Isn't the series here divergent? doesn't that mean it cannot be represented as a riemann sum
Answers
No issues with convergence here. If you actually expand the summand you can use the well-known Faulhaber formulas to compute the sum.
[tex]\displaystyle \sum_{i=1}^n 1 = n[/tex]
[tex]\displaystyle \sum_{i=1}^n i = \frac{n(n+1)}2[/tex]
[tex]\displaystyle \sum_{i=1}^n i^2 = \frac{n(n+1)(2n+1)}6[/tex]
[tex]\displaystyle \sum_{i=1}^n i^3 = \frac{n^2(n+1)^2}4[/tex]
and so on. You would end up with
[tex]\displaystyle L_n = \frac2n \times \frac{96-8796n^2+40283n^3-49458n^4}{n^3}[/tex]
As [tex]n\to\infty[/tex], we have [tex]L_n\to-98916[/tex].
Now, when [tex]i=1[/tex], the first term of the sum is
[tex]7(5+0)^3 - 6(5+0)^5[/tex]
so the left endpoint of the first subinterval is [tex]a=5[/tex].
At the other end, when [tex]i=n[/tex], the last term of the sum is
[tex]7\left(5+\dfrac{2(n-1)}n\right)^3 - 6\left(5+\dfrac{2(n-1)}n\right)^5[/tex]
which converges to
[tex]7(5+2)^3 - 6(5+2)^5[/tex]
so the left endpoint of the last subinterval converges to [tex]b=5 + 2 = 7[/tex].
From here it's quite clear that [tex]f(x)=7x^3-6x^5[/tex]. So, the Riemann sum converges to the definite integral
[tex]\boxed{\displaystyle \int_5^7 (7x^3 - 6x^5) \, dx}[/tex]
Related Questions
The population of Kenya is 50 000 000. The population of Pakistan is 4 times greater than the population of Kenya. What is the population of Pakistan?
Answers
Answer:
Step-by-step explanation:
Comment
I would think Pakistan should be more than just 4 times as large as Kenya. However if you are given that Kenya is 50 000 000 then Pakistan will be 4 times the size of Kenya.
Pakistan = 4 * Kenya
Pakistan = 4 * 50 000 000
Pakistan = 200 000 000
Answer: Pakistan = 200 000 000
Please help me with this asap
Answers
Answer:
18
Step-by-step explanation:
So since the two lines are parallel, 3x is congruent to the angle to the left of 6x+18 and since the two angles together are a straight line it's equal to 180 degrees. So
6x + 18 + 3x = 180
9x + 18 = 180
9x = 162
x = 18
Find the area under the standard normal curve to the left of z=2.63. Round your answer to four decimal places, if necessary.
Answers
The area under the standard normal curve to the left of z = 2.63 is given by calculator will be 0.995.
What is a normal distribution?The Gaussian distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.
The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.
The area under the standard normal curve to the left of z = 2.63 is given by calculator will be
Area = 0.995
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A social security number is a sequence of nine digits. Determine the number of social security numbers that satisfy the following conditions:
a. There are no restrictions.
b. The digit 8 is never used.
c. The sequence does not begin or end with 8.
d. No digit is used more than once.
Answers
Answer:
765314290
Step-by-step explanation:
doesn’t use 8
Not start with 8
Digits used only 1’cd
Glenn, the owner of a hardware store, originally paid $54.60 for 15 tool sets. At his year-end clearance sale, he sold the last tool set for 24.00 How much money did he lose on the last tool set.
Answers
The amount of money he lose on the last tool set is: $30.60.
Amount loseUsing this formula
Amount lose=Original amount paid -Selling price
Where:
Original amount paid=$54.60
Selling price=$24.00
Let plug in the formula
Amount lose=$54.60-$24.00
Amount lose=$30.60
Therefore the amount of money he lose on the last tool set is: $30.60.
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the length of the flagpole is ?
Answers
The length of the flagpole is x - 5 yards
Area of a squareThe formula for calculating the area of the flagpole is expressed as:
A = L²
Given that;
A = x² - 10 + 25
Factorize
A = x² - 5x - 5x + 25
A =(x - 5) - 5(x - 5)
A = (x-5)²
Compare
L = x - 5 yards
Hence the length of the flagpole is x - 5 yards
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the arc corresponding to the central angle of 35 degrees in a circle of radius 10 feet measures __feet. Round your answer to two decimal places.
Answers
Answer:
[tex]\huge\boxed{\sf Arc \ length = 6.11 \ ft.}[/tex]
Step-by-step explanation:
Given data:Theta = θ = 35°
Radius = r = 10 ft.
Required:Arc length = ?
Formula:[tex]\displaystyle Arc \ length = 2 \pi r(\frac{\theta}{360} )[/tex]
Solution:Put the givens in the above formula
[tex]\displaystyle Arc \ length = 2 (3.14)(10)(\frac{35}{360} )\\\\Arc \ length = 2(3.14)(10)(0.097)\\\\Arc \ length = 6.11 \ ft.\\\\\rule[225]{225}{2}[/tex]
-. A medical test has been designed to detect the presence of a certain disease. Among those who have the disease, the probability that the disease will be detected by the test is 0.95. However, the probability that the test will erroneously indicate the presence of the disease in those who do not actually have it is 0.04. It is estimated that 4% of the population who take this test have the disease .If the test administered to an individual is positive, what is the probability that the person actually has the disease? Suppose 20% of the people who were referred to a clinic for the test did in fact have the disease. If the test administered to an individual from this group is positive, what is the probability that the person actually has the disease?
Answers
Answer:
TV focusing urgency hangs amateur ushers sex tendency yachting
triangle abc is equal to triangle pqr, angle p=8x+4, angle a=5x+16 , and angle q=10x+2. find angle r
a. 36
b.not enough info
c. 42
d. 102
Answers
Answer: b.not enough info
Step-by-step explanation:
Corresponding angles of congruent triangles are congruent, so [tex]\angle A =\angle P[/tex]
However, we don't have all 3 interior angles of either triangle, so we cannot conclude anything.
What is the best approximation for the perimeter of polygon ABCDE? A. 11.0 units B. 17.0 units C. 24.3 units D. 22.1 units
Answers
TheThe best approximation for the perimeter of polygon ABCDE is: C. 24.3 units.
Perimeter of polygonCoordinate:
A=(-2,3)
B=(0,6)
C=(5,4)
D=(4,-1)
E=(-1,-2)
Distance AB=√(0+2)²+(6-3)²
Distance AB=√4+9
Distance AB=√13
Distance BC=√(5-0)²+(4-6)²
Distance BC=√25+4
Distance BC=√29
Distance CD=√(4-5)²+(-1-4)²
Distance CD=√1+25
Distance CD=√26
Distance DE=√(-1-4)²+(-2+1)²
Distance DE=√25+1
Distance DE=√26
Distance EA=√(-2+1)²+(3+2)²
Distance EA=√1+25
Distance EA=√26
Perimeter of pathogen ABCDE
=AB+BC+CD+DE+EA
=√13+√29+√26+√26+√26
=√13+√29+3√26
=24.2877 units
= 24.3 units (Approximately)
Therefore the correct option is C.
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Step-by-step explanation:
PLEASEEE HELP !!!
Review the graph of a piecewise function.
On a coordinate plane, a curve goes through closed circle (negative 3, negative 1) and curves up and approaches x = negative 1 in quadrant 1. A line starts at closed circle (negative 1, negative 3) and goes to open circle (1, negative 1). It then goes to open circle (3, negative 1). A horizontal line starts at open circle (3, negative 3) and goes to (5, negative 3). A closed circle is at (3, negative 4).
For which value of x is the function continuous?
Answers
Using the continuity concept, it is found that the function is continuous at x = -3.
What is the continuity concept?A function f(x) is continuous at x = a if it is defined at x = a, and:
[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]
In this problem, the function is continuous at x = -3, as:
f(3) = -1.[tex]\lim_{x \rightarrow -3^-} f(x) = -1[/tex].[tex]\lim_{x \rightarrow -3^+} f(x) = -1[/tex].At x = -1, we have that [tex]\lim_{x \rightarrow -1^-} f(x) = \infty[/tex], hence it is not continuous.
The function is not defined for x = 1, and at x = 3, the lateral limits are different.
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Using an Algebraic Expression to Represent a Problem
CAR
WASH
Fundraiser !!!
Raising money
The science club sponsors a car
wash every year to raise money for
the state robotics competition.
This year, the club raised $20 more
than twice what it raised last year.
Answer these questions to write an algebraic expression for the car wash problem.
Check Your Understanding- Question 1 of 3
Attempt 1 of 2
What missing piece of information would help you write an algebraic expression to
represent the amount of money raised this year?
A. The number of cars that were washed
B. The number of club members going to the robotics competition
C. The price of each car wash
D. How much the science club raised during last year's car wash
Answers
Answer:
x= what they raised last year
2x+20= what they raise this year or y
d
Hope This Helps!!!
Volume and surface area
Answers
By applying the volume formulae for composite figures, cones and hemispheres, we obtain that the volume is approximately equal to 558.9 cubic centimeters.
How to determine the volume of a composite figure
The volume of the composite figure is the sum of the volumes of the two figures: (i) a cone, (ii) a hemisphere. The volume formula of the figure is shown below:
[tex]V = \frac{2\pi}{3} \cdot r^{3} + \frac{\pi}{3}\cdot r^{2}\cdot h[/tex]
If we know that r = 5.3 cm and h = 8.4 cm, then the volume of the composite figure is:
V = (2π/3) · (5.3 cm)³ + (π/3) · (5.3 cm)² · (8.4 cm)
V ≈ 558.900 cm³
By applying the volume formulae for composite figures, cones and hemispheres, we obtain that the volume is approximately equal to 558.9 cubic centimeters.
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Please solve this for me thank you!
Answers
Answer:
620.14
Step-by-step explanation:
Original Equation:
[tex]\frac{4y}{1.025^4}+y-2y(1.05)^2=1500[/tex]
Calculate exponents
[tex]\frac{4y}{1.103812890625}+y-2y(1.1025)=1500\\[/tex]
Simplify:
[tex]3.6238025791990193084270042653997y + y - 2.205y = 1500[/tex]
Add like terms
[tex]2.4188025791990193084270042653997y \approx 1500[/tex]
Divide both sides by 7.012
[tex]y\approx 213.91[/tex][tex]y\approx620.14[/tex]
Answer:
y = $620.14 (nearest cent)
Step-by-step explanation:
Given equation:
[tex]\dfrac{4y}{1.025^4}+y-2y(1.05)^2=\$1,500[/tex]
Factor out y from the left side:
[tex]\implies y\left(\dfrac{4}{1.025^4}+1-2(1.05)^2\right)=\$1,500[/tex]
Carry out the arithmetic operations inside the parentheses by following the order of operations PEMDAS:
Calculate the exponents:
[tex]\implies y\left(\dfrac{4}{1.103812891...}+1-2(1.1025)\right)=\$1,500[/tex]
Carry out the multiplication and division from left to right:
[tex]\implies y\left(3.623802579...+1-2.205\right)=\$1,500[/tex]
Carry out the addition and subtraction from left to right:
[tex]\implies y\left(4.623802579...-2.205\right)=\$1,500[/tex]
[tex]\implies y\left(2.418802579...\right)=\$1,500[/tex]
Finally, divide both sides by the coefficient of y to isolate y:
[tex]\implies \dfrac{y\left(2.418802579...\right)}{2.418802579...}=\dfrac{\$1,500}{2.418802579...}[/tex]
[tex]\implies y=\$620.141558...[/tex]
Therefore, y = $620.14 (nearest cent)
The difference......
Answers
Answer:
[tex] log_{7}(3) [/tex]
Step-by-step explanation:
According to the
Law of logarithms,[tex] log_{7}(18) \: - log_{7}(6) \\ \\ = \frac{ log_{7}(18) }{ log_{7}(6) } = log_{7}(3) [/tex]
How many significant figures are in the measurement 1.050 l? a. 1 b. 2 c. 3 d. 4 please select the best answer from the choices provided a b c d
Answers
There are 4 significant figures in the measurement 1.050 (Option d)
What are significant figures?
Significant figures are the number of digits that add to the correctness of a value, frequently a measurement. The first non-zero digit is where we start counting significant figures. We can determine how many significant figures in a given numbers by counting the number of digits that are significant to indicate the quantity or value of something.
How the measurement 1.050 has 4 significant figures?
Since the quantity 1.050 starts with 1, that is a non-zero digit, we start counting the significant figures starting from this digit. Thus, 1 is the first significant digit here. 0, 5, and 0 are the second, third, and fourth significant digit respectively.
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Answer:
option D
Step-by-step explanation:
just took the test
use the interactive expression equivalent to 4x-4-2x+3.
Answers
Answer: x = 1/2
Step-by-step explanation:
4x - 2x - 4 + 3
2x - 1
x = 1/2
match each equation to one of the graphs
Answers
Answer:
I can only see one graph in that screenshot, so I graphed all of them. The one on your screenshot was B.
•Mr. Jones and Mr. Thomas
entered into partnership
I with capital of $12600
and $19200 respectively.
after 3 months they!
were joined by Mr.Forson with a capital of $ 16200.It is agreed that the profit should be shared in proportion to their capitals.During the first 3 month of the year,………..
Answers
The profit should be shared in proportion to Mr Jones, Mr Thomas and Mr forson capitals in the ratio 21 : 32 : 27 respectively.
ProportionMr Jones capital = $12600Mr Thomas capital =$19200Mr forson capital = $16200Total capital = $12600 + $19200 + $16200
= $48,000
Mr Jones proportion = $12600 / $48,000
= 21/80
Mr Thomas proportion = $19200 / $48,000
= 32/80
Mr forson proportion = $16200 / $48000
= 27/80
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Giselle works as a carpenter and as a
blacksmith.
She earns $20 per hour as a carpenter and
$25 per hour as a blacksmith. Last week,
Giselle worked both jobs for a total of 30
hours, and earned a total of $690.
How long did Giselle work as a
carpenter last week, and how long did
she work as a blacksmith?
Giselle worked as a carpenter for
hours and as a blacksmith for
hours last week.
Answers
Answer:
12 hours as a carpenter and 18 as a blacksmith.
Step-by-step explanation:
So she earns 20$ per hour as a carpenter. c can represent the amount of hours she worked as a carpenter, and the coefficient will be 20 (salary)
So she earns 25$ per hour as a blacksmith, b can represent the amount of hours she worked as a blacksmith, and 25 will be the coefficient (salary)
So we have the two equations:
c + b = 30
20c + 25b = 690
Now we can solve for c in terms of b and substitute that into the second equation:
Original equation:
c + b = 30
Subtract b from both sides
c = -b + 30
Original equation:
20c + 25b = 690
Substitute -b + 30 as c
20(-b + 30) + 25b = 690
Distribute the 20
-20b + 600 + 25b = 690
Simplify the equation
600 + 5b = 690
Subtract 600 from both sides
5b = 90
Divide both sides by 5
b = 18
Now plug this into either of the original equations to solve for c, but the first equation b + c = 30 is the easiest, so I'll use that equation
Original equation
b + c = 30
Substitute 18 as b
18 + c = 30
Subtract 18 from both sides
12 = c
Andrew has a new job at the local pizza store as a delivery boy
Answers
The distance of the entire trip is 15 minutes and distance far away from the house to the pizza store is 9 blocks away.
Distancea. The entire trip based on the given graph is 15 minutes.
b. Distance:
Distance=10-1
Distance=9 block away
c. Andrew stopped for 3 minutes for 1 minutes between third minutes and fourth minutes.
d. Distance:
Distance=10-2
Distance=8
Distance=15-8
Distance=7 minutes
Distance=5-1
Distance=4 minutes
Therefore the distance of the entire trip is 15 minutes and distance far away from the house to the pizza store is 9 minutes.
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What is the final transformation in this sequence of transformations mapping pre-image VWXYZ to final image V''W''X''Y''Z''?
a translation up and to the right
a reflection across point Z'
a rotation 90° about V'
a rotation 180° about Z'
Answers
Polygon ABCD was rotated 270° about point Z to form polygon A"B"C"D"
What is a transformation?Transformation is the movement of a point from its initial point to a new location. Types of transformation are reflection, rotation, translation and dilation.
Polygon ABCD was rotated 270° about point Z to form polygon A"B"C"D"
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Answer:
It's D
Step-by-step explanation:
Got it right
Bobby is at a county fair and is participating in "The Height Game". To play, the booth owner attempts to guess a participant's height. If the owner's guess is no more than 1 inch from the actual height, the owner wins the participant’s money. Otherwise, the participant wins a prize. If Bobby's height is 75 inches, what inequality would give the range of values that the owner could guess (g) in order to for Bobby to win a prize?
Answers
The required range for the owner to win the participant's money is given by
g ≤ 76 inches.
In the game of the Height, there is a participant named bobby and the guess maker a booth owner, if the booth owner makes the right guess than he will get the money of the participant who are participating in the game.
What is range?Range, it is the set of the values that come out to an outcome for certain mathematical operation.
As per the condition, the booth owner can guess the height of the participants more than 1 inches of the actual height.
so the range (g) ≤ 76, so the booth owener wins the money
Thus, the required inquility for the condition is given by (g) ≤ 76.
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The price p (in dollars) and the demand X for a particular clock radio are related by the equation X = 3000 -10p. Find and answer A - D
Answers
The price p based on the equation given is p = 3000 - 0.1x.
How to express the price?The equation given in the question is x = 3000 - 10p. The price(p) will be:
x = 3000 - 10p.
Make p the subject of the formula
x + 10p = 3000
10p = 3000 - x
p = (3000 - x)/10
p = 3000 - 0.1x
The revenue will be price multiplied by quantity. This will be:
= (3000 - 0.1x) × x
= 3000x - 0.1x²
The marginal revenue will be calculated after differentiating. This will be:
= 3000x - 0.1x²
= 3000 - 0.2x
The demand which is the quantity based on the information will be:
3000 - 0.2x = 0
0.2x = 3000
x = 1500
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Type the correct answer in each box. Use numerals instead of words. A group of students were surveyed about what they want to be when they grow up. The table provided shows the choices that the students made. Use the information in the table to answer the following questions. Round all answers to the nearest whole number. Teacher Doctor Athlete Boys 24 28 56 Girls 45 31 26 The marginal relative frequency of boys and girls who want to be a teacher is %. The joint relative frequency of girls who want to be an athlete is %. The conditional relative frequency of students that selected doctor, given that those students are boys is %.
Answers
The marginal relative frequency of boys and girls who want to be a teacher is 32 %. The joint relative frequency of girls who want to be an athlete is 25.4%. The conditional relative frequency of students that selected doctor, given that those students are boys is 51.85 %.
according to the question, the table given is
Teacher - Doctor - Athete
boys 24 28 56 Total boys = 108
girls 45 31 26 Total girls = 102
What is average?Average of the values is the ratio of total sum of values to the number of values.
Conditions
1) for boys and girls whom opt for teacher,
[tex]=\frac{69}{210} \\[/tex]
= 32%
2) for the girls who opt for athlete relative to girls,
[tex]=\frac{26}{102}[/tex]
= 25.4%
3) for the boys whom opt for doctors in boys
= [tex]\frac{28}{108}[/tex]
= 25.9%
Thus, The required values of conditions 1,2,3 is 32%, 25.4%, 25.9% respectively
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Answer:
the answer is 33. 12. and 26
Step-by-step explanation:
The principal P is borrowed at a simple interest rate r for a period of time t.
Answers
Answer:
simple interest of the given question is 495
Step-by-step explanation:
SIMPLE INTEREST=P*T*R/100
Otto has some whipping cream that is 30%, butterfat, and some milk that is 2%, butterfat. He wants to make a 500 ML mixture of them that is 12%, percent butterfat.
What does point K represent in this context?
Answer:
CORRECT (SELECTED)
The mixture has the intended volume and has the intended percent of butterfat.
Explanation: Point K is on line b, so it represents a scenario where the mixture has a volume of 500 \,\text{mL}500mL500, start text, m, L, end text. Point KKK is on line aaa, so it represents a scenario where the mixture has 12\%12%12, percent butterfat.
Answers
The inference illustrates that the point K in this context represents that the mixture has the intended volume and has the intended percent of butterfat.
How to illustrate the information?It should be noted that an inference simply means the conclusion that can be deduced based on the information given.
In this case, the inference illustrates that the point K in this context represents that the mixture has the intended volume and has the intended percent of butterfat.
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Answer: It The mixture has less than the intended volume and has more than the intended percent of butterfat.
Step-by-step explanation:
At the beginning of the year (January 1), a company has $11,000 of common stock outstanding and retained earnings of $7,900. During the year, the company reports net income of $8,200 and pays dividends of $2,900. In addition, the company issues additional common stock for $7,700.
Answers
The preparation of the statement of stockholder's equity at the end of the year (December 31) is presented below in the form of table.
How to find the stockholder's equity?The preparation of the statement of stockholder's equity at the end of the year (December 31) is presented as:
Statement of stockholder's equity
Particulars Common stock Retained earnings Total stockholder
Equity
Beginning
balance $11,000 $7,900 $18,900
Add: Additional
common stock $7,700 $7,700
Add: Net income $8,200 $8,200
Less - dividend -$2,900 -$2,900
Ending balance $17,000 $5,300 $5,300
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If Jonathan has 2 times as many dimes as quarters and they have a combined value of 360 cents, how many of each coin does he have?
Answers
Answer:
16 dimes8 quartersStep-by-step explanation:
When ratios of quantities are given, it is often convenient to consider a group of objects in which the objects have that ratio.
How many groups?Here, we have 2 dimes for each quarter, so a group of 2 dimes and 1 quarter is a useful group for this problem. Its value is 2×$0.10 +0.25 = $0.45.
The total value of all of the groups is $3.60, so there must be ...
$3.60/($0.45/group) = 8 groups
The 8 groups of coins will have 16 dimes and 8 quarters.
Suppose we write down the smallest (positive) $2$-digit, $3$-digit, and $4$-digit multiples of $7$.
What is the sum of these three numbers?
Answers
Step-by-step explanation:
Smallest two digit number which is multiple of 7 = 14 (7*2)
Smallest three digit number which is multiple of 7 = 105 (7*15)
Smallest four digit number which is multiple of 7 = 1001 (7*143)
Sum = 14+105+1001 = 1120.