Test each of the following series for convergence by the Integral Test. If the Integral Test can be applied to the series, enter CONV if it converges or DIV if it diverges. If the integral test cannot be applied to the series, enter NA. (Note: this means that even if you know a given series converges by some other test, but the Integral Test cannot be applied to it, then you must enter NA rather than CONV.) n +4 NA NA 8-มี 8-JI 8-12-18 DIV CONV CONV ก=1 2(In(5n))
Answers
The answer is DIV.
How to determine the convergence or divergence of given series?To test the given series for convergence using the Integral Test, we need to first identify the series and rewrite the question clearly. It seems there are some typos and irrelevant parts in the question. After omitting those, the series can be identified as:
∑(n+4) from n=1 to infinity
Now let's apply the Integral Test:
1. The function f(n) = n+4 is continuous for n≥1.
2. The function f(n) = n+4 is positive for n≥1.
3. The function f(n) = n+4 is decreasing for n≥1.
Since all three conditions are met, we can apply the Integral Test. Now, we need to evaluate the improper integral:
∫(n+4)dn from n=1 to infinity
To do that, first find the antiderivative:
F(n) = (1/2)n^2 + 4n
Now, evaluate the improper integral:
lim (t -> infinity) [ (1/2)t^2 + 4t - (1/2)(1)^2 - 4(1) ]
Since the limit does not exist, the integral diverges. By the Integral Test, the series also diverges.
Your answer: The series ∑(n+4) from n=1 to infinity diverges by the Integral Test, so the answer is DIV.
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Related Questions
Find the perimeter of this complex figure
Answers
Answer:
38
Step-by-step explanation:
9 + 10 + 2 + 6 + (9 - 2) + (10 - 6) = 38
Container A holds 5 times as much milk as Container B. After 1.25 L of milk from Container A is poured into Container B, both containers have the same amount of milk. How much milk does each container have at first?
Answers
Answer:
Container A: 3.125 L
Container B: 0.625 L
Step-by-step explanation:
Let x represent the starting amount for Container A.
Let y represent the starting amount for Container B.
Set up an equation to represent what is happening.
Note that milk poured out Container A is poured INTO Container B, so the overall value of the equation should remain the same when subtracting 1.25 L from Container A.
\(5(y) = x\\x-1.25 = 1.25 + y\) → \(x = 2.5 +y\)
This is now a solvable system of equations. Use substitution to set the equations equal to each other and solve for y.
\(5y = 2.5 + y\\4y = 2.5\\y = 0.625 L\\\\x = 5y\\x = 5(0.625)\\x = 3.125 L\)
Container A started with 3.125 L and Container B started with 0.625 L.
Figure 1
Figure 2
Figure 3
If this pattern continues, how many squares will be in the 10th figure?
0
A. 14
B. 20
C. 26
D. 29
o D
E 32
Answers
Answer:
Step-by-step explanation:
E
Answer:
answer is 32
Step-by-step explanation:
keep adding 3 to the figures and that is how you will get the answer
things about physical science
Answers
Answer:
Physical science is the study of matter and energy. It includes chemistry, which focuses on the matter, and physics, which focuses on energy. Physical science explains everyday observations and actions. Its advances make modern life possible.
What is the area of a section of pavement that is 10 ft wide and 80 yd long? Give your answer in square feet.
Answers
Answer:
The area of this section of pavement is 800 square feet
Step-by-step explanation:
10 ft times 80 ft = 800 square feet
Give me brainliest if that helped :)
1. -10 = 5+y
2. 10x = 40
3. -2 = -4m = +10
if you can answer this I will brainliest
Answers
The solution to the equation -2 = -4m + 10 is m = 3.
Here are the solutions to the given equations:
1. -10 = 5+y
To solve for y, we need to isolate y on one side of the equation.
We can do this by adding 10 to both sides of the equation.
-10 + 10 = 5 + y + 10
Simplifying,
-0 = 5 + y
We can further simplify the equation by subtracting 5 from both sides of the equation.
-5 = y
Therefore, the solution to the equation -10 = 5+y is y = -5.2.
10x = 40
To solve for x, we need to isolate x on one side of the equation.
We can do this by dividing both sides of the equation by 10.10x/10 = 40/10
Simplifying,
x = 4
Therefore, the solution to the equation 10x = 40 is x = 4.3.
-2 = -4m + 10To solve for m, we need to isolate m on one side of the equation.
We can do this by subtracting 10 from both sides of the equation.-2 - 10 = -4m.
Simplifying,
-12 = -4mWe can further simplify the equation by dividing both sides of the equation by -4.-12/-4 = m3 = m.
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expand and simplify completely (log). PLEASEE HELP ASAP!!! I WILL GIVE BRAINLIEST!! thank you so much!!!!
Answers
Answer:
c. \(2 log3(y)+1+log3(x)\)
Step-by-step explanation:
When expanding and simplifying, we can see that the answer is \(1+log3(x) + 2log3(y)\), which matches Answer Choice C.Answer:
( C ) 1+log3x+2log3y
Step-by-step explanation:
suppose sum(an3^n) converges and sum(an6^n) diverges. what can you say about a). the radius of convergence of the power series
Answers
Since the power series involves terms of the form an3^n and an6^n, we can conclude that the radius of convergence of the power series must be at least 3.
This is because the series converges for values of x that are within a distance of 3 from the origin. However, we cannot say anything about the radius of convergence beyond 3, as the fact that sum(an6^n) diverges tells us nothing about how the power series behaves for values of x greater than 3.
If you have a power series sum(an * x^n) and you're given that sum(an * 3^n) converges while sum(an * 6^n) diverges, we can analyze the radius of convergence (R) using the ratio test.
The ratio test states that if the limit as n approaches infinity of |a_(n+1) * x^(n+1) / (a_n * x^n)| exists and is less than 1, the series converges. If the limit is greater than 1, it diverges. In this case, we have:
1. Convergent series: sum(an * 3^n)
2. Divergent series: sum(an * 6^n)
By applying the ratio test to the convergent series, we get:
lim (n→∞) |(a_(n+1) * 3^(n+1)) / (a_n * 3^n)| < 1
For the divergent series:
lim (n→∞) |(a_(n+1) * 6^(n+1)) / (a_n * 6^n)| > 1
Comparing the two inequalities, we can conclude that the radius of convergence (R) for the power series sum(an * x^n) lies between 3 and 6, i.e., 3 < R < 6.
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Helppp
Alberto and Bianca run 50km race. The illustration below the graph of the position of the two runners as a function of time. complete the following sentence based on the graph of the function.
- Early in the race,__ runs faster.
- Alberto maintains a speed of __ km/h during the first hour of the race.
- meanwhile, Bianca’s running speed __
-The first person to cross the finish line is__
Answers
Answer:
- Early in the race,_Alberto_ runs faster.
- Alberto maintains a speed of _20_ km/h during the first hour of the race.
- meanwhile, Bianca’s running speed _Is exponential_
-The first person to cross the finish line is_Bianca_
A bug begins to crawl up a vertical wire at time t = 0. The velocity v of the bug at time t, 0 < t < 8, is given by the function whose graph is shown behind this text. At what value of t does the bug change direction? a. 2
b. 4
c. 6.5
d. 7
Answers
The bug changes direction at t = 4. This can be answered by the concept of velocity.
To determine when the bug changes direction, we need to find when its velocity changes sign from positive to negative. From the graph, we see that the bug's velocity is positive for t < 4 and negative for t > 4. Therefore, the bug changes direction at t = 4.
To verify this, we can look at the behavior of the bug's velocity as it approaches t = 4. From the graph, we see that the bug's velocity is increasing as it approaches t = 4 from the left, and decreasing as it approaches t = 4 from the right. This indicates that the bug is reaching a maximum velocity at t = 4, which is when it changes direction.
Therefore, the bug changes direction at t = 4.
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A bedroom is 10 ft. by 12. ft. with 8 ft. high walls. How much would it cost to put padding and carpet in this room
Answers
Answer $2,295.60:
Step-by-step explanation: i just did this assignment and got it right, hope this helps
what is
6
+0.2
————-
Answers
Answer:
Your correct answer will be 6.2
Step-by-step explanation:
First, we line up the decimal points, 0.2 plus 6.0, always add 0 to the number without the decimal.
Last, you just add them, and you will get 6.2
Mark me brainliest and have a good day!
the magnitude of earthquakes recorded in a region of north america can be modeled as having an exponential distribution with mean 2.4, as measured on the richter scale. find the probability that an earthquake striking this region will exceed 5.0 on the richter scale.
Answers
The probability that an earthquake striking this region will exceed 5.0 on the richter scale is approximately 0.121 or 12.1%.
To find the probability that an earthquake striking this region will exceed 5.0 on the richter scale, we need to use the cumulative distribution function (CDF) of the exponential distribution.
The CDF of the exponential distribution is given by:
\(F(x) = 1 - e^{(-\lambda x)}\)
where λ is the rate parameter, which is equal to 1/mean for the exponential distribution.
So in this case, λ = 1/2.4 = 0.4167.
To find the probability that an earthquake will exceed 5.0 on the richter scale, we need to calculate:
P(X > 5) = 1 - P(X ≤ 5)
= 1 - F(5)
= \(1 - (1 - e^{(-0.4167*5))\)
=\(e^{(-2.0835)\)
= 0.121
Therefore, the probability that an earthquake striking this region will exceed 5.0 on the richter scale is approximately 0.121 or 12.1%.
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ABCD is a Rhombus with side length 10 cm. Angle ADC = 40. DAC is a sector of a circle with center D. BAC is a sector of a circle with center B. Calculate the shaded area.
Answers
The value of the shaded area is approximately 34.907 square centimeters.
How to calculate the area between a rhombus and a circle
According to the description in statement we prepared a representation of the figure in the image attached below. The shaded area is equal to the area of the circle sector (\(A\)), in square centimeters:
\(A = \frac{\theta\cdot \pi \cdot R^{2}}{360}\) (1)
Where:
\(R\) - Length of the radius, in centimeters. \(\theta\) - Angle of circle arc, in degrees.If we know that \(\theta = 40^{\circ}\) and \(R = 10\,cm\), then the area of the circle is:
\(A = \frac{(40)\cdot \pi\cdot (10\,cm)^{2}}{360}\)
\(A\approx 34.907\,cm^{2}\)
The value of the shaded area is approximately 34.907 square centimeters. \(\blacksquare\)
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1.4f + 1.1 = 8.3 - f
Answers
Answer: correct
Step-by-step explanation:
Work:
1.4f + f = 8.3 - 1.1
2.4f= 7.2
f=3
Complete the equation that has (3,4) as a solution.
Answers
The equation representing (3,4) as a solution is given by y = 2x - 2.
Solution of the equation is equal to ( 3, 4 ).
Equation is equals to ,
y = __x - 2
To find the value of the missing coefficient in the equation y = __x - 2,
We can substitute the given solution (3, 4) for x and y .
And solve for the missing coefficient of the equation.
let us consider missing coefficient be represented by variable 'm'.
y = mx - 2
Substituting x = 3 and y = 4 in the equation , we get,
⇒ 4 = m × 3 - 2
Add 2 on both the side of the equation we get,
⇒ 4 + 2 = m × 3 - 2 + 2
⇒ 6 = m × 3
Now divide both the side of the equation by 3 we get,
⇒ 6 / 3 = m × 3 / 3
⇒ m = 2
Required equation is equal to
y = 2x - 2
Therefore, the equation that has (3,4) as a solution is equal to y = 2x - 2
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The above question is incomplete, the complete question is:
Complete the equation that has (3,4) as a solution.
y = __x -2
Anthony wants to find out the percentage of students at his school who are vegetarians. Which of the following is the most representative group of students for him to surve
A. 50 students at a icecream parlor
B. 5 students at a icecream parlor
C. 50 students at a hamburger restaurant
D. 5 students at a hamburger restaurant
Answers
Answer:
I think c
Step-by-step explanation:
i might be wrong so dont trust my answer but i would've picked C
Use basic trigonometric identities to simplify the expression: tan^3(x) + tan (x)=?
Answers
Step 1
Simplify the expression.
\(\tan (x)(\tan ^2(x)\text{ +1)}\)Step 2
Find a trigonometric identity that can be used to simplify the expression in step 1
\(\tan ^2(x)+1=sec^2(x)\)Step 3
Get the final answer after substitution.
\(\tan (x)sec^2(x)\)Hence the right answer is option B
A square of side 4cm is enlarged by a scale factor 2.5. What is the are of the enlarged square
Answers
Answer:
10
Step-by-step explanation:
4 * 2.5 = 10
Find the exact value of each expression. sin75 degrees and cos(-75 degrees).
Answers
Answer:
0.965925826
0.258819045
Step-by-step explanation:
→If you were to calculate \(sin(75)\), you would have a total of:
0.965925826
→If you were to calculate \(cos(-75)\), you would have a total of:
0.258819045
you have a cake that is 16 inches by 18 inches.you want each piece to be exactly the same size.how many people can u serve equal sized piece of cake
Answers
The number of people are 72.
What is HCF?Highest Common Factor is the full name for HCF in mathematics.
According to the laws of mathematics, the highest positive integer that divides two or more positive integers without leaving a residual is known as the greatest common divisor, or gcd.
What is LCM?Least Common Multiple is the full name for LCM in mathematics.
LCM (a,b) in mathematics stands for the least common multiple, or LCM, of two numbers, such as a and b. The smallest or least positive integer that is divisible by both a and b is known as the LCM.
We need to know the size of the pieces in order to calculate how many people can be fed equal-sized pieces of cake from a 16 by 18-inch cake.
Assume that each piece is a square with sides measuring "x" in length. Each piece's area would be x², and the cake's overall area would be 16 x 18 inches, or 288 square inches.
We must divide the entire area of the cake by the area of each piece to determine the maximum number of pieces that can be cut from the cake:
288 / x² = (16*18) / x² = 288 / x²
Choosing a "x" value that evenly splits into 16 and 18 is necessary if we want every piece to be the exact same size. Since 2 is the greatest possible value, we can divide the cake into 8 rows of 9 squares, yielding a total of 72 pieces.
As a result, a cake measuring 16 inches by 18 inches can be divided into 72 equal-sized pieces, each measuring 2 inches by 2 inches.
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We can serve 18 people equal-sized pieces of cake from a cake that is 16 inches by 18 inches, assuming each piece is a square and we want the pieces to be exactly the same size.
What is area?A two-dimensional figure, form, or planar lamina's area is a measurement of how much space it takes up in the plane.
To find out how many people can be served equal-sized pieces of cake from a cake that is 16 inches by 18 inches, we need to first determine the size of each piece of cake.
The total area of the cake is:
16 inches x 18 inches = 288 square inches
To divide the cake into equal-sized pieces, we need to determine the size of each piece. Let's assume we want each piece to be a square. To find the size of each square, we need to find the square root of the total area of the cake:
√(288 square inches) ≈ 16.97 inches
Since we want the pieces to be exactly the same size, we'll round down to the nearest inch, which gives us:
Each piece of cake will be approximately 16 inches by 16 inches.
To find out how many people can be served equal-sized pieces of cake, we need to divide the total area of the cake by the area of each piece:
288 square inches ÷ (16 inches x 16 inches) = 18
Therefore, we can serve 18 people equal-sized pieces of cake from a cake that is 16 inches by 18 inches, assuming each piece is a square and we want the pieces to be exactly the same size.
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Select one of the following functions to match the graph.
A. y = (7) x
B. y = (7)-x
C. y = (-7) x
D. y = (-7)-x
Answers
Answer:
B
Step-by-step explanation:
The explanation is attached below.
Erin's family has completed 70% of a trip. They have traveled 35 miles.
How far is the trip?
Answers
Answer:
Their trip is 50 mile long.
Step-by-step explanation:
I first divided 70 by 35 to get two.The two represents 1 mile = 2%. So then I subtracted 70 from 100 to get 30 then I divided 30 by 2 to get 15. Then I added 15 to the original 35 to get 50 miles for their 100%/destination of their trip. Hope this helps! Have a great day!
A jeweler designs necklaces that are perfectly round open- circles each with a radius of 8.4mm. (1m= 1000mm) What is the largest number of open- circle necklaces that can be made from a wheel of spooled gold that is 42m long?
Answers
Answer:
795
Step-by-step explanation:
First, we find the circumference of 1 ring.
c = 2πr
c = 2 × 3.14159 × 8.4 mm
c = 52.7787 mm
The circumference of 1 ring is the length of spooled gold used for 1 ring.
The spool has a total length of 42 m.
42 m × 1000 mm / 1 m = 42,000 mm
The spool has a total length of 42,000 mm.
Now we divide the length of the spool by the length of 1 ring.
42,000 mm / 52.7787 mm = 795.78
He can make 795 rings.
what is the answer??????
Answers
Answer:
1) B 1 1/32 2) A 1.8
Step-by-step explanation:
1) 2 3/4÷2 2/3
Turn into improper fractions.
11/4÷8/3
Keep Change Flip
11/4x3/8
Multiply.
33/32
=1 1/32
2) 1 4/5 as a decimal.
Turn into an improper fraction.
9/5
Divide.
=1.8
Hope this helps :)
Centimeter using decimal
63mm
Answers
Answer:
6.3cm
Step-by-step explanation:
10mm=1cm
63mm=?cm
(cross multiply)
?=(63mm×1cm)/10mm
?=6.3cm
x^3x^5=x^p, where p=
Answers
Here, we use the property of multiplication of exponential expression which states when we multiply two exponential expressions with the same base, we keep the base and add the exponents.
Therefore,
\(x^(3+5) = x^8\)
Now,
\(x^(3+5) = x^8\)
is of the form:
\(x^b = x^p\)
When we have two equal expressions on either side of the equation, the power of the base remains the same. Therefore,
p = 8
There we have it. The value of p is 8. The full solution is shown below:
\(x^3 × x^5 \\= x^px^8\\ = x^p\)
We can see that the base of the exponential expression on either side is equal.
Therefore, the power of the base must be equal as well. In other words
,p = 8.
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Four years after paying 3100 for shares in a startup company you sell the shares for 2500 at a loss the total return is what percentage
Answers
The tοtal return is a lοss οf apprοximately 19.35%.
What is the percentage?Percentage is a way οf expressing a number as a fractiοn οf 100.
The tοtal return is the difference between the selling price and the purchase price, which is:
2500 - 3100 = -600
Since the difference is negative, we have a lοss. Tο find the percentage οf the lοss, we need tο divide the lοss by the οriginal investment and multiply by 100:
-600 / 3100 * 100 ≈ -19.35%
Hence, the tοtal return is a lοss οf apprοximately 19.35%.
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What is the slope-intercept form of y+2=1/2(x+6)
Answers
Answer:
y=1/2x+1
Step-by-step explanation:
slope-intercept form: y=mx+b
y+2=1/2(x+6)
solve distributive property
y+2=1/2x+3
subtract 2 from both sides
y=1/2x+1
HELP PLEASE I WILL GIVE 50 POINTS AND MARK BRAINLESS TO BEST ANSWER
Answers
Answer:
The answer is 15
Step-by-step explanation:
I know and is not stupid
Answer:
x=15
x+3x+8x=180(sum of interior angle of triangle)
12x=180
x=180/12=15