain.
Answers
Answer:
B
Step-by-step explanation:
Answer:
I think its B
Step-by-step explanation:
put me as brainliest
If both numerator and denominator are negative, then what would be its negative or additive inverse.
The question is -6/-5 and the answer is -6/5 . But what's the reason??
Answers
The additive inverse of 6/5 is -6/5. The reason is that when you add a number and its additive inverse, the result is always zero: 6/5 + (-6/5) = 0.
In mathematics, when we have a fraction with a negative numerator and a negative denominator, we can simplify the fraction by dividing both the numerator and denominator by the greatest common factor (GCF) of the absolute values of the numerator and denominator. This process does not change the sign of the fraction.
In the case of -6/-5, the absolute value of the numerator is 6 and the absolute value of the denominator is 5, and the GCF of 6 and 5 is 1. Dividing both the numerator and denominator by 1 gives us -6/-5, which is equivalent to 6/5, with the negative sign indicating that the fraction is negative.
So the negative or additive inverse of -6/-5 is simply its equivalent positive fraction, which is 6/5. This is because the additive inverse of any fraction is a fraction that, when added to the original fraction, results in 0. In this case, adding -6/-5 and 6/5 results in 0.
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HELP ME GRAPH THIS
(slope problem )
Answers
Answer:
y = -5x - 19
Explanation:
y = mx +b
-4 = -5(-3) + b
-4 = 15 + b
-19 = b
y = -5x - 19
help plsssssssssssss
Answers
Answer:
it would be 4
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
4*2/4*25= 8/100=0.08 or 8%
Which equation represents the graphed function?
Answers
Answer:
y=-2x+3
Step-by-step explanation:
for one, you can see that the y-intercept is at 3, so for y=m*x+b, b is 3
next, you can count to get the slope. it moves 2 units down and one unit to the left, so for slope, which is rise over run, you are -2/1= -2
so y = -2x + 3
A line contains
the Point (8,3) and
(-4, 9) what is the
equation of the
ine?
Answers
Answer:
y = - \(\frac{1}{2}\) x + 7
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)
with (x₁, y₁ ) = (8, 3 ) and (x₂, y₂ ) = (- 4, 9 )
m = \(\frac{9-3}{-4-8}\) = \(\frac{6}{-12}\) = - \(\frac{1}{2}\) , then
y = - \(\frac{1}{2}\) x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (- 4, 9 ) , then
9 = 2 + c ⇒ c = 9 - 2 = 7
y = - \(\frac{1}{2}\) x + 7 ← equation of line
What is the best description of thermal energy?(1 point) Responses Thermal energy is the kinetic energy contained in an object or substance due to the movement of its atoms and/or molecules. Thermal energy is the kinetic energy contained in an object or substance due to the movement of its atoms and/or molecules. Thermal energy is a measure of an object or substance’s heat. Thermal energy is a measure of an object or substance’s heat. Thermal energy is kinetic energy. Thermal energy is kinetic energy. Thermal energy is the energy stored in an object’s chemical bonds. Thermal energy is the energy stored in an object’s chemical bonds.
Answers
Answer:
A. Thermal energy is the kinetic energy contained in an object or substance due to the movement of its atoms and/or molecules.
Explanation:
Just took the Quick Check :)
The best description of thermal energy is that it is the kinetic energy contained in an object or substance due to the movement of its atoms and/or molecules.
What is thermal energy?Thermal energy is the kinetic energy contained in an object or substance due to the movement of its atoms and/or molecules.
It is a type of internal energy, which is the energy possessed by a system due to the movement and interactions of its constituent particles.
We have,
Thermal energy is a measure of an object or substance’s heat:
While thermal energy and heat are related, they are not exactly the same thing.
Heat is the transfer of thermal energy between objects or substances due to a temperature difference.
Thermal energy, on the other hand, is the energy contained in an object or substance due to the movement of its particles.
Thermal energy is kinetic energy:
While thermal energy is related to kinetic energy, they are not exactly the same thing.
Kinetic energy is the energy of motion, while thermal energy specifically refers to the kinetic energy of an object's particles.
Thermal energy is the energy stored in an object’s chemical bonds:
While chemical bonds do store energy, this is not the best description of thermal energy.
Thermal energy specifically refers to the energy stored in the movement of an object's particles.
Therefore,
The best description of thermal energy is that it is the kinetic energy contained in an object or substance due to the movement of its atoms and/or molecules.
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Use Excel to solve this: You want to buy a car for $50,000 and you can put $10,000 as a down payment and borrow the remaining $40,000. The bank will make a bank loan at a 9% per year over 3 years and monthly payments. What is the monthly payment?
Answers
In this case, the monthly payment for the car loan would be approximately $1,299.13.
To calculate the monthly payment for a bank loan using Excel, you can use the PMT function.
Here's how to do it:
1. Open Excel and create a new spreadsheet.
2. In cell A1, enter the loan amount: -40000 (negative because it's an outgoing payment).
3. In cell A2, enter the annual interest rate: 9%.
4. In cell A3, enter the loan duration in years: 3.
5. In cell A4, enter the formula to calculate the monthly payment: =PMT(A2/12, A3*12, A1).
6. The result in cell A4 will be the monthly payment.
So, in this case, the monthly payment for the car loan would be approximately $1,299.13.
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What is the value of the expression below when y=8y=8 and z=9z=9?
5y-2z
Answers
Answer:
22
Step-by-step explanation:
multiply 5 and 8 , then multiply 2 and 9 . once you get your answer you subtract the 40-18
The value of the equation 5y - 2z = 22
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the expression be A = 5y - 2z
The value of y = 8
The value of z = 9
So , substituting the value of y and z in the equation , we get
A = 5y - 2z
A = 5 ( 8 ) - 2 ( 9 )
A = 40 - 18
A = 22
Therefore , the value of A = 22
Hence , the value of the equation 5y - 2z = 22
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Simplify. Show your work.
a. |5 - 7| =2
b. -3|11 - 15|=-12
Answers
Answer:
|5 - 7| =2
What you want to do first is to do the equation 5-7 which is -2 but there is an absolute value sign so 2.
-3|11 - 15|=-12
For this one it is a little more difficult but all you have to do is do the equation 11-15 which is -4 but there is an absoulte value sign so 4 you then multiply 4 by -3 which is -12 bam.
Identify the correct graph of the system of equations. 3x − y = 12 x + 4y = 4 The graph shows a line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma 1. There is a second line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma 12. The graph shows a line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma 1. There is a second line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma negative 12. The graph shows a line with an x--intercept at 4 comma 0 and a y-intercept at 0 comma negative 1. There is a second line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma 12. The graph shows a line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma negative 1. There is a second line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma negative 12.
Answers
The correct graph of the system of equations is D) The graph shows a line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma negative 1. There is a second line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma negative 12.
What is the system of equations?
A system of equations is a set of two or more equations with the same variables. The goal of a system of equations is to find the values of the variables that simultaneously satisfy all the equations in the system.
The given equations are
3x + y = 12
x + 4y = 4
To graph the system of equations, we can start by finding the x-intercepts and y-intercepts of each line.
The x-intercept is the point where the line crosses the x-axis, which means that the y-value is 0. To find the x-intercept, we can set y = 0 and solve for x:
3x + y = 12
3x + 0 = 12
3x = 12
x = 4
So, the x-intercept of the first line is (4, 0).
Next, we can find the y-intercept, which is the point where the line crosses the y-axis, meaning that the x-value is 0. To find the y-intercept, we can set x = 0 and solve for y:
3x + y = 12
0 + y = 12
y = 12
So, the y-intercept of the first line is (0, 12).
We can repeat this process for the second line to find its x-intercept and y-intercept:
x + 4y = 4
x + 4 * 0 = 4
x = 4
So, the x-intercept of the second line is (4, 0).
Next, we can find the y-intercept by setting x = 0:
x + 4y = 4
0 + 4y = 4
4y = 4
y = 1
So, the y-intercept of the second line is (0, 1).
Now that we have found the x-intercepts and y-intercepts of each line, we can plot these points on a coordinate plane and draw lines through them to obtain the graph of the system of equations.
The graph shows a line with an x-intercept at (4, 0) and a y-intercept at (0, 12). There is a second line with an x-intercept at (4, 0) and a y-intercept at (0, 1).
Therefore, the correct graph of the system of equations is D) The graph shows a line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma negative 1. There is a second line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma negative 12.
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please help!! this is algebra 2
Answers
Answer: The last one bc it the same thing!
Step-by-step explanation: one 5/3 is the exact same as 5/3! and for the last one says -5/3
It would be the last one!
Addison is shooting a free throw. The initial height of the ball is represented by the ______
.A Maximum
B. Minimum
C. x-intercept
D. y-intercept
Answers
Answer:
B
Step-by-step explanation:
Solve for x.
x =
30
27
33
Answers
Answer:
the answer is 27
Step-by-step explanation:
3x+9+90=180
3x+99=180
3x=180-99
x=81/3
x=27
Answer:
Step-by-step explanation:
3x + 9 + 90 = 180
3x + 99 = 180
3x = 81
x = 81/3
x = 27
3(27) + 9 = 81 + 9 = 90
5. Where will the image of point J. (2, - 7) be located using the translation (x,y) —> (x-8.5, y +0.5)?
A. (-5.5, -7.5)
B. (-6, -7)
C. (-6.5, -6.5)
D. (10.5, -7.5)
Answers
(2 - 8.5, -7 + 0.5) = (-6.5, -6.5)
Therefore, the answer is C. (-6.5, -6.5).
-4p+(-6p) combine like terms to create an equivalent expression
Answers
Answer:
-10p
Step-by-step explanation:
-4p+(-6p) for me I like to think of the negative or subtraction sign
overpowering the positive or addition sign
so in this case
-4p-6p
then since the variable p is the same -4-6 is -10
the end result is -10p
with which measurement procedure is the target behavior recorded if it occurs at any point within the scoring interval?
Answers
If the target behavior is recorded whenever it occurs at any point within the scoring interval, the measurement procedure used is called continuous recording or event recording. This method involves observing and recording each instance of the behavior without considering its duration or intensity.
Continuous recording is typically used when the target behavior is discrete and occurs relatively infrequently or has a short duration. With this measurement procedure, each occurrence of the behavior is recorded as a separate event, regardless of when it starts or ends within the scoring interval. Examples of behaviors that can be measured using continuous recording include vocalizations, hand clapping, or instances of aggression.
Continuous recording provides a comprehensive account of the frequency or rate at which the behavior occurs, allowing for a detailed analysis of its occurrence patterns. This method is particularly useful when a precise count of behavior instances is needed and when the duration or intensity of the behavior is not a focus of measurement.
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how would you determine the exact concentration of the solution made?
Answers
To determine the exact concentration of the solution made, one can divide the mass of the solute with the volume of the solution.
A solution is the substance formed by the mixture of solute in solvent. The solute may or may not be dissolved in the solution. One can determine the exact concentration of the solution if the mass of solute added in the specific volume of solution is known. If the solution is made by someone else, then its concentration can be determined by process of titration.
The concentration of a solution is expressed in the form of moles or grams per unit liter. If the solution is unknown and only its dissolved chemical is known, then titration will help in determining the closest value of concentration if performed without human error. In titration, the use of glassware that that is more precise than the flasks, beakers, and graduated cylinders are used.
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Refer to complete question below:
How do we determine concentration a solution? If it is a solution that we have made up, we can readily do the calculations required. But what if it is a solution that someone else has made? What technique can be used to gather information about a solution that we are given with no other information than the name of the chemical dissolved.
How do i solve this paper?
I feel like my answers are gone and i need help.
Answers
Answer:
you have it correct sir
Step-by-step explanation:
(100 POINTS)
Error Analysis - Describe and correct the error a student made in factoring.
x² + 2x - 3 = 5
(x - 1)(x + 3) = 5
x - 1 = 5 or x + 3 = 5
x = 6 or x = 2
Answers
Answer:
Step-by-step explanation:
x² + 2x - 3 = 5 >You cannot start factoring until you
set =0
(x - 1)(x + 3) = 5
x - 1 = 5 or x + 3 = 5
x = 6 or x = 2
Should be:
x² + 2x - 3 = 5 >Subtract 5 from both sides
x² + 2x - 8 = 0 >Now factor
(x - 2)(x + 4) = 0 >Set each parenthesis =0
x - 2 = 0 or x + 4 = 0 >Solve for x's
x = 2 or x = -4
50 points What is the value of g? 25(g−7)=3 Enter your answer as a mixed number in simplest form in the box. g =
Answers
Answer: g=14 1/2
Step-by-step explanation:
i took the k12 quiz
Answer:
its 14 1/2
Step-by-step explanation: i took the test;)
0.005680 is how much greater than 0.0004359
Answers
Answer:
Answer is: 0.0052441
Answer:
0.0052441
hope it helps.
if 20% of ms.moore's class earned a d how many of her 30 students earned a d what percent of students earned a different grade
Answers
Answer:
6 students earned a d and 80% got other
Step-by-step explanation:
Answer:
6 students, 80% of students
Step-by-step explanation:
20% of her 30 students earned a D. To find exactly how many students earned a D, we can convert the 20% into a fraction and thereby multiply the fraction by 30.
\(20\)%\(=\)
\(\frac{20}{100}=\\\frac{1}{5}\)
Ok, \(\frac{1}{5}\) of Ms. Moore's 30 students earned a D. Let's multiply.
\(\frac{1}{5}*\frac{30}{1} =\\6\)
6 students in Ms. Moore's class earned a D.
Therefore, the rest of the class earned a different grade. \(30-6=24\) students had a different grade. To find the percentage, we simply divide by the total number of students and multiply by 100%
\(\frac{24}{30} =\\\frac{4}{5} =\\0.8=\)
\(80\)%
80% of students in Ms. Moore's class got a grade other than D.
I hope this helps! Let me know if you have any questions :)
What are the factors of x2 – 144?
Answers
Answer:
(x+12) and (x-12)
Step-by-step explanation:
This is the square formula.
a^2 - b^2 =(a+b)(a-b)
In this case, a is x and b is 12.
The inner terms cancel, leaving x^2 - 144.
how find a ratio of the area of a circle and a square
Answers
Answer:
CIRCLE : CIRCLE
Ratio of area is the scale factor squared. So find the radii of the two circles, square both values, and simplify the ratio.
SQUARE : SQUARE
Ratio of area is the scale factor squared, So find the side lengths of the two squares, square both values, and simplify the ratio.
SQUARE : CIRCLE
Using the formulas A = s*s and A = pi*r^2, find the areas of the circle and the square. Then simplify the ratio.
Please help me I got a bad grade and I need to redo them
Find the slope
Answers
Answer:
The first one has a slope of 4
The second one has a slope of 0.3 repeating
Step-by-step explanation:
You pick two points on the graph.
You find the x and y coordinates of each point.
You find the difference between the two x coordinates.
You find the difference between the two y coordinates.
Divide the difference in the y coordinates by the x coordinates.
If im wrong sorry owo im only in elementary school... <3
Answer:
4/6
Step-by-step explanation:
Drag the slider to change the value of h, and observe the effect of h on the graph of the cosine function.
When h = π, the orange graph shifts ____ units to the ______
When h = −π, the orange graph shifts ____ units to the ______
Answers
Answer:
1: pi, right
2: pi, left
3: coincides with
Step-by-step explanation:
When h = π, the orange graph shifts pi units to the right. When h = −π, the orange graph shifts pi units to the left.
What is mathematical graph?In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between multiple things are frequently represented by the points on a graph. Here, for example, we can plot a graph showing the type and quantity of school supplies in use by pupils in a class based on the data provided below.
A bar graph can also be used to display the data. Bar graphs show how many of each supply there are. The more supplies or goods are used, the higher the bar's height. When h = π, the orange graph shifts pi units to the right. When h = −π, the orange graph shifts pi units to the left.
Therefore, when h = π, the orange graph shifts pi units to the right. When h = −π, the orange graph shifts pi units to the left.
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Someone explain to me how to solve and write out an equation in slope-intercept form for example: 4x-6y=12
Answers
Answer:
y = mx + b
Step-by-step explanation
for your example:
y = 4x + 6
i think.... UHHHH