Answers
Part (a)
This sequence is convergent because all we care about are the leading terms for the numerator and denominator. As n gets really large, the leading terms dictate what happens.
The leading term up top is 9n
The leading term down below is 7n
Divide the two items to get (9n)/(7n) = 9/7
We don't have to worry about dividing by zero because n will go off to infinity, and as it does so, the sequence [tex]\{a_n\}[/tex] converges to 9/7
========================================================
Part (b)
As n heads to infinity, the terms of the sequence are approaching 9/7 (they never quite hit the exact value though).
Note how 9/7 = 1.2857 approximately which is larger than 0
So effectively for very large values of n, we're adding on 1.2857 each time or close to it, meaning that this infinite series diverges.
------
For a series like this to converge, the answer to part (a) must be 0. This way at some point, we're effectively adding 0 to the series and we approach some fixed sum.
For example, consider the sequence 1/(7n+1)
As n goes to infinity, the terms of the sequence approach 0
This means that for some very large n, the 1/(7n+1) is basically 0 and we aren't adding much onto the sum to change it. So this sum will converge to a fixed value.
Related Questions
Which of polygons B, C, D, E, andF are similar to polygon A? Select All of
Answers
The answer is E bro bro
He negotiated a 7% decrease on a 6 500 car he will pay the full balance in 12 equal months how much will he pay
Answers
Answer:
£503.75
Step-by-step explanation:
100-7=93
6500×0.93=6045
6045/12=503.75
Answer:
$503.75 per month
Step-by-step explanation:
%7 of 6500= 455
6500-455=6045
6045 divided by 12=503.75
(03.06 MC) What expression represents the value of y?
Answers
Answer:
[tex] y = \sqrt{wz} [/tex]
Step-by-step explanation:
The figure given shows the altitude (y) of a right triangle which is perpendicular to the hypotenuse (CA) of the triangle. The hypotenuse is divided by the altitude into two segments, w and z.
According to right triangle altitude theorem the relationship between y, w, and z is represented as follows:
[tex] y = \sqrt{wz} [/tex]
This expression represents the value of the altitude, y.
Answer:
y = wz with that check mark thingy over it
Step-by-step explanation:
i got the test
Which diagram has all the correct lines of reflectional symmetry for the rectangle?
A rectangle is folded diagonally on both corners.
A rectangle is folded by a vertical and horizontal line going through its center.
A rectangle is folded 4 ways. It is folded horizontally, vertically, and diagonally on both corners.
A rectangle is folded 4 ways. It is folded diagonally at each midpoint of every side.
Answers
Answer:
answer is b. a rectangle is folded by a vertical and horizontal line going through its center
Step-by-step explanation:
if you folded it along the lines of symmetry, the rectangle would line up with itself
A rectangle is folded by a vertical and horizontal line going through its center, has all the correct lines of reflectional symmetry for the rectangle.
What is reflectional symmetry?A well-balanced proportion in which two images or figures are the same size and shape is referred to as symmetry.
When the same figure is obtained following a transformation in geometry whether it be a reflection or a rotation symmetry has occurred.
An example of a shape with reflection symmetry is a rectangle. A line of reflection that passes through the center of two different sides will always be symmetrical.
There are two symmetry lines in a rectangle.
Each side of the rectangle would match up exactly if the rectangle were folded along each line of symmetry.
Keep in mind that a shape must possess at least one line of symmetry in order to qualify as having reflection symmetry.
learn more about reflectional symmetry here :
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Write down all the whole numbers between 1035 and 1041
Answers
Answer:
1035
1036
1037
1038
1039
1040
1041
Step-by-step explanation:
pls heart and brainliest
Answer:1036, 1037, 1038, 1039, 1040.
Step-by-step explanation:
In a lab, a 30% acid solution is being mixed with a 5% acid solution to create a 10% acid solution. What is the ratio of the amount of the 30% solution to the amount of 5% solution used to create the 10% solution?
Answers
Answer:
1:4
Step-by-step explanation:
you invest $2000 in an account that pays simple interest of 2% for twenty years. what amount of money will you have in 20 years
Answers
Answer:
$2971.9
Step-by-step explanation:
2000*(1+2%)^20 = 2971.895
If 23 is subtracted from 8 times the number, the result is the square of 2 less than the number.
Answers
23-8=15
8*15=120
sqrt2=4
the number 120-4=116
that’s what i got not sure if that is correct
17. The absolute value of -6 and 6 is
Answers
Answer:
6
Step-by-step explanation:
..................
Find the equation of the line that is perpendicular to the given line and passes through the given point. Enter your answer in slope-intercept form (y = mx + b) with the values of m and b given as decimals, rounded to the nearest hundredth if necessary.
y = 2x ; (4, −4)
Answers
Answer:
y = -0.5x -2
Step-by-step explanation:
if two lines are perpendicular, their product equals -1
_________________________________________
let the equation of required line be
y = mx + b as given in the problem to be slope intercept form
m = slope
given line
y = 2x
it is also in y = mx + b , comparing this with y =2x
m = 2 and b =0
now
as product of two perpendicular lines = -1
m*2 = -1
thus
m = -1/2 = -0.5
thus,
slope of required line is -0.5
in y = mx + b
m = -0.5
thus,
y = -0.5x + b
given that this line passes through(4,-4)
putting y = -4 and x = 4 in this equation we can find value of b
-4 = -0.5*4 + b
-4 = -2 + b
=> -4 + 2 = b
thus, b = -2
Thus, slope intercept form of equation is y = -0.5x -2
What is the range of the function represented by this graph?
Answers
Answer:
No answer but...
Step-by-step explanation:
Look at the graph, subtract the smallest number from the largest number.
Answer:
where is the graph
Step-by-step explanation:
take a screeshot and upload it next time
Based on the number line about how many ounces are there in 8 pounds
Answers
A video store charges $12 for used games and $25 for new games. Jonathan has saved $300 to spend on video games. X=number of used games y=number of new games which linear equation, written in standard form, expresses the scenario?
Answers
Answer:
12x+25y=300.
he can buy 25 used games .hope this helped!
Answer:
12x+25y=300
Step-by-step explanation:
Standard Form= Ax+Bx=C
12x, because $12 for each old video game (x) he gets.
25y, because for each new game (y) it costs $25.
total=300
plug in for standard form
Please help this is my last question
Answers
Answer:
14(3x-1) / 5x^2 (3x+ 1)
Step-by-step explanation:
Please let me know if I gloss over something you don't understand
1) First simplify the complex fraction:
This can be written as
18x-6/ 15x + 5 * 21x^2 / 9x^5
which can be simplified to
18x-6/ 15x + 5 * 7/ 3x^3
which can be written as
(18x-6) * 7 / 3x^3 (15x+ 5)
2)
factor 3 from the top of the expression
3(6x-2) * 7 / 3x^3 (15x + 5)
3)
reduce the fraction with 3
3(6x-2) * 7 / 3x^3 (15x + 5)
(6x-2) * 7 / x^3 (15x + 5)
4)
Distribute 7 through the parenthesis on the top
42x-14/ x^ 3 (15x+ 5)
5)
Distribute x^3 through the parenthesis on the bottom
42x-14/ 15x^4 + 5x^3
6)
factor 14 from the top of the expression
14 (3x -1)/ 15x^4 + 5x^3
7)
factor 5x^3 from the bottom
14 (3x -1)/ 5x^3 (3x + 1)
on comparing the ratios a1/a2 b1/b2 and c1/c2 find out whether the pair of linear equations 2x -3y=8 and 4x-6y =9 are consistent or inconsistent
Answers
Answer:
The given linear equation are
⇒9x+3y+12=0....eq1
⇒a1 =9,b1 =3,c1 =12
⇒18x+6y+24...eq2
⇒a2 =18,b2 =6,c2 =24
⇒a1/a2 =9/18 =1/2
⇒ b1/b2= 3/6 = 1/2
⇒ c1/c2= 12/24= 1/2
comparing
⇒ a1/a2,b1/b2,c1/c2
⇒ a1/a2=b1/b2=c1/c2
Hence, the line represented by eq1 and eq2 are coincidents
Step-by-step explanation:
I NEED SOME HELP
Bobby rich dude has $120,000 in his account that pays him 5.5% compounded daily. What amount and how much interest will his money earn in 30-days?
Answers
Answer:
Interest: Amount Gained: $198,000
Final Balance: Amount After 30 days of Interest: $318,000
Step-by-step explanation:
Equation Used to Solve:
120,000 · 0.055 = 120,000 + (xy)
Let x represent 5.5% of 120,000
Let y represent the number of days.
Solving the equation:
120,000 · 0.055 = 6,600
x = 6,600; y = 30
120,000 + (6,600 · 30) = 120,000 + 198,000
120,000 + 198,000 = 318,000
Which of the following points does not lie on the graph of y=5x-5?
(0-5)
(1.0)
(-5.0)
Answers
0=5x-5
-5x=-5
X=1
4. The value of y is directly proportional to the value of x. If y = 45 when x = 180, what is the value of y when x = 80?
Answers
Answer:
y=8⇒8=24x
x=24/8=3
Step-by-step explanation:
The value of y when x = 80 is 20.
It is required to find the value of y.
What is arithmetic?Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.
Solution:
"Y is directly proportional to X" can be rewritten as a mathematical expression of the form Y = KX
"K" is the constant of proportionality and must be determined from the initial information.
According to given question we have,
If Y = 45 when X=180
It means
45 = 180K
K = 45/180
K = 0.25
Now that we know the value of K, we can use it to calculate the value of Y when X=80
Y = (0.25)(80)
Y=20
Therefore, the value of y when x = 80 is 20.
Learn more about arithmetic here:
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-3x + 4 = -8
A. X = 4
B. X = -4
C. No solution
D. X= -4/3
Answers
Answer:
x=4
Step-by-step explanation:
subtract both sides then divide
Since every square has 4 sides that are equal in the length, write an expression to determine the perimeter of a square in terms of the length of the squares sides?
Answers
9514 1404 393
Answer:
4s
Step-by-step explanation:
Let s represent the length of each of the four sides of the square. The perimeter is the sum of the lengths of the sides, so is ...
s + s + s + s
We use multiplication to signify repeated addition. So, this can be written more simply as ...
4s . . . . perimeter of a square of side length s
PLZ HELP IM RUNNING OUT OF TIME!!! THIS IS A SIMPLE EXPLANATION PROBLEM PLEASE HELP!!!
The equation 7(x − 4) = 8(x + 8) has one solution. Which of the following best explains why?
A.
The x-terms are the same, but the constant terms are different.
B.
The x-terms are different, and the constant terms are different.
C.
The x-terms are the same, and the constant terms are the same.
D.
The x-terms are different, but the constant terms are the same.
Answers
Answer:
C. The x-terms are the same, and the constant terms are the same.
Step-by-step explanation:
Solve for x:
7 (x - 4) = 8 (x + 8)
Hint: | Write the linear polynomial on the left-hand side in standard form.
Expand out terms of the left hand side:
7 x - 28 = 8 (x + 8)
Hint: | Write the linear polynomial on the left-hand side in standard form.
Expand out terms of the right hand side:
7 x - 28 = 8 x + 64
Hint: | Move terms with x to the left-hand side.
Subtract 8 x from both sides:
(7 x - 8 x) - 28 = (8 x - 8 x) + 64
Hint: | Combine like terms in 7 x - 8 x.
7 x - 8 x = -x:
-x - 28 = (8 x - 8 x) + 64
Hint: | Look for the difference of two identical terms.
8 x - 8 x = 0:
-x - 28 = 64
Hint: | Isolate terms with x to the left-hand side.
Add 28 to both sides:
(28 - 28) - x = 28 + 64
Hint: | Look for the difference of two identical terms.
28 - 28 = 0:
-x = 64 + 28
Hint: | Evaluate 64 + 28.
64 + 28 = 92:
-x = 92
Hint: | Multiply both sides by a constant to simplify the equation.
Multiply both sides of -x = 92 by -1:
(-x)/(-1) = -92
Hint: | Any nonzero number divided by itself is one.
(-1)/(-1) = 1:
Answer: x = -92
Please help me i need help!! How do you solve for M? Explain each step of the solution in a short paragraph
Answers
Answer:
M = 4pi²a³ / GT²
Step-by-step explanation:
Cross multiply: T² × GM = GMT²
1 × 4pi²a³ = 4pi²a³
It becomes: GMT² = 4pi²a³
Divide both sides by GT² to solve for M
We have : M = 4pi²a³ / GT²
Can Someone Help Me. ?
Answers
Answer:
angles BED and DEA, and angles AEC and BEC are supplementary angles
Step-by-step explanation:
If you do not know what supplementary angles are, then just know that it means two angles added together that equal 180 degrees. So, all you need to do is find two angles on the picture that equal 180 degrees when added together.
I hope this helps! :)
the day Janella and her family left Hawaii, the temperature was 73°F above 0°F. what would a thermometer read at this temperature?
Please Answer
Answers
Answer:
73° F
Step-by-step explanation:
Add 73° F to 0° F
The answer is 73° F
Hope I helped :)
Please consider Brainliest :)
Answer:
I think it would be 0 because I devided but i'll try a nother way
Step-by-step explanation:
Find the missing number in the figure?
4
?
6
3
Answers
Answer:
2, cause 4/2=2,6/2=3
Step-by-step explanation:
Answer:
5
Step-by-step explanation:
which value would make the statement true?
2 4
— > —
? 12
O 4
O 6
O 12
O 24
Pls help guys.
Answers
Answer:
the answer is 6
Step-by-step explanation:
the answer is 6
Estimate the product 4x279
Answers
Answer:
116
Step-by-step explanation:
es 116 porque lo cheque
pleas y'all help me with this
Answers
Answer:
[tex]-\frac{26}{2}/ -\sqrt{9}/ 13.5(percent)/ 0/ 13.5[/tex]
Step-by-step explanation:
Write an equation for the proportional relationship. Let X represent a length measured in meters and y represent the same length measured in centimeters.
Answers
Answer:
[tex]y=100x[/tex]
Step-by-step explanation:
Given that [tex]x[/tex] is the length measured in meters and
[tex]y[/tex] represents the same length measured in centimeters.
Let us first have a look at the relationship between meters and centimeters units of length.
1 unit of length in meters = 100 units of length in centimeters
Therefore, it can be said that:
2 units of length in meters = 200 units of length in centimeters
3 units of length in meters = 300 units of length in centimeters
4 units of length in meters = 400 units of length in centimeters
OR
[tex]x[/tex] units of length in meters = 100[tex]x[/tex] units of length in centimeters
It is given that [tex]y[/tex] is the length in centimeters.
Therefore, the proportional equation can be written as:
[tex]y=100x[/tex]
Again I’m struggling and need some help please?!