The nth term test, also known as the Test for Divergence, is a useful tool for determining the divergence of a given series. All of the given series - A) arctan(n), B) 61, C) n(n+3)/(n+4), and D) ln(n) - diverge according to the nth term test.
In order to use this test, you should analyze the limit of the sequence's terms as n approaches infinity. If the limit is not zero, then the series diverges.
For each of the series provided, let's apply the nth term test:
A) arctan(n), n=1 to infinity:
The limit as n approaches infinity of arctan(n) is π/2, which is not zero. Therefore, the series diverges.
B) 61:
Since the series consists of a constant term, the limit as n approaches infinity is 61, which is not zero. Therefore, the series diverges.
C) n(n+3)/(n+4), n=1 to infinity:
As n approaches infinity, the limit of n(n+3)/(n+4) is 1, which is not zero. Therefore, the series diverges.
D) ln(n), n=1 to infinity:
The limit as n approaches infinity of ln(n) is infinity, which is not zero. Therefore, the series diverges.
In conclusion, all of the given series - A) arctan(n), B) 61, C) n(n+3)/(n+4), and D) ln(n) - diverge according to the nth term test.
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Mark jogged 3 5/7 km. His sister jogged 2 4/5 km. How much farther did Mark jog than his sister?
Step-by-step explanation:
so therefore mark jogged 2 36/70km more than his sister
The number of kilometers that Mark jog more than his sister will be 32 / 35 km.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Mark jogged 3 ⁵/₇ km. His sister jogged 2 ⁴/₅ km.
Convert the mixed fraction number into a fraction number. Then we have
3 ⁵/₇ = 3 + 5/7 = 26/7
2 ⁴/₅ = 2 + 4/5 = 14/5
Then the number of kilometers that Mark jog more than his sister will be given as,
⇒ 26/7 - 14/5
⇒ 32 / 35 km
The number of kilometers that Mark jog more than his sister will be 32 / 35 km.
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what is -6x - 8 < 4
on a number line
Answer:
x > -2
Step-by-step explanation:
-6x - 8 < 4
-6x < 12
x > -2
Find the are of the circle use 3.14 and round to your nearest hundredth using 14m
Answer:
The question is incorrect. Please rewrite the question.
Ms. Fleener's fish tank has a bottom area of 102 square
centimeters. If the height of the fish tank is 12 centimeters, how
many cubic centimeters of water does the fish tank hold?
I
Answer:
1224 cm^3
Step-by-step explanation:
volume = bottom area x height
102x12=1224
The fish tank holds 1224 cc of water.
What is volume?In mathematics, volume is the space taken by an object.
Here, given that,
The area of the bottom of the tank =A= 102 cm²
now, the height of the water in tank = h= 12cm
we know, volume of water= A× h
=102×12 cc
=1224 cc
Hence, required volume is 1224 cc
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3c+2d=-24 and 2c+5d= -38
Answer:
c=-4, d=-6
Step-by-step explanation:
Find an ordered pair (x, y) that is a solution to the equation. 6x-y=9
Answer:
(0, -9)
Step-by-step explanation:
-y= -6x + 9
y = 6x -9
plug in 0 for x
(0, -9)
On an inch ruler, which mark is halfway between the 12-inch mark and the 3-inch mark?
Answer:
8 and half 8/2 8.5, wait or 7/5 or 7.5
Step-by-step explanation:
Answer:
7 1/2
Step-by-step explanation:
The sum of the first 8 terms of a GP is five times the sum of first 4 terms. Find the common ratio.
Answer:
1Step-by-step explanation:
Sum of nth term of a GP is expressed as;
Sn = a(r^n-1)/r-1
The sum of the first 8 terms of a GP is expressed as;
S8 = a(r^8 - 1)/r-1
The sum of first 4 terms is expressed as;
S4 = a(r^4 - 1)/r-1
If the sum of the first 8 terms of a GP is five times the sum of first 4 terms then
S8 = 5S4
a(r^8 - 1)/r-1 = 5[a(r^4 - 1)/r-1]
r^8 - 1 = 5(r^4 - 1)
r^8 - 1 = 5r^4 - 5
r^8 - 5r^4 = -5+1
r^4(r^4 - 5) = -4
r^4 - 5 = -4
r^4 = -4+5
r^4 = 1
r = 1
Hence the common ratio is 1
What's the diameter of 2.5ft
Answer:
5
Step-by-step explanation:
An equation of the line tangent to the graph of f(x)= (4x^2-8x+3)^4 at the point where x=1 is:
A.y-81=384(x-1)
B.x=1
C.y=1
D.y-1=3.37497(x-1)
E.y=5(x-1)
Pls help me with this I have 5 minutes to do this I will give brainleast plzz
Answer:
The answer for the first one is 1/2.
The answer for the second one is -1/1
Step-by-step explanation:
Hope that helps you :)
A jar contains 6 yellow and 8 blue gumballs. Two gumballs will be drawn at random without being replaced. If the first gumball drawn is blue, what is the probability that the second gumball will also be blue?
Answer:
I believe the answer would be 8/13 or 61.5%.
Step-by-step explanation:
Hope this helps :))
Rewrite using the
distributive property.
14 + 35?
whats the answer plz
Answer 7+7+35
Step-by-step explanation:
Answer:
I think (10*1)+4+(10*3)+5??
Step-by-step explanation:
the * represents a multiplication sign btw
How can the decimal 1.245 repeating be written as a quotient of two integers?
Answer:
1244/999
Step-by-step explanation:
So we have 1.245245245245.... which we call x.
If we times this by 1000 (because 3 digits repeat) we get
1000x = 1245.245245245....
Subtract x from both sides:
999x = 1245.245245245... - 1.245245... = 1244
This means that x = 1244/999
This fraction cannot be simplified so this is the answer.
If you want to include the 1 in the repeating (1.2451245...) do the same but the sequence is 4 digits so times by 10000 instead.
lamont cotton is 4% comission on the first 10,000 of monthly sales mens 10% on all sales over 10,000. last month his 38,00. what was his comission
Given:
Lamont cotton is 4% commission on the first 10,000 of monthly sales and 10% on all sales over 10,000.
Consider his last month sales is 38,000.
To find:
The total commission.
Solution:
4% commission on the first 10,000 of monthly sales is
[tex]10,000\dfrac{4}{100}=400[/tex]
Sales over 10,000 is
[tex]38,000-10,000=28,000[/tex]
10% commission on all sales over 10,000 is
[tex]28,000\times \dfrac{10}{100}=2,800[/tex]
Now, the total commission is
[tex]400+2,800=3,200[/tex]
Therefore, the total commission is 3,200.
Rhonda planted green beans on 67% of her farm. Rhonda's farm has 598 acres of land. Estimate the number of acres of green beans on Rhonda's farm.
Answer: 400 acres.
Step-by-step explanation:
We know that 598 is very close to 600, so we can round that amount up.
We also know that 67% is very close to [tex]\frac{2}{3}[/tex] because 2÷3≈0.67 & 67%=0.67
So, we can estimate [tex]\frac{2}{3}[/tex] of 600, which is about 400.
What is the value of (-4) (68) (1/4
Answer:
The answer is A
Step-by-step explanation:
Answer:
the correct answer is -68
algebra work needed please help
Consider the following two linear equations.
2x + y = 5
-2x + 2y = 4
Solve for the point of intersection using elimination
Point of intersection:
Answer:
(1,3)
Step-by-step explanation:
:)
I need help using the Expand Group and Factoring method on this problem.
27a^2+72a+28
Answer:
1 x (27a^2+72a+28) or 1(27a^2+72a+28)
Step-by-step explanation:
First find the GCF (greatest common factor) of 27a squared 72a and 28. It is 1 because there is nothing else that can go in.
So put 1 outside the parentheses and keep the terms
1 x (27a^2+72a+28)
Find the number of terms and the degree of this polynomial. -9
[tex]9 {r}^{9} [/tex]
Number of terms: Degree:
Answers:
Number of terms: 1Degree: 9===============================================
Explanation:
This is consider a monomial since we only have one term. Terms are separated by a plus sign, so something like 5x^2+10x has two terms.
The degree of a polynomial is the largest exponent when dealing with single variables. In the case of 9r^9, the largest exponent is 9, so the degree is 9. Going back to an example like 5x^2+10x, the largest exponent is 2 so this is the degree of this example.
Need help please and thank you
Perimeter= 4x+8 and Area= 2x+1x^2+2
I posted a photo on how I found these two answer.
Hope this helped
The sum of 7 times the number and 3 times the 2nd numbers 54 if the 1st number is 2 more than the 2nd number what are the 2 numbers right as this movie equations that can be used to find the numbers
Answer:
1) The series of equations that can be used to find the numbers are
7·x + 3·y = 54...(1)
x = y + 2...(2)
2) The first number is 6
The second number is 4
Step-by-step explanation:
1) The given parameters for the numbers are;
7 times the first number + 3 times the 2nd number = 54
The first number = The 2nd number + 2
Let 'x' represent the first number and let 'y' represent the second number
The following series of equations can therefore be used in finding the numbers;
7·x + 3·y = 54...(1)
x = y + 2...(2)
2) By substituting the value of x = y + 2 from equation (2) into equation (1) gives;
7·x + 3·y = 54
∴ 7×(y + 2) + 3·y = 54
7·y + 14 + 3·y = 54
10·y + 14 = 54
10·y = 54 - 14 = 40
y = 40/10 = 4
The second number = y = 4
The first number, x = y + 2 = 4 + 2 = 6
The first number, x = 6.
what are the missing values, and what is the equation for the table
Answer:
Step-by-step explanation:
This is a linear equation. Mx+b=y.
m=slope
x=x coordinate
y=y coordinate
b=y intercept (where x=0)
For this problem, you need to plug in 2 "coordinates", ex (1,16), and (0,__). You would need to find the slope, which would be y2-y1/x2-x1 (find two "coordinates" and then put it in, order doesn't matter.)
Hope this helps!
9514 1404 393
Answer:
see attached for table valuesexponential equation: y = 8·2^x; linear equation: y = 60x -44Step-by-step explanation:
Two points are not sufficient to define a graph, so the equation could be anything that gives the listed values.
We note that the given y-values are powers of 2. Specifically, they are 2^4 and 2^8. These powers differ by 4, just as the corresponding x-values differ by 4. This suggests an exponential equation might be good fit:
y = 2^(x+3)
Simplified, this is ...
y = 8·2^x . . . . . exponential equation for table values
__
Alternate solution
Often, when only two points are given, a linear function is indicated. We can use the two given points in the 2-point form of the equation for a line to find what the linear equation might be.
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
y = (256 -16)/(5 -1)(x -1) +16 . . . . with values filled in
y = 240/4(x -1) +16 . . . . . . . . . . . find the ratio
y = 60x -60 +16 . . . . . . . . . . . . . eliminate parentheses
y = 60x -44 . . . . . linear equation for table values
__
The two answers we looked at here are shown in the attached table. There are an infinite number of other possibilities.
Maggie wants to make a special card for Valentine’s Day. She starts with a
square piece of red paper with a side length of 12 cm. She then pastes two white
semi-circles, each with radius 3 cm, and a white triangle onto the square sheet of
red paper, as shown below. Determine the total amount of area available in the white region for Maggie’s special valentine greeting.
Answer:
I don't know
Step-by-step explanation:
I tried to search it up to get it correct but all it showed me was useless websites that didn't give me the answer
Question: Which set of directions correctly describes how to plot the point (6, 2) on the coordinate plane?
A.Start at the origin. Move 6 units to the right, then move 2 units up.
B.Start at the origin. Move 6 units up, then move 2 units to the right.
C.Start at the origin. Move 6 units to the left, then move 2 units up.
D.Start at the origin. Move 6 units up, then move 2 units to the left.
I GIVE BRAINLIEST!
Select the correct days. Gina tracks the low temperatures for a city over six days. Identify the days colder than -1.75°F.
Answer:
[tex]Monday = -2.5F[/tex]
[tex]Tuesday = -1.9F[/tex]
Step-by-step explanation:
Given
See attachment
Required
Days colder than -1.75°F
From the attachment, we have:
[tex]Monday = -2.5F[/tex]
[tex]Tuesday = -1.9F[/tex]
[tex]Wednesday = 0F[/tex]
[tex]Thursday = -1.5F[/tex]
[tex]Friday = 0.5F[/tex]
Days with temperature less than -1.75°F are colder.
-2.5 and -1.9 are less than -1.75
So, we have:
[tex]Monday = -2.5F[/tex]
[tex]Tuesday = -1.9F[/tex]
Answer:
:)
Step-by-step explanation:
I need help with this question answer withing 5 mins URGENT!!!!
why did u click on this and what is 5 + 2
tbh I don't know why I clicked on it. I'm bored and the answer is 7
Tell whether the two ratios form a proportion. 120 baskets made in 3 days and 720 baskets made in 18 days.
Answer:
Yes they form a proportion.
Step-by-step explanation:
120:3 = 720:18 because:
3x6=18 so multiply 120 by 6 and you get 720. Which means the ratios are proportionate.
The y-intercept is the point where the line crosses the
A. origin
B. slope
C. y-axis
D. x-axis