(1) Use the Integral Test to determine whether the series is convergent or divergent. ∑[infinity]n=1nn2+9 (2) Evaluate the following integral. ∫[infinity]1xx2+9dx
Answers
(1) By using the Integral Test, the series ∑[infinity]n=1nn2+9 is divergent.
(2) The value of integral ∫[infinity]1xx2+9dx is ∑(n=1 to ∞) (n/(n^2 + 9))
(1) To determine whether the series ∑(n=1 to ∞) (n/(n^2 + 9)) is convergent or divergent using the Integral Test, we first consider the function f(x) = x/(x^2 + 9) for x ≥ 1. This function is positive, continuous, and decreasing.
Now, we evaluate the improper integral ∫(1 to ∞) (x/(x^2 + 9)) dx.
(2) To evaluate the integral, ∫(1 to ∞) (x/(x^2 + 9)) dx, we use substitution. Let u = x^2 + 9, then du = 2x dx. The limits change to: when x=1, u=10, and as x→∞, u→∞. The integral becomes:
(1/2)∫(10 to ∞) (1/u) du
Now, integrate with respect to u:
(1/2)[ln|u|] (evaluated from 10 to ∞)
As u→∞, ln(u)→∞, so the integral diverges.
Since the integral diverges, by the Integral Test, the series ∑(n=1 to ∞) (n/(n^2 + 9)) also diverges.
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Related Questions
find the slope of the parallel and perpendicular line of y=3/4x+4
Answers
Answer:
16
Step-by-step explanation:
Answer:
To find the slope of the parallel and perpendicular lines to the equation y = 3/4x + 4, we need to use the fact that parallel lines have the same slope, while perpendicular lines have opposite reciprocal slopes.
The given equation is in slope-intercept form, y = mx + b, where m is the slope of the line and b is the y-intercept.
Therefore, the slope of the given line y = 3/4x + 4 is 3/4.
To find the slope of a line parallel to this one, we know that it must have the same slope. Therefore, the slope of the parallel line is also 3/4.
To find the slope of a line perpendicular to this one, we need to take the opposite reciprocal of the slope. The opposite reciprocal of 3/4 is -4/3. Therefore, the slope of the perpendicular line is -4/3.
In summary, the slope of the parallel line is 3/4, and the slope of the perpendicular line is -4/3.
simplyfy using appropiate properties 1/4×2/5+-1/6×3/2+3/7×2/5
Answers
Answer:
-1/35
Step-by-step explanation:
* means multiply
because of pemdas you should do three multiplication parts first
(1/4×2/5)+(-1/6×3/2)+(3/7×2/5)
1/20 - 3/12 + 6/35
3/60 - 15/60 + 6/35
-12/60 + 6/35
-1/5 + 6/35
-7/35 + 6/35
-1/35
Answer:
3/140
Step-by-step explanation:
1/4 × 2/5 + (-1/6) × 3/2 + 3/7 × 2/5 =
= 2/20 - 3/12 + 6/35
**********************************************
We need the LCD of 20, 12, 35.
20 = 2^2 * 5
12 = 2^2 * 3
35 = 5 * 7
LCD = 2^2 * 3 * 5 * 7 = 420
**********************************************
= 42/420 - 105/420 + 72/420
= 9/420
= 3/140
What does m equal and what is the slope
Answers
Answer:
The slope (m) = 2/3
Step-by-step explanation:
Taking any two points on the line:
(0,-2) & (3,0)
Using the slope formula to calculate the slope (m):
m = \(\frac{y2-y1}{x2-x1}\)
= (0-(-2))/(3-0)
= (0+2)/3
= 2/3
Hence, the slope (m) is 2/3.
Hope this helps and be sure to have a wonderful time ahead at Brainly! :D
8x2 – 7x + 4x3 – 2 – 3x2 + 9x - 4
Answers
Answer:
16+2x is your answer
Step-by-step explanation:
2 Simplify 4\times 34×3 to 1212.
16-7x+12-2-3\times 2+9x-416−7x+12−2−3×2+9x−4
3 Simplify 3\times 23×2 to 66.
16-7x+12-2-6+9x-416−7x+12−2−6+9x−4
4 Collect like terms.
(16+12-2-6-4)+(-7x+9x)(16+12−2−6−4)+(−7x+9x)
5 Simplify.
16+2x16+2x
Done
Some researchers have suggested that obesity is due to a change in ""set point"" in the brain that is related to the number of calories a person needs. People whose set point has increased eat more than they need and gain weight. Permanently raising the set point would involve a permanent change in which of the answer choices?.
Answers
For a person to become obese, the "Set point" must change and this would be due to a permanent change in the sensor.
What is obesity?The term obesity refers to a situation in which a person gathers excess fat in the body to a point that it becomes unhealthy and a potential health risk to the individual. A person is said to be obese if he/she has a body mass index above 25.
For a person to become obese, the "Set point" must change and this would be due to a permanent change in the sensor.
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2x-3=4(x+2) step by step plz
Answers
Answer:
The answer is -5.5
Step-by-step explanation:
2x-3=4(x+2)
2x-3=4x+8
-2x=11
X=-5.5
The graphs of y=f(x) and g(x) are shown below: a: -5 and 6 b: 4 and 7 c: -3,-1, and 4 d: -3,1,3 and 5
Answers
Brainliest goes to whoever answers correctly and explains also if you want extra points answer my other questions
Answers
Answer:
1) y= 2x
for every 5 x-steps to the right the graph goes up by ten. 10/5 is simplified to 2/1 or just 2
it starts at 0/0, so no need to add and absolute value
2) x: number of days
y: number of vidits (roughly2 per day, but you don't need to write this in the box)
3) 35 days. it's just y=70
and we could write this as
70 = 2*x | devide by 2 on both sides to get x
35 = x
what is the answer to number 2 at the top?
Answers
The equation of the transformed exponential function g(x) is g(x) = 2^-x - 1
Writing an exponential function for the graph of g(x)From the question, we have the following parameters that can be used in our computation:
Parent function: y = 2^x
The graph of the transformed exponential function g(x) passes through the points (-2,3), (-1,1), (0,0), (1,-0.5) and (2, -0.75)
So, we have the following transformation steps:
1st Transformation:
Reflect y = 2^x across the y-axis
So, we have
y = 2^-x
2nd Transformation:
Translate y = 2^-x down by 1 unit
So, we have
y = 2^-x - 1
This means that
g(x) = 2^-x - 1
Hence, the equation of the function g(x) is g(x) = 2^-x - 1
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Carl's grandfather is exactly 5 times older than Carl.
Which three statements must be true?
Answers
Answer:
g = 5c
5*c = g
g/5 = c
Step-by-step explanation:
g = grandfather
c = carl
Answer:
The age of Carl's grandfather is a composite number.
Carl's age is a factor of the age of his grandfather.
The number 5 is a factor of the age of Carl's grandfather.
Pump A and Pump B fill the pool in 35 minutes, Pump B and Pump C fill it in 40
minutes, and Pump A and Pump C fill it in 56 minutes. How many minutes will it take
all three pumps, working together, to fill the pool?
Answers
It will take all three pumps, Working together, 1.56 minutes to fill the pool.
The given information, we can write three equations as follows:
1) (1/A + 1/B)*35 = C ---(Equation 1)
2) (1/B + 1/C)*40 = C ---(Equation 2)
3) (1/A + 1/C)*56 = C ---(Equation 3)
We want how many minutes it will take all three pumps, working together, to fill the pool, so let's represent the time taken by all three pumps working together as "t".
When all three pumps work together, they can fill the pool in one minute, so their combined rate is 1/C.
Using the rate formula, we can write the following equation:
1/A + 1/B + 1/C = 1/t ---(Equation 4)
We have four unknowns (A, B, C, and t), so we need to solve for one of them to get the answer. Let's solve for "t".
First, we can simplify Equations 1, 2, and 3 as follows:
1) 1/A + 1/B = C/35
2) 1/B + 1/C = C/40
3) 1/A + 1/C = C/56
Next, we can substitute these equations into Equation 4 to get:
(C/35) + (C/40) + (C/56) = 1/t
Now, we can simplify and solve for "t":
LCD = 39200
1120C + 980C + 700C = 39200
2800C = 39200
C = 14
Substituting this value of "C" into any of the simplified equations, we can solve for "A" and "B". Let's use Equation 1:
1/A + 1/B = 14/35
5(A+B) = 98
A+B = 19.6
Now we can use A+B+C = 1/t to solve for "t":
t = 1 / (A+B+C) = 1 / (19.6 + 14) = 0.026 hours = 1.56 minutes
Therefore, it will take all three pumps, working together, 1.56 minutes to fill the pool.
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A flooring tile ha a hape of a parallelogram Hight i 10cm and bae i 24cm how many tile do you need to fill a room with area 1080 mq
Answers
We must first calculate the area of a single tile in order to figure how many floor tiles are required to cover a space that is 1080 square meters.
Since the area of a parallelogram is equal to its base times its height, the tile's area is 24 x 10 cm, or 240 \(cm^{2}\).
Since one square meter equals 10,000 square centimeters, we divide by 10,000 to convert this area to square meters: 240 \(cm^{2}\) / 10,000 = 0.024 c\(m^{2}\)
Thus, a single tile has a surface area of 0.024 square meters.
We divide a room's 1080 square meters by a tile's area to determine how many tiles are required to completely cover the space:
1080 \(m^{2}\) / 0.024 \(m^{2}\)= 45,000
Therefore ,45,000 floor tiles would be required to cover a space that is 1080 square meters in size.
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A farmstand sells apples, a, for $4 a bucket; peaches, p, for $6 A bucket; and strawberries, s, for $9 a bucket. The stand earn $229 in revenue last month. The stand sold half as many strawberry buckets as peach buckets, and eight were apple buckets then peach buckets. Using the substitution method how many apples peaches and strawberries did the farmstand sell?
A. a=10; p=18; s=9
B. a=4; p=6; s=9
C. a=18; p=10; s=9
D. a=9; p=18; s=10
Answers
Answer:
A.
Step-by-step explanation:
process of elimination. They sold half as many strawberries as peaches.
Can somebody help me on this thanks
Answers
Answer:
Add 3/4 to both sides (the last option)
Step-by-step explanation:
Since you want to isolate f and the expression on one side is f - 3/4, you have to add 3/4 so that the -3/4 cancels out. When you do that, you also have to add 3/4 to the other side so that the equation stays balanced.
Most experts believe that young children’s not being
given physical affection, this interferes with their
normal development.
(A) young children’s not being given physical
affection, this interferes
(B) for young children who have had physical
affection withheld from them, it interferes
(C) the failure at giving young children physical
affection would interfere
(D) when withholding physical affection from
young children, it interferes
(E) the withholding of physical affection from
young children interferes
Answers
(E) "the withholding of physical affection from young children interferes"
The mistake here is in the punctuation. The subject ("young...affection") and its verb are needlessly separated by a comma ("interferes"). Furthermore, the sentence's structure is complicated. Only E fixes these mistakes without introducing any new ones.
There is improper punctuation in Option (A). The subject ("young...affection") and its verb are needlessly separated by a comma ("interferes"). Uncertain pronoun references are present in Option (B). It's unclear to what the pronoun "it" refers.
The incorrect usage of a definite article is in Option (C). The words "the failure" implies that the failure has already been discussed, yet this is false. Choice (D) uses inappropriate wording. "Withholding" is a verb without a subject.
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What is a possible first step to solving the rational equation: A Subtract the numerators and denominators B Find the common denominator C Cross multiply D Use the quadratic formula
Answers
The answer is B, which is to find the common denominator.
In solving a rational equation, the first step is usually to find a common denominator for all the fractions in the equation. This allows us to combine the fractions into a single fraction and simplify the equation.
To find the common denominator, we need to identify the factors of the denominators and determine the least common multiple (LCM) of these factors. Then, we multiply each fraction by the appropriate factor(s) to get the common denominator. For example, if we have the equation:
(3/x) + (4/2x) = 1/4
The denominators are x and 2x, which have factors of x and 2. The LCM of these factors is 2x, so we need to multiply the first fraction by 2 and the second fraction by 1 to get:
(6/2x) + (4/2x) = 1/4
Then we can combine the fractions and simplify the equation to get:
(10/2x) = 1/4
From here, we can continue to solve for x by cross multiplying and manipulating the equation.
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Please help me I will mark the one who gives me the answer first.
Find the value of the given pic in the attachment
Answers
Answer:
I believe it is D.
Step-by-step explanation:
Hope it helps! =D
If (xn) is a convergent sequence and (yn) is such that for any ϵ>0,∃M such that |xn−yn|<ϵ,∀n≥M. Is (yn) convergent?
Answers
According to the given information, (yn) is convergent.
What is the convergence and divergence of the sequence?
Convergence: A sequence approaches a fixed number as the number of terms increases.
Divergence: A sequence does not approach a fixed number as the number of terms increases.
Yes, (yn) is convergent.
Since (xn) is a convergent sequence, it has a limit L, which means that for any ε > 0, there exists an N such that |xn - L| < ε for all n ≥ N.
Now, let ε > 0 be given. Then, there exists an M such that |xn - yn| < ε for all n ≥ M.
Combining these two inequalities, we have:
|yn - L| = |yn - xn + xn - L|
≤ |yn - xn| + |xn - L|
< ε + ε (for all n ≥ M)
Therefore, we have shown that for any ε > 0, there exists an M such that |yn - L| < 2ε for all n ≥ M.
Since 2ε can be made arbitrarily small by choosing ε small enough, this implies that (yn) converges to L, the limit of (xn).
Hence, (yn) is also convergent.
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Use the sketch tool to mark the picture with the given
information. Then choose what postulate proves the
triangles congruent
SAS
SSS
AAS
ASA
HL
Answers
Answer:
SAS
Step-by-step explanation:
We know that segment PR is congruent to segment SQ, because of the a line bisects the segment the segments are on. We also know that angle PRQ is congruent to angle SRQ, because of the reflexive property. Using the same property, QR is congruent too QR.
By knowing that, we can conclude that the two triangles are congruent because of SAS.
In a recent town election, 1,860 people voted for either candidate A or candidate B for the position of supervisor.
If candidate A received 55% of the votes, how many votes did candidate B receive?
Answers
EXPLANATION:
if candidate A recieved 55% of the votes,
Then candidate B recieved 45% of the votes, because it must equal 100%
45% of 1860 is 837.
Hope this helpz!
What is the scale factor that will carry the segment AB into segment MN?
Given: A (-4,4) B (-2,3) and M (-3,6), N (1,4)
Answers
The scale factor that will carry line segment AB into line segment MN is 2.
Now, we are given two lines AB and MN,
And points are given
A(-4,4),B(-2,3),M(-3,6) and N(1,4)
Now, to find the scale factor first find out the length of each line segment,
we can find out the length by using manipulation of Pythagorean theorem,
which gives
\(\sqrt{(X_{2}-X_{1} )^{2}-(Y_{2}-Y_{1} )^{2} }\)
now use A and B points to put in the formula
AB=\(\sqrt{(-2+4)^{2}+(3-4)^{2} }\)
AB=\(\sqrt{4+1}\)
AB=\(\sqrt{5}\)
and now to find MN line segment,
use points M and N to put in the formula
MN=\(\sqrt{(1+3)^{2}+(4-6)^{2} }\)
MN=\(\sqrt{16+4}\)
MN=\(\sqrt{20}\)
Now, line segment AB is carry into MN line segment that means the new line segment is MN and original line segment is AB
To find out the scale factor divide new line segment by original line segment.
scale factor =\(\frac{\sqrt{20} }{\sqrt{5} }\)
scale factor=2
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Find the slope between:
(1, -4)
(-6, -1)
Answers
use the slope formula: y2-y1 over x2-x1
-1-(-4) over -6-(-1) = -3/7
PLEASE HELP I WILL MARK YOU BRAINLIEST
Answers
Answer:
B
Step-by-step explanation:
\(\frac{2}{3}\) × 63 = 2 × 21 = 42
Her prediction was correct as \(\frac{2}{3}\) of 63 = 42 → B
Question 6 mathematics
Answers
The quadratic regression equation is given as follows:
y = -0.02x² + 0.14x + 19.6.
How to obtain the regression equation?Regression equations are obtained inserting the points of a data-set into a calculator.
In this problem, we want to find the quadratic regression equation, hence a quadratic regression calculator is used.
The points for this problem are given as follows:
y = -0.02x² + 0.14x + 19.6.
Meaning that the fourth option is the correct option.
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Kaylee made ten cups of snack mix for the pool party. She used one and two-thirds cups of mixed nuts, one and two-thirds cups of pretzel sticks, and crispy cereal to make the snack mix. How many cups of crispy cereal did she use?
Answers
Answer:
6 2/3 cups
Step-by-step explanation:
10- 1 2/3- 1 2/3= 8 1/3- 1 2/3= 6 2/3
Answer:
\(6 \frac{2}{3}\) cups of crispy cereal.
Step-by-step explanation:
\(10- 1 \frac{2}{3} - 1 \frac{2}{3} =\)
\(\frac{30}{3} -\frac{5}{3} -\frac{5}{3} =\)
\(\frac{20}{3} =\)
\(6 \frac{2}{3}\) cups of crispy cereal.
I finished all my other questions but i don't know how to do this one. could someone help me? I added 100 points. It is attached. :)
Answers
The answers are mentioned below.
What is Acceleration ?Acceleration is the change of speed with respect to time.
It is given that ,
The mass of the person is 50kg
Weight is 490 N
He has boarded an elevator with a bathroom scale.
1. The elevator is going down at constant speed , Force = 0N as acceleration is zero , The reading is 50kg.
2. The elevator is going up an slowing down . The magnitude of the acceleration is 4.9 m/sq.s , Force = mass * acceleration = 50 * 4.9 = 245N acting upward but the net force will be acting downward.
490 - 245 = 145N , reading 14.79 kg.
3.The elevator is free falling with an acceleration of 9.8m/sq.s force 0 N , as the gravitational force is pulling you down and the scale pushes up with the same force , Reading is 0 kg.
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Consider the series ∑n=1[infinity]an∑n=1[infinity]an where
an=(n+2)!en−6n+5‾‾‾‾‾√an=(n+2)!en−6n+5
In this problem you must attempt to use the Ratio Test to decide whether the series converges.
Answers
Thus, as the limit is less than 1, by the Ratio Test, the series ∑n=1[infinity]an converges absolutely.
The Ratio Test is a useful tool for determining whether an infinite series converges or diverges.
To use the Ratio Test, we take the limit of the absolute value of the ratio of successive terms as n approaches infinity. If this limit is less than 1, then the series converges absolutely.
If the limit is greater than 1, then the series diverges. If the limit is equal to 1, then the Ratio Test is inconclusive, and we must try another test.
To apply the Ratio Test to the series ∑n=1[infinity]an, we need to compute the ratio of successive terms:
|an+1/an| = |(n+3)! e(n+1) - 6(n+2) + 5‾‾‾‾‾√| / |(n+2)! e(n) - 6(n+1) + 5‾‾‾‾‾√|
Simplifying this expression, we get:
|an+1/an| = [(n+3)/(n+2)]e / [6(n+2)/(n+3) + 5‾‾‾‾‾√]
As n approaches infinity, both the numerator and the denominator approach infinity, so we can apply L'Hopital's Rule to find the limit:
lim n→∞ |an+1/an| = lim n→∞ [(n+3)/(n+2)]e / [6(n+2)/(n+3) + 5‾‾‾‾‾√]
= lim n→∞ e(n+1) / (6 + 5(n+2)/(n+3)‾‾‾‾‾√)
= e/5‾‾‾‾‾√
Since the limit is less than 1, by the Ratio Test, the series ∑n=1[infinity]an converges absolutely. This means that the series converges regardless of the order in which the terms are summed, and we can find its value by summing the terms in any order.
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Please help thank you :)
Answers
Answer:
Step-by-step explanation:
Angle 1 is equal to angle 3 because they are opposite each other so
Angle 1=43 degrees
Angle 1 and angle 2 have a sum of 180 degrees because they are adjacent to each other.
angle 2=180-43=137 degrees.
angle 2 and 4 are opposite each other so they are equal
angle 4=137 degrees.
Answer:
Angle 1 = 43°
Angle 2 = 137°
Angls 4 = 137°
Step-by-step explanation:
To get angle 1, l and m intersect and there are two angles which cause vertical opposite angles. When there are vertical opposite angles, both angles have the same degree. For angle 2, you need to find angle 1 and 3, after that you deduct both angle 1 and 3 from 360° which is the angle of whole figure. 360 - 43 - 43 = 274° for angle 2 and 4, since they're also vertically opposite angles, both 2 and 4 have the same angle. All you need to do to find 2 and 4 is 274 ÷ 2 = 137°.
There is an equilateral triangle, ABC, inscribed in a circle with center D. What is the smallest angle you can rotate triangle ABC around D so that the image of A is B?
Answers
Answer:
correct answer is "B"...
Please help!!!!!!
The figure shows the graph of the quadratic function Find the average rate of change between points F and G and between points G and H.
Write down the greater rate of change.
Answers
Answer: 5
Step-by-step explanation:
Between F and G: \(\frac{-5-0}{-3-(-2)}=5\)
Between G and H: \(\frac{3-0}{-1-(-2)}=3\)
So, the greater rate of change is 5.
