Answers
Answer:
bn = 1 / n
Step-by-step explanation:
We want to show the series an diverges. So we need to find a smaller function bn that diverges. That means we can eliminate options C and D, both of which converge.
an = (3 + sin(n) + e⁻ⁿ) / (2n − 1)
Sine is between -1 and +1, and e⁻ⁿ approaches 0 as n approaches infinity. So the numerator is a minimum of 2 as n approaches infinity. So we can make a new function:
an = 2 / (2n − 1)
Let's look at option B: bn = 4 / √n = 2 / (½√n).
½√n is less than 2n − 1, so bn is greater than an. We can't use that to show that an diverges.
Now let's look at option A: bn = 1 / n = 2 / (2n).
2n is greater than 2n − 1, so bn is less than an. Since bn diverges, an must also diverge.
Related Questions
The Distance between the school and the park 6km there 1.6km in 1 mile how many miles are between the school and the park
Answers
Answer:
3.75
Step-by-step explanation:
6 km = 1.6 km
1 km = x
6 / by 1.6 = 3.75
HOPE ITS HELPFUL!
Chloe runs the after-school cookery club.
The group will be baking 36 scones using the following recipe.
Recipe for 12 scones:
• 250 g self-raising flour
• 60 g butter
• 30 g caster sugar
• 175 ml milk
How much milk will be used?
ml
Answers
Answer:
525 ml
Step-by-step explanation:
12 : 175 ml
36 : x
= 175 × 36
= 6300
x = 6300/12
= 525 ml
The amount of milk that is used while baking 36 scones will be 525 mL.
What are ratio and proportion?A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.
Chloe runs the after-school cookery club. The group will be baking 36 scones using the following recipe.
Recipe for 12 scones:
250 g self-raising flour60 g butter30 g caster sugar175 mL milkThe amount of milk that is used while baking 36 scones will be given as,
⇒ 175 x 36 / 12
Simplify the expression, then we have
⇒ 175 x 36 / 12
⇒ 175 x 3
⇒ 525 mL
The amount of milk that is used while baking 36 scones will be 525 mL.
More about the ratio and the proportion link is given below.
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If a crew of loggers cleared 1
acre of lumber in 4 days, how
long will it take the same crew to
clear 5 acres of lumber?
Answers
Answer:
1 acre of lumber takes 4 days so we have to do acres times days here so 4 x 1 = 1 that's for the first day. For 5 acres we would do 5 x 4 = (20 Days) Hope this helped! :))
Step-by-step explanation: 5 times 4 = 20
4h + 3f + 3c + f + 2c + h + 2c pls help
Answers
Answer:
5h + 4f + 7c
Step-by-step explanation:
Combine like terms!
4h + h = 5h
3f + f = 4f
3c + 2c + 2c = 7c
And you can't put numbers together that have different variables.
Please help me solve this, I will give you brainliest.
Answers
Answer:
5h+10=50
Step-by-step explanation:
What is the value of the expression -7+-4
Answers
Answer:
-11
Step-by-step explanation:
This is the answer because:
1) First, multiply the negative sign with the positive sign.
Negative x Positive = Negative
Equation: -7 - 4
2) Now, multiply the negative sign with the negative sign.
Negative x Negative = Positive
Equation: 7 + 4 = 11
3) Finally, add the greater number's sign (-7) in front of the number.
-11
Hope this helps! :D
Please help!! Will give brainliest if correct!
If triangle RST is an equilateral triangle, find x and y.
A. x = 70, y = 35
B. x = 80, y = 40
C. x = 120, y = 30
D. x = 120, y = 40
Answers
Answer:
C.
Step-by-step explanation:
Find Mx, My, and (x, y) for the lamina of uniform density rho bounded by the graphs of the equations. y = x2/3, y = 0, x = 1
Answers
The required value for the lamina of uniform density [tex]\bar x\\[/tex] and [tex]\bar y[/tex] are written below,
[tex]\bar x = \dfrac{5}{8}\\[/tex]
[tex]\bar y = \dfrac{5}{14}[/tex]
Given that:
The density of lamina: ρThe graph for the lamina: [tex]y = x^{\frac{2}{3}}[/tex], y = 0, and x = 1Calculus's core idea of integration entails determining a function's integral. It is a reverse process of differentiation that enables us to compute cumulative numbers, find the area under a curve, solve differential equations, and more.
The function can be written as,
[tex]m = \rho\int_0^1x^{\frac{2}{3}}dx\\= \rho\left[\dfrac{x^{\frac{5}{3}}}{\frac{5}{3}}}\right]\\=\dfrac{3}{5}\rho[/tex]
The value of Mx can be calculated as,
[tex]M_x = \rho\int_0^1\dfrac{x^{\frac{2}{3}}}{2}}\times x^{\frac{2}{3}}dx\\=\dfrac{\rho}{2}\left[\dfrac{x^{(\frac{2}{7})}}{\frac{7}{3}}\right]_0^1\\=\dfrac{3}{14}\rho[/tex]
Calculate the value of My,
[tex]M_y =\rho \int_0^1 x\times x^{\frac{2}{3}}dx\\=\rho \left[\frac{x^\frac{8}{3}}{\dfrac{8}{3}}\right]\\=\dfrac{3}{8}{\rho[/tex]
The value of [tex]\bar x\\[/tex] will be calculated as,
[tex]\bar x = \dfrac{M_x }{m}\\=\dfrac{ \dfrac{3}{8}\rho}{\dfrac{3}{5}\rho}\\=\dfrac{5}{8}[/tex]
The value of [tex]\bar y\\[/tex] is calculated as,
[tex]\bar y= \dfrac{M_y }{m}\\=\dfrac{ \dfrac{3}{14}\rho}{\dfrac{3}{5}\rho}\\=\dfrac{5}{14}[/tex]
Therefore, the required values are [tex]\bar x = \dfrac{5}{8}\\[/tex] and [tex]\bar y = \dfrac{5}{14}[/tex].
To know more about the area of the region follow
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5 7/12 + 4 6/12 = 9 13/12 = 1 1/12 what's the error analysis?
Answers
Answer:boo
Step-by-step explanation:booooo
Answer:
5 7/12 + 4 6/12 = 9 13/12 is correct but 9 13/12 is equal to 10 1/12 not 1 1/12 because 13/12 is 1 1/12 and you have to add 1 1/12 to 9. So the error analysis is simplifying 9 13/12 to 1 1/12.
Question 2
Explain the difference between the graphs y = x3 and y = 3(x – 4)3 + 7.
Answers
Answer:
The first graph , y=x³ is a cubic function graph and that of the second graph, y = 3(x – 4)3 + 7 is a linear graph.
Step-by-step explanation:
The graph of y=x³ is a cubic function graph where the x term has the highest power of x as 3. As attached in the first graph.
The second graph for y = 3(x – 4)3 + 7. is a linear graph that can be written as;
y=(3x-12)3 +7
y=9x-36 + 7
y=9x - 29
which is a linear graph with a slope of 9 and cuts the y-axis at -29 as shown in the second attached graph.
While attending a baseball game, Eva buys hamburgers and hotdogs for her family. The number of hot dogs bought is five more than the number of hamburgers bought. Hamburgers cost $6.25 each and hot dogs cost $3.75 each. Eva spent a total of $58.75 on the hamburgers and hot dogs.
Answers
Answer:
2.35 hamburgers
Step-by-step explanation:
H6.25 + H18.75 = 58.75
Can anyone solve this for me. Thanks
Answers
Answer:
y=-1/3x+3
Step-by-step explanation:
one fourth of a number is 12 find the number
Answers
Answer:
48
Step-by-step explanation:
If 12 is one-fourth of a number, just multiply 12 by four to find the whole number.
12 x 4 = 48
You could have also set this up as an equation
12 = 1/4x
And then divide 12 by one-fourth
12/(1/4) = 48
How do i turn 80% 0f 86- i know the answer but i don't know how to do it
Can someone please teach me
Answers
We know that of refers to multiplication (from BODMAS)
% means per hundred, i.e., 1/100
So, 80% of 86 is:
(80/100) × 86
or (4/5) × 86
or 4 × 17.2
or 68.8
Hope you understand
Answer:
68.8
Step-by-step explanation:
Let x be 80% of 86.
To find 80% of 86
[tex] \frac{80}{100} = \frac{x}{86} [/tex]
[tex]80 \times 86 = 100x[/tex]
[tex]6880 = 100x[/tex]
[tex]68.8 = x[/tex]
Or you can simply do it as:
[tex]86 \times 80\%[/tex]
[tex]86 \times \frac{80}{100} [/tex]
[tex] \frac{86 \times 80}{100} [/tex]
[tex] \frac{6880}{100} [/tex]
[tex]68.8[/tex]
Darin needs to know the price per pound of clementines. What needs to change in the table so that the data on clementines is in units of pounds and cost?
Answers
Answer:
the table gives the cost for the number of three pounds bag of clemintines we need to change the number of bags to pounds to get the data or clemintines in units of pounds and cost.
Answer:
The table gives the cost for the number of three-pound bags of clementines. We need to change the number of bags to pounds to get the data for the clementines in units of pounds and cost.
Step-by-step explanation:
THIS IS THE SAMPLE ANSWERThe sum of two numbers is 49 and the difference between these two numbers is 9.
What are these two numbers?
Answers
Answer:
the answer is 39 and 14.
The solution is, the numbers are 20 and 29.
What is Subtraction?Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.
Here, we have,
given that,
The sum of two numbers is 49
and the difference between these two numbers is 9.
let, the numbers are x & y
so, we get,
according to question:
x+y = 49 ...1
x-y = 9 ....2
so, simplifying we get,
2x = 58
or, x = 29
so, we get,
y = 20
Hence, The solution is, the numbers are 20 and 29.
To learn more on subtraction click:
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grrrrrr please help i’ll give u a cookie :)
Answers
im only in 6th grade
Step-by-step explanation:
I WILL MARK BRAINLIEST BUT PLEASE ANSWER FAST
Answers
Answer:
B
Step-by-step explanation:
It had this question on my test. I already answered it. I put c and got it wrong. The answer is B.
Pls help - Solve for x
Answers
Answer:
-3
3x/(x^2+6x) = 1 is this the qstn?
if so then the ans is -3
Someone plz help me with this I will mark you as brainlyest
Answers
All the Xs are the inputs and all the Ys are the outputs. (X,Y)
So I basically just used the Xs it gave us and then I put it in the function equation to solve for the outputs
Nate and his brother are saving money to buy a gaming system. The system they want cost $349. The store is having a sale and the system is 30% off. State sales tax 6%.
Answers
Answer:
258.96
Step-by-step explanation:
%30 = 0.3
%6 = 0.06
so..
349 - (349 × 0.3)
349 - 104.7
244.3
then do the tax which is %6 or 0.06
244.3 + (244.3 × 0.06)
244.3 + 14.66
258.96
Good Job! Pls Brailniest! it would mean a lot ;) !
8s + 6 + 2s - 4 + 4s
Answers
Answer:
14s + 2
Step-by-step explanation:
add the s values up and you’ll get 14s (8s + 2s + 4s) and then add the regular ones and you’ll have 2 (6 + -4)
A architect made a scale drawing of a house to be built. The scale is 2 inches to 3 feet. The house in the drawing is 24 inches tall. How tall is the actual house?
Answers
Answer:
36 feet.
Step-by-step explanation:
2 goes into 24 12 times, 12 times 3 is 36 therefore the actual house is 36 feet tall.
SOMEONE HELP WITH MY LAST TWO PROBLEMS
Answers
Answer:
What are your last 2 problems m8
Step-by-step explanation:
Dean walked from the library to the mall. For the
first 12 minutes, he walked at a speed of 80
m/min, but then he slowed his speed to 68
m/min for next 7 minutes. If he was still 130 m
away from the mall, what was the distance
between the library and the mall?
Answers
Three workers arrive at work 15 minutes late, at a cost of $11 hour.
Answers
Answer:
They earned 8.25
Step-by-step explanation:
If they arrived late 15 minutes, then they lose a 1/4 of the pay. So they'd be making $8.25, and not the full $11 for that first hour.
A box contains three types of fruits:
apples, bananas, and pears. There are
20 pieces of fruit in all. Of these, 3 are
apples and 11 are bananas. What is the
ratio of pears to bananas?
А
6 3 11
B 11 26
C 3: 11
D
11: 3
Ο Α
o
D
Answers
Answer:
d
Step-by-step explanation:
Scarlett stopped at a campground along the Appalachian trail. The campground had a 1
2
acre area for tents, divided into 6 equal campsites. Scarlett picked one of the sections to pitch her tent.
Which expression would give you the size of Scarlett’s campsite? Check all that apply.
One-half divided by 6
StartFraction 6 Over 7 EndFraction divided by 6
6 divided by one-half
StartFraction 6 Over 12 EndFraction divided by 6
6 divided by StartFraction 3 Over 6 EndFraction
Answers
Answer:
1/2 divided by 6
6/12 divided by 6
Step-by-step explanation:
Answer:
a - d
Step-by-step explanation:
Island Water Sports provides rental equipment and instruction for a variety of water sports in a resort town. On one morning, a decision must be made on how many Wildlife Raft Trips and how many Group Sailing Lessons should be scheduled. Each Wildlife Raft Trip requires one captain and one crew person and can accommodate six passengers. The revenue per raft trip is $120. Ten rafts are available, and at least 30 people are on the list for reservations this morning. Each Group Sailing Lesson requires one captain and two crew people for instruction. Two boats are needed for each group. Four students form each group. There are 12 sailboats available, and at least 20 people are on the list for sailing instruction this morning. The revenue per group sailing lesson is $160. The company has 12 captains and 18 crew available this morning. The company would like to maximize the number of customers served while generating at least $1800 in revenue and honoring all reservations. Define the decision variables as follows and formulate the problem as a linear program. Let x be the number of Wildlife raft Trips to be scheduled. Let y be the number of Group Sailing Lessons to be scheduled.
The following constraints complete the problem:
120x + 160y ≥ 1800 (1)
x ≤ 10 (2)
2y ≤ 12 (3)
6x ≥ 30 (4)
4y ≥ 20 (5)
x + y ≤ 12 (6)
x + 2y ≤ 18 (7)
1) What does constraint (1) represent?
A) The maximum number of captions who can be deployed.
B) The maximum number of crews who can be deployed.
C) The minimum revenue requirement.
D) The maximum quantity of the rafts available.
E) The maximum quantity of the sailboats available.
F) The demand of raft trips that must be satisfied.
G) The demand of sailing lessons that must be satisfied.
2) What does constraint (4) represent?
A) The maximum number of captions who can be deployed.
B) The maximum number of crews who can be deployed.
C) The minimum revenue requirement.
D) The maximum quantity of the rafts available.
E) The maximum quantity of the sailboats available.
F) The demand of raft trips that must be satisfied.
G) The demand of sailing lessons that must be satisfied.
3) What does constraint (6) represent?
A) The maximum number of captions who can be deployed.
B) The maximum number of crews who can be deployed.
C) The minimum revenue requirement.
D) The maximum quantity of the rafts available.
E) The maximum quantity of the sailboats available.
F) The demand of raft trips that must be satisfied.
G) The demand of sailing lessons that must be satisfied.
Answers
Answer:
1) C
2) F
3) A
Step-by-step explanation:
Given that : X = number of Wildlife raft Trips to be scheduled.
while Y = number of Group Sailing Lessons to be scheduled.
1) Constraint (1) : 120x + 160y ≥ 1800
Represents the Minimum revenue requirement
2) Constraint (4) : 6x ≥ 30
Represents The demand of raft trips that must be satisfied.
3) Constraint (6) : x + y ≤ 12
Represents The maximum number of captions who can be deployed.
The last school year enrollment of Genoa Middle school was 465 students. This year the enrollment is 525.
Answers
Answer:
465 to 525
Step-by-step explanation:
60 difference