(10 points) The series Înky" converges when 0 < <1 and diverges when r > 1. This is true regardless of the value of the constant k. When r = 1 the n=1 oo series is a p-series. It converges if k < -1 and diverges otherwise. Each of the series below can be compared to a series of the form nk pn. For each series n=1 determine the best value of r and decide whether the series converges. 00 A. (7+n(7)")-7 n=1 r = converges or diverges (c or d)? с B. n" 72n 6" + n 9 n=1 r= converges or diverges (c or d)? d C. n + 2 no +7 n T= converges or diverges (c or d)? с 3 D. 2n2 + In +7-31 gn+2 +6n +7/n n=1 r = converges or diverges (c or d)? C
Answers
The a) , c) & d) are convergent series and b) is divergent series.
a)
Given series,
\(\sum \limits^\infty_{n=1} (7+n(7))^{-7}\\ \\=\sum \limits^\infty_{n=1}7^{-7}+\sum \limits^\infty_{n=1}(7^nn)^{-7}\\\)
consider,
\(\sum \limits^\infty_{n=1}(7^nn)^{-7}=\sum \limits^\infty_{n=1}(n)^{-7}(7)^{-7}\\\\=\sum \limits^\infty_{n=1}(n)^{-7}(7)^{-7}\\\\=\sum \limits^\infty_{n=1}(n)^{-7}(\frac{1}{7})^{7}\)
comparing \(=\sum \limits^\infty_{n=1}(n)^kr^n\) we get,
\(k=-7\ and\ r=\frac{1}{7^7}=\frac{1}{823543}\)
here, \(|r|=|\frac{1}{7^7}|=1.2142*10^{-6}\) which is < 1
here |r| < 1,
Thus, the given series converges.
b)
Given series,
\(\sum \limits^\infty_{n=1} n^{\pi}(\frac{7^{2n}}{6^n+n^9})=\sum \limits^\infty_{n=1}n^kr^n\)clearly, k=π
To find r we need to use ratio test for \(a_n\)
\(a_n=\frac{7^{2n}}{6^n+n^9}\\\\L= \lim_{n \to \infty}|\frac{a_n+1}{a_n} |\\\\=\lim_{n \to \infty}|\frac{7^{2n+2}}{6^{n+1}+(n+1)^{9}}*\frac{6^{n}+(n)^{9}}{7^{2n}}|\\\\=\lim_{n \to \infty}|\frac{7^2(6^n+n^9)}{6{n+1}+(n+1)^9}|\\\\=\lim_{n \to \infty}|\frac{49(6^n+n^9)}{6^{n+1}+(n+1)^9}|\)
here \(r=\frac{49}{6}\) > 1
hence. the series diverges.
c)
Given series,
\(\sum \limits^\infty_{n=1}\frac{n^5+2}{n^6+7}\)
let \(u_n=\frac{n^5+2}{n^6+7}\)
take \(v_n=\frac{n^5}{n^6}=\frac{1}{n}\)
Now,
\(\lim_{n \to \infty} \frac{u_n}{v_n}= \lim_{n \to \infty}\frac{n^5+2}{n^6+2}*\frac{n}{1}\\=1\\Now,\\\\\sum v_n=\sum \frac{1}{n}\\\\=\sum (n)^{-1}(1)^n\\\\\)
comparing with \(\sum n^kr^n\) we get,
k=-1 and r=1
So, the series converges.
d)
Given series,
\(\sum \limits^\infty_{n=1} (\frac{2n^2+7n+7^{-3n}}{8^{n+2}+6n+7\sqrt{n}})^3\)
The dominant terms are \(2n^2\) and \(8^{n+2}\), the sum can be approximated as,
\(\sum \limits^ \infty_{n=1} (\frac{2n^2}{8^{2+n}})^3\\\\=\frac{2^3}{8^6}\sum \limits^ \infty_{n=1} n^6(\frac{1}{512})^n\)
comparing with \(\sum n^kr^n\) we get,k=6 and \(r=\frac{1}{512}\)
here also 0 < r <1,
Thus, the series converges.
To learn more about converges & divergences refer here
https://brainly.com/question/15415793
#SPJ4
Related Questions
2. Taj works as a hydrologist for the federal government. He earns an annual salary of $82,900. In addition, he earns a bonus equal to 6% of his annual salary, which is $4,974. What is Taj's annual gross pay? Your answer
Answers
Step-by-step explanation:
Please marks me as brainliests..please for my effort...and follow me...
when an object 1.00 cm tall is placed 12 cm from a lens, the lens produces an upright image of the object that is 5.00 cm tall. what is the focal length of the lens?
Answers
The focal length of the lens is -15 cm. The negative sign indicates that the lens is a diverging lens.
To find the focal length of the lens, we can use the lens formula:
1/f = 1/v - 1/u
where f is the focal length of the lens, v is the image distance, and u is the object distance.
Given:
Object height (h_o) = 1.00 cm
Object distance (u) = 12 cm
Image height (h_i) = 5.00 cm
We can use the magnification formula to relate the object and image heights:
Magnification (m) = h_i / h_o
Given:
m = h_i / h_o = 5.00 cm / 1.00 cm = 5.00
Now, let's substitute the values into the lens formula:
1/f = 1/v - 1/u
Since the image is upright, the image distance (v) will be positive.
1/f = 1/v - 1/u
1/f = 1/v - 1/12
To find the value of v, we can use the magnification formula:
m = v / u
5.00 = v / 12
v = 5.00 * 12
v = 60 cm
Now, substitute the values of v and u into the lens formula:
1/f = 1/60 - 1/12
Simplifying:
1/f = (1 - 5) / 60
1/f = -4/60
1/f = -1/15
Taking the reciprocal of both sides:
f = -15 cm
Know more about focal length here:
https://brainly.com/question/31755962
#SPJ11
find the exact value of cos-1 (sqrt 3/2)
Answers
The exact value of cos^-1( √3/2) = 30°
What is trigonometric ratio?The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.
There are special angles in trigonometry, this angles have exact value and can be obtained without using calculator. Examples of this calculator are; 30°, 60°, 45°
sin30 = 1/2
cos 30 = √3/2
tan 30 = 1/√3
cos 60 = 1/2
sin 60 = √3/2
tan 60 = √3
Therefore, if cos^-1( √3/2) = x
cos x = √3/2
cos 30 = √3/2
cos x = cos 30
therefore x = 30
learn more about trigonometric ratio from
https://brainly.com/question/24349828
#SPJ1
Explain how to find the lengths of the remaining two sides of the 45°-45°-90° triangle using the special right triangle theorem. You should state why the legs are the lengths that they are. Make sure that you mention important vocabulary in your explanation such as leg, hypotenuse, and rationalize the denominator, if necessary.
Answers
Answer:you use divition
Step-by-step explanation:
algerbra
Someone please ill mark you the brainliest! No cheating or else i’ll report you.
Answers
Answer:
............................
derive the transfer function h() = vout()/vin() for the filter, using the values of r = 10 kω and c = 0.01 µf.
Answers
To derive the transfer function H(s) = Vout(s)/Vin(s) for an RC filter with R = 10 kΩ and C = 0.01 µF, we can follow these steps:
1. Convert the given values to standard units: R = 10000 Ω, C = 10^-8 F.
2. Determine the filter type. Since R and C are in series, this is a low-pass filter.
3. Write the impedance of the resistor (Z_R) and capacitor (Z_C) in the Laplace domain: Z_R = R, Z_C = 1/(sC), where s is the Laplace variable.
4. Apply the voltage divider rule: Vout(s) = (Z_C/(Z_R + Z_C)) * Vin(s).
5. Substitute the values of Z_R and Z_C: Vout(s) = (1/(s(10^-8))/(10000 + 1/(s(10^-8)))) * Vin(s).
6. Simplify the expression to find the transfer function H(s) = Vout(s)/Vin(s): H(s) = 1/(1 + sRC).
In this case, R = 10000 Ω and C = 10^-8 F, so the transfer function is H(s) = 1/(1 + s(10000)(10^-8)).
If you need to learn more about transfer function, click here
https://brainly.in/question/15353527?referrer=searchResults
#SPJ11
Write an equation in slope-intercept form for
the line perpendicular to y = -6x + 6 that
passes through the point (8,6).
Answers
Simple interest calculation
Answers
Answer:
$ 1374.75
Step-by-step explanation:
Simple interest = Principle amount * Rate * Time period / 100
= 9750 * 2.35 * 6 / 100
= $ 1374.75
a ball of radius 14 has a round hole of radius 4 drilled through its center. find the volume of the resulting solid.
Answers
Therefore, the volume of the resulting solid is approximately 35728.458 cubic units.
To find the volume of the resulting solid, we can subtract the volume of the hole from the volume of the ball.
Volume of the ball: V_ball = (4/3) * π * (radius)^3
Volume of the hole: V_hole = (4/3) * π * (radius_hole)^3
In this case, the radius of the ball is 14, and the radius of the hole is 4.
Volume of the resulting solid = V_ball - V_hole
= (4/3) * π * (14^3) - (4/3) * π * (4^3)
= (4/3) * π * (14^3 - 4^3)
= (4/3) * π * (2744 - 64)
= (4/3) * π * 2680
≈ 35728.458 cubic units
To know more about volume,
https://brainly.com/question/28027938
#SPJ11
a tank contains 200 liters of fluid in which 30 grams of salt is dissolved. brine containing 1 gram of salt per liter is then pumped into the tank at a rate of 4 l/min, the well mixed solution is pumped out at a rate of 6 l/min. find the number a(t) of grams of salt in the tank at time t.
Answers
The number of grams of salt in the tank at time t is given by the differential equation \(A(t)=200-170e^{-\frac{1}{50}t}\).
What is rate?The rate is basically a measurement of something's number, amount, or degree in relation to another item. Its the ratio of some quantity to some other quantity.
An equation with a function and one or more of its derivatives is referred to as a differential equation:
At the start, the tank contains A(0) = 30 g of salt.
Salt flows in at a rate of
(1 g/L) * (4 L/min) = 4 g/min
and flows out at a rate of
(A(t)/200 g/L) * (6 L/min) = 3A(t)/100 g/min
so that the amount of salt in the tank at time t changes according to
A'(t) = 4 - A(t)/50
So,
\(A'(t) = 4 - \frac{A(t)}{50}\)
The solution of linear differential equation y' + ay = g(x) is in the form,
\(e^{ax}y=\int {e^{ax}g(x)} \, dx +c\)
Now, putting the values,
\(a=\frac{1}{50} \\g(x)=4\)
\(e^{\frac{1}{50}t}A(t)=\int {e^{\frac{1}{50}t}4} \, dt +c\\=4\int {e^{\frac{1}{50}t}} \, dt +c\\=4\times50e^{\frac{1}{50}t}+c\\=200e^{\frac{1}{50}t}+c\\\)
Now,
\(A(t)=200+Ce^{-\frac{1}{50}t}\\\)
Putting the initial value,
\(30=200+Ce^{-\frac{1}{50}(0)}\\\\200+C=30\\C=-170\)
So, the function will be \(A(t)=200-170e^{-\frac{1}{50}t}\).
Therefore, the number of grams of salt in tank at time t is given by differential equation \(A(t)=200-170e^{-\frac{1}{50}t}\).
To learn more about the Linear Differential Equation visit here:
https://brainly.com/question/19130837
#SPJ4
Can You Guys Help Me Plz
Answers
Answer:
I'm pretty sure the answer is F
Answer:
IS F
Step-by-step explanation:
I already did this work.
Find four consecutive odd numbers such that the sum of the numbers is equal to 152. (Let the smallest consecutive odd number =
x, and let each consecutive odd number be 2 more than the last.)
Answers
Answer:
X is 1st
X + 2 is 2nd
X + 2 + 2 = X + 4 is 3rd
X + 4 + 2 = X + 6 is 4th
therefore
X+X+2+X+4+X+6=152
X+X+X+X+2+4+6=152
4x+12=152
4x=152-12ou
the answer are
35,37 ,39,41
Answer:
35,37,39,41
Step-by-step explanation:
steps to describe an inscribed regular hexagon.
Answers
Answer:
many sides
unique shape
NEED HELP ASAP PLEASE!
Answers
The length of ST is 3.61 units.
The length of TU is 3.16 units.
How to find the length of ST and TU?Distance between two points is the length of the line segment that connects the two points in a plane.
The formula to find the distance between the two points is usually given by:
d=√((x₂ – x₁)² + (y₂ – y₁)²)
Length of ST:
The coordinates of S and T are:
S(0, 0) : x₁ = 0 , y₁ = -5
T(2, 3) : x₂ = 2 , y₂ = -2
Using the distance formula with the given values:
d=√((x₂ – x₁)² + (y₂ – y₁)²)
d=√((2 – 0)² + (-2 – (-5))²) = 3.61 units
Thus, the length of ST is 3.61 units.
Length of TU:
The coordinates of S and T are:
T(0, 0) : x₁ = 2 , y₁ = -2
U(2, 3) : x₂ = 3 , y₂ = -5
Using the distance formula with the given values:
d=√((x₂ – x₁)² + (y₂ – y₁)²)
d=√((3 – 2)² + (-5 – (-2))²) = 3.16 units
Thus, the length of ST is 3.16 units.
Learn more about the distance between two points on:
brainly.com/question/17704491
#SPJ1
The most likely outcomes for a particular project are estimated as follows;
Unit price:
§ 80
Variable cost:
§ 60
Fixed costi
§ 440,800 Expected
sales:
40,600 units per year However, you recognize that some of these estimates are subject to error. Suppose each variable turns out to be either 5% higher or 5% lower than the initial estimate. The project will last for 10 years and requies an initial investment of $14 milion, which wil be depreciated straight line over the projeci life to a final value of
zero. The firm's tax rate is 21%, and the required rate of retum is 14%. a. What is project's NPV in the best-case scenario, that is, assuming all variables take on the best possible
value?
b. What is project's NPV in the worst-case scenario? Note: For all the requirements, a negative amount should be indicated by a minus sign. Enter your answers in dollars, not in millions. Do not round intermediate calculations. Round your answers to the
nearest dollar amount.
Answers
To calculate the project's NPV in the best-case scenario, we need to consider the best possible values for each variable.
Here are the steps-
Step 1: Calculate the annual cash inflow.
Annual revenue = Unit price * Expected sales
= $80 * 40,600
= $3,248,000
Step 2: Calculate the annual cash outflow.
Annual variable cost = Variable cost * Expected sales
= $60 * 40,600
= $2,436,000
Annual fixed cost = Fixed cost
= $440,800
Annual depreciation = Initial investment / Project life
= $14,000,000 / 10
= $1,400,000
Annual tax = (Annual revenue - Annual variable cost - Annual fixed cost - Annual depreciation) * Tax rate
= ($3,248,000 - $2,436,000 - $440,800 - $1,400,000) * 0.21
= $208,720
Step 3: Calculate the annual net cash flow.
Annual net cash flow = Annual revenue - Annual variable cost - Annual fixed cost - Annual depreciation - Annual tax
= $3,248,000 - $2,436,000 - $440,800 - $1,400,000 - $208,720
= $162,480
Step 4: Calculate the NPV using the best-case scenario cash flows.-
\(NPV = Initial investment + (Annual net cash flow / (1 + Required rate of return)^n)\)
\(= -$14,000,000 + ($162,480 / (1 + 0.14)^1) + ($162,480 / (1 + 0.14)^2) + ... + ($162,480 / (1 + 0.14)^10)\)
To know more on Revenue visit:
https://brainly.com/question/27325673
#SPJ11
guys I need help
please help me
Answers
From January to June, there are more daylight hours as June approaches.
What is the dependent variable?
Answers
Answer:
The daylight depends on the month so daylight is the dependent and the months are independet
Step-by-step explanation:
Volume=
Help me please! Thank u so much I appreciate it
Answers
the volume of the oblique pyramid is 16 cubic units
How to determine the volumeThe formula for finding the volume of a oblique pyramid is given as;
Volume = \(\frac{1}{3}\) × base area/ height
Where
base area = area of a right triangle
From the lengths of the triangle given, we can deduce that the opposite side is 24unit and the adjacent side or the base is 10 unit
let's put in the values to the formula
Base area = 10 × 24
Base area = 240 units
height = 5 units
Since we have both the height and the base area, let's find the volume
Volume = \(\frac{1}{3}\) × \(\frac{240}{5}\)
Volume = \(\frac{1}{3}\) × \(48\)
Find the division
Volume = 16 cubic units
Thus, the volume of the oblique pyramid is 16 cubic units
Learn more about an oblique pyramid here:
https://brainly.com/question/24249430
#SPJ1
pls pls pls help me Find x.
Answers
Answer:
29 degrees
Step-by-step explanation:
The arc intercepted by inscribed angle x = 360 -180 -122 = 58 degrees
inscribed angles intercept twice as many degrees of arc
x = 58/2 = 29 degrees
How did you find (h, k) ?
Answers
Answer:
será un posible gráfica de grado
Answer:
(h, k ) = (3, 1 )
Step-by-step explanation:
The coordinates of the vertex of a parabola are (h, k )
The vertex is the turning point of the graph and
(h, k ) = (3, 1 )
Find the common ratio for the geometric sequence defined by the formula: an=40(2‾√)n−1 a n = 40 ( 2 ) n − 1
Answers
The ratio of the geometric sequence 40\(2^{n-1}\) is 2.
Given that geometric sequence is 40*\(2^{n-1}\) and we have to find the common ratio of all the terms.
Geometric sequence is a sequence in which all the terms have a common ratio.
Nth termof a GP is a\(r^{n-1}\) in which a is first term and r is common ratio.
Geometric sequence=40*\(2^{n-1}\)
We have to first find the first term, second term and third term of a geometric progression.
First term=40*\(2^{1-1}\)
=40*\(2^{0}\)
=40*1
=40
Second term=40*\(2^{2-1}\)
=40*\(2^{1}\)
=40*2
=80
Third term=40*\(2^{3-1}\)
=40*\(2^{2}\)
=40*4
=160
Ratio of first two terms=80/40=2
Ratio of next two terms=160/80=2
Hence the common ratio of geometric sequence is 2.
Learn more about geometric progression at https://brainly.com/question/12006112
#SPJ1
Which equation matches the graph shown ?
A. Y=8x^2 +2x -5
B. Y= 8x^2 +2x +5
C. Y=2x^2 + 8x +5
D. Y=2x^2 + 8x -5
Answers
Answer:
D
Step-by-step explanation:
Simply put 0 in the equations and see if it's true then put -2 instead of x and see if it matches. this is the easiest way.
Find the volume of a right circular cone that has a height of 2. 7 ft and a base with a diameter of 14. 4 ft. Round your answer to the nearest tenth of a cubic foot
Answers
The volume of a right circular cone is given by the formula: V = (1/3)πr²h, Where, r is the radius of the base, h is the height of the cone. So the volume of the right circular cone is approximately 120.4 cubic feet (rounded to the nearest tenth).
Given: Height (h) = 2.7 ft, Diameter of base = 14.4 ft, Radius (r) of the base = (14.4/2) = 7.2 ft
Now, using the formula, we can find the volume of the right circular cone as follows:
V = (1/3)πr²h= (1/3) × π × (7.2²) × 2.7≈ 120.4 cubic feet
Therefore, the volume of the right circular cone is approximately 120.4 cubic feet (rounded to the nearest tenth).Answer: 120.4
For more questions on: right circular cone
https://brainly.com/question/31538241
#SPJ8
Simplify the equation: (3√-5+2)(4√-12-1)
Answers
Answer: 8/x+5 - 6/x+9
2/x-9 * 5/x-4
Step-by-step explanation: Multiply The numbers 3 * 5 =15 =(15√- +2)(4 * 12√- -1) then multiply the numbers 4 * 12=48 =(15√- +2)(48√- -1) then apply minus -plus rules +(-a)= -a = 15 *48√-√- -15 *1 *√- +2 * 48√- -2 *1 then simplify =81√- -722
(6×10 to the ninth power)divided by (2.4×10 to the third power)
Answers
Answer:
2.5×10 to the sixth power
Step-by-step explanation:
6÷2.4=2.5
10^9÷10^3=6
Neglecting the curvature of the corners, what is the distance traveled and the displacement in running from point a to point b?.
Answers
To summarize: If points a and b are in a straight line, the distance traveled and the displacement will be the same. If points a and b are not in a straight line, the distance traveled will be greater than the displacement.
The distance traveled refers to the total length covered during the journey, regardless of the direction taken. On the other hand, displacement refers to the change in position from the starting point to the ending point, taking into account the direction of travel.
Neglecting the curvature of the corners implies that the path taken is a straight line. In this case, the distance traveled and the displacement will be the same if the points a and b are in a straight line.
If points a and b are not in a straight line, then the distance traveled will be greater than the displacement. This is because the distance traveled considers the entire path covered, while displacement only considers the change in position.
To know more about displacement,
https://brainly.com/question/13258147
#SPJ11
Write equations for the vertical and horizontal lines passing through the point (−6, -2)
vertical line:
horizontal line:
Answers
Answer:
Vertical line: x = -6
Horizontal line y = -2
Step-by-step explanation:
A vertical line will have a constant x value for all values of y so it will be of the form x = k where k is a constant. Since it passes through (-6,-2), where the x value is -6, we get the equation x = -6
A horizontal line will have a constant y value for all values of x so it will be of the form y = k where k is a constant. Since it passes through (-6,-2), where the y value is -2, we get the equation y = -2
The attached graph shows the two lines and the point (-6, -2)
Pls help and answer all questions I will give brainly for whoever answers are correct!.
Answers
Answer:
x=-5/2
Step-by-step explanation:
x=-5/2
Answer:
12x+4=20x+24
Add negative 4 to both sides
6x+9=4x-3
Add -9 to both sides
-5x/4=4 Multiply both sides by 04
-4(5x-7)=-18 Distribute -4 on the left side
Step-by-step explanation:
12x+4=20x+24
Add negative 4 to both sides
6x+9=4x-3
Add -9 to both sides
-5x/4=4 Multiply both sides by 04
-4(5x-7)=-18 Distribute -4 on the left side
2 Classify the triangle by its sides. The diagram is not to scale. A straight B equilateral C scalene D isosceles (sides are 8,6,6)
Answers
Answer:
D) Isosceles
Step-by-step explanation:
An isosceles triangle is the triangle that has 2 sides that are the same.
When relevant markets are localized, the use of national data to establish concentration ratios tends to Multiple choice question. have no effect on the degree of concentration. understate the degree of concentration. overstate the degree of concentration. improve the concentration estimate.
Answers
The correct answer is b. understate the degree of concentration.
When relevant markets are localized, using national data to establish concentration ratios tends to underestimate the degree of concentration. This is because national data might not accurately reflect the concentration of market power within specific localized markets. Concentration ratios measure the market share of a few large firms in an industry, and when relying on national data, it may not capture the specific market dynamics and competition at the local level.
In localized markets, there may be regional or local competitors that have significant market share and influence but are not adequately represented in national data. By only considering national data, the concentration ratios may not capture the true extent of market concentration within specific localized markets. Therefore, the use of national data tends to underestimate the degree of concentration in such cases. To obtain a more accurate assessment of market concentration in localized markets, it is important to gather and analyze data specific to those markets. This localized data can provide a better understanding of the competitive landscape and the concentration of market power within the relevant markets.
To know more about using national data to establish concentration ratios, click here: brainly.com/question/28272670
#SPJ11