Answers
Step-by-step explanation:
(a) ∫₋ₒₒ°° f(x) dx
We can split this into three integrals:
= ∫₋ₒₒ⁻¹ f(x) dx + ∫₋₁¹ f(x) dx + ∫₁°° f(x) dx
Since the function is even (symmetrical about the y-axis), we can further simplify this as:
= ∫₋₁¹ f(x) dx + 2 ∫₁°° f(x) dx
The first integral is finite, so it converges.
For the second integral, we can use comparison test.
g(x) = e^(-½ x) is greater than f(x) = e^(-½ x²) for all x greater than 1.
We can show that g(x) converges:
∫₁°° e^(-½ x) dx = -2 e^(-½ x) |₁°° = -2 e^(-∞) − -2 e^(-½) = 0 + 2e^(-½).
Therefore, the smaller function f(x) also converges.
(b) The width of the intervals is:
Δx = (3 − -3) / 6 = 1
Evaluating the function at the beginning and end of each interval:
f(-3) = e^(-9/2)
f(-2) = e^(-2)
f(-1) = e^(-1/2)
f(0) = 1
f(1) = e^(-1/2)
f(2) = e^(-2)
f(3) = e^(-9/2)
Apply Simpson's rule:
S = Δx/3 [f(-3) + 4f(-2) + 2f(-1) + 4f(0) + 2f(1) + 4f(2) + f(3)]
S ≈ 2.5103
Related Questions
4 people will equally split 142.6 acres of land. How much land will each person get? acres
Answers
Answer:
35.65 acres
Step-by-step explanation:
Answer:
35.65 acres
Step-by-step explanation:
Just divide 142.6 by 4 for the (four people)
. Andrew is deciding whether to purchase Car A or Car B. He wants
to buy the car that has the best mileage per gallon of gas. Car A
gets 23.7 miles per gallon of gas. Car B can travel 374 miles on
17 gallons of gas. Which car has the better gas mileage?
A. Car A
B. Car B
C. They have the same mileage. D. You need more information. .
Answers
Answer:
B. Car A
Step-by-step explanation:
To find the unit rate divided 374 and 17
374 ÷ 17 = 22
Car B 22 miles per gallon
Car A 23.7 miles per gallon
Car A is a better by because it has more mileage.
GIVING BRAINLIEST AND 100 POINTS! (Only if you include explanation)
6- 1 4/6?
Answers
Answer:
4 1/3
Step-by-step explanation:
6-1 4/6
5 6/6-1 4/6
66-4/6=1/3
4+1/3
=4 1/3
Answer:
[tex]\sf 4\dfrac{1}{3}[/tex]
explanation:
[tex]\hookrightarrow \sf 6 - 1\dfrac{4}{6}[/tex]
turn mixed to improper fraction
[tex]\hookrightarrow \sf 6 - \dfrac{10}{6}[/tex]
make the denominators same
[tex]\hookrightarrow \sf \dfrac{6(6)}{6} - \dfrac{10}{6}[/tex]
expand
[tex]\hookrightarrow \sf \dfrac{36}{6} - \dfrac{10}{6}[/tex]
simplify, join both fractions together
[tex]\hookrightarrow \sf \dfrac{36-10}{6}[/tex]
simplify
[tex]\hookrightarrow \sf \dfrac{26}{6}[/tex]
[tex]\hookrightarrow \sf \dfrac{13}{3}[/tex]
change improper to mixed fraction
[tex]\hookrightarrow \sf 4\dfrac{1}{3}[/tex]
On each of ner birthdays. Bernadette blew out a number of candles
equal to her age in years. She lived to be 107. How many candles
did she blow out during her lifetime? (She had some help the first
few years but they all count)
Answers
Answer:
5778
Step-by-step explanation:
1+2+3+4+5+....+105+106+107
The sequence of numbers (1, 2, 3, … , 107) is arithmetic and when we are looking for the sum of a sequence, we call it a series. Thanks to Gauss, there is a special formula we can use to find the sum of a series:
S=n(n+1)/2=11556÷2=5778
S is the sum of the series and n is the number of terms in the series, in this case, 107
There are other ways to solve:
This is an arithmetic series, for which the formula is:
S = n[2a+(n-1)d]/2
where a is the first term, d is the difference between terms, and n is the number of terms.
For the sum of the first 107 whole numbers:
a = 1, d = 1, and n = 107
Therefore, sub into the formula:
S = 107[2(1)+(107-1)(1)]/2 =
107(2+106)/2=107*108/2=5778
so she blow out 5778 candless during her lifetime
Grade 7 lesson 5 terminating and repeating decimals quiz
Answers
Answer:
I need more context.
Step-by-step explanation:
3( x + 2 ) = 2( 2 - x )
Answers
Answer:
x=2
Step-by-step explanation:
3x+6=4-2x
3x+2x=6+4
5x=10
x=10/5
x=2
1/3 equivalent fraction
Answers
Answer:
Equivalent fractions are the fractions that have different numerators and denominators but are equal to the same value. For example, 2/4 and 3/6 are equivalent fractions, because they both are equal to the ½. A fraction is a part of a whole.
2/6
3/9
4/12
Step-by-step explanation:
1 × 2 / 3 × 2 = 2/6
1 × 3 / 3 × 3 = 3/9
1 × 4 / 3 × 4 = 4 /12
Answer:
2/6
Step-by-step explanation:First, you multiply both numbers then you have 2/6. :)
Josiah downloads 44 songs, including 16 songs by his favorite band. A. Express as a decimal the amount of songs by his favorite band that Josiah downloaded our od the total number of downloads
Answers
I need really good support in this!
Answers
Answer:
○ D. [tex]\displaystyle -8, -3, 1, 5[/tex]
Explanation:
The greatest negative quantity will ALWAYS be the least. That is all there is to it. ♂️
I am joyous to assist you at any time.
A 12-ounce box of cereal costs $3.29. An 18-ounce box of cereal
costs $4.59. Which box of cereal is the better deal?
A. The 18-ounce box
C. Both boxes cost the same
per ounce.
B. The 12-ounce box
D. You need more information.
72
Answers
Answer:
12 ounce of cereal it will be a far one
Help !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
B
Step-by-step explanation:
PLEASE PLEASE HELP ASAP!!
Answers
Answer: B
Step-by-step explanation:
Group the variables together: 3i + 2i -3i = -4i
Then for the fractions: 3/4 - 9/3 = -9/4
Answer:
B. (-9/4 -4i)
Step-by-step explanation:
The polynomial equation x^(3)-x=0 has exactlty one positive root and exactly one negative real root. Please select the best answer from the choices provided T F
Answers
Answer: T
Step-by-step explanation:
Which equation is true for x = 1.8?
Answers
Answer:
I found the full question online, the answer is 5.4 = 3.6 + x
Are the ratios 9:18 and 1:2 equivalent?
Answers
Answer:
yes
Step-by-step explanation:
(1:2)x2=9/18
yes the ratios 9:18 and 1:2 equivalent
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
We need to check whether the ratios 9:18 and 1:2 are equivalent.
Equivalent ratios are the ratios that are the same when we compare them.
Two or more ratios can be compared with each other to check whether they are equivalent or not.
Here the two ratios are 9:18 and 1:2
We can write 9:18 as fraction 9/18
When we simplify it we get 1/2
Hence, yes the ratios 9:18 and 1:2 equivalent
To learn more on Ratios click:
https://brainly.com/question/13419413
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Need help please please
Answers
Answer:
A
Step-by-step explanation:
Translates up 2 right 3.
Rotates 180 degrees.
[tex]\rm \lim \limits_{n \to \infty } {n}^{ - \frac{1}{2} ( \frac{n + 1}{n} )} (1 \times {2}^{2} \times {3}^{2} \times \dots \times {n}^{n} {)}^{ \frac{1}{ {n}^{2} } } [/tex]
[tex]\rule{200pt}{2pt}[/tex]
[tex] \rm I= \sum \limits_{k = 1}^{98} \int_{k}^{k + 1} \frac{k + 1}{x (x+ 1)} \: dx, then \\ [/tex] [tex] \rm[A] \phantom{gg}I>log_e99 \\ \\ \rm [B] \phantom{gg}I < log_e99 \\ \\ \rm[C] \phantom{hffgg} I < \frac{49}{50} \\ \\ \rm[D] \phantom{gfffg} I > \frac{49}{50} \\ [/tex]
Answers
Using the exp-log technique,
[tex]\displaystyle \lim_{n\to\infty} \frac{\left(1 \times 2^2 \times 3^3 \times \cdots \times n^n\right)^{\frac1{n^2}}}{n^{\frac{n+1}{2n}}}[/tex]
[tex]\displaystyle = \exp\left(\lim_{n\to\infty} \frac{\ln\left(\prod\limits_{k=1}^n k^k\right)}{n^2} - \frac{n+1}{2n} \ln(n)\right)\right)[/tex]
[tex]\displaystyle = \exp\left(\lim_{n\to\infty} \frac{\sum\limits_{k=1}^n k\ln(k)}{n^2} - \frac{n+1}{2n} \ln(n)\right)\right)[/tex]
We have ln(k) = ln(k/n) + ln(n), and so we can rewrite the limand as
[tex]\displaystyle = \exp\left(\lim_{n\to\infty} \left(\frac1n \sum\limits_{k=1}^n \frac kn \ln\left(\frac kn\right) + \frac{\ln(n)}{n^2} \sum_{k=1}^n 1 - \frac{n+1}{2n} \ln(n)\right)\right)[/tex]
Then the first sum converges to a definite integral,
[tex]\displaystyle \lim_{n\to\infty} \frac1n \sum_{k=1}^n \frac kn \ln\left(\frac kn\right) = \int_0^1 x \ln(x) \, dx = -\frac14[/tex]
while the remaining terms vanish since
[tex]\displaystyle \frac{\ln(n)}{n^2} \sum_{k=1}^n 1 = \frac{\ln(n)}{n^2} \times \frac{n(n+1)}2 = \frac{n+1}{2n}\ln(n)[/tex]
So the limit is [tex]\boxed{e^{-1/4}}[/tex].
Since
[tex]\dfrac1{x(x+1)} = \dfrac1x - \dfrac1{x+1}[/tex]
it's easy to show that the integral reduces to
[tex]\displaystyle \int_k^{k+1} \frac{k+1}{x(x+1)} \, dx = (k+1) \ln\left(\dfrac{(k+1)^2}{k(k+2)}\right)[/tex]
so we can write the sum as
[tex]I = \displaystyle \sum_{k=1}^{98} \int_k^{k+1} \frac{k+1}{x(x+1)} \, dx = \sum_{k=2}^{99} k \ln\left(\frac{k^2}{k^2-1}\right)[/tex]
We have k²/(k² - 1) > 1 for all k, so that ln(k²/(k² - 1)) > ln(1) = 0. We can see the first 3 terms of the sum already exceed 1 > 49/50, so (D) is true.
Numerical computation of the sum suggests I < ln(99), but I have yet to come up with an analytical solution for this bound...
What is the range of the following relation? {(2, 3), (-4, 1), (5, -2), (0, 0)}
due in soon hours
Answers
Answer:
range is {-2, 0, 1, 3}
Step-by-step explanation:
Range is all the y's. Those are the second number in each ordered pair. I put them smallest to biggest, but it doesn't have to be. All the y-numbers in the set brackets should work for correct.
Determine the absolute value. Type the numerical answer only. -l12l
Answers
Answer:
-12
cause l12l is 12 then u add the negative sign.
Step-by-step explanation:
You have listed a property. The seller told you that he must net at least $14,000 after all the fees and expenses are paid. You estimate the seller's closing cost to be $3,500, and he must payoff an existing loan of $108,750. In addition, you are going to charge 7 percent commission on the sale. What is the LEAST amount that the property can sell for to return the seller's desired net?
Answers
Answer:
wow
Step-by-step explanation:
Answer with step-by-step explanation:
Step 1: $14,00 - $3,500 + $108,570 = $10,500 + $108,750 = $119,250
Step 2: 7% of $119,250 = $8,347.50
Step 3: $119,250 + $8,347.5 = $127.597.50
Hope this was helpful! (brainliest please)
Find the height of a cone with a diameter of 12 m whose volume is 904 m3.
Use 3.14 for 1 and round your answer to the nearest meter.
A. 24 m
B. 8 m
C. 48 m
D. 6 m
Answers
Answer:
24 m that is the answer to the question
The height of the cone is 24 meters.
Option A is the correct answer.
What is a cone?It is a shape of a Christmas tree where there is a base of radius r and a top point called the apex.
We have,
The formula for the volume of a cone.
V = (1/3)πr²h
Where r is the radius of the base and h is the height.
The diameter of the cone = 12 m.
So,
The radius is half of the diameter:
r = 12/2
r = 6 m
Now,
The volume of the cone is 904 m³.
Substituting the known values into the formula.
904 = (1/3) × 3.14 × 6 x 6 × h
Simplifying the equation.
904 = 37.68 h
Dividing both sides by 37.68.
h = 23.99
h = 24
Therefore,
The height of the cone is 24 meters.
Learn more about cones here:
https://brainly.com/question/13798146
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Emma spent $60.20 on 5 dozen bagels and a gallon of iced tea. The price of the gallon of iced tea was $5.25. The following equation can be used to find d, the price of each dozen of bagels. 5d + 5.25 = 60.2 What was the price of each dozen of bagels?
Answers
23.23 - 5.25 = 17.98
d = 17.98 ÷ 2
d = 8.99
The answer is B. $8.99
What is the probability the student rolls a 6 and flips the quarter on tails?
Answers
Answer:
1/12
Step-by-step explanation:
the probability of landing on 6 is 1/6 and the probability of a tails is 1/2, so 1/6*1/2=1/12
write an equation that you can use to determine the number of hours for which it would cost $270 to hire brian then solve the equation
Answers
Answer:
How do you write an equation for problem solving?Here are some steps to follow:Understand the problem. Understand all the words used in stating the problem. Understand what you are asked to find. ... Translate the problem to an equation. Assign a variable (or variables) to represent the unknown. ... Carry out the plan and solve the problem.
Step-by-step explanation:
What is the value of tan(A) in the diagram?
Answers
Find the distance between the points (-7,-6) and (4,-6)?
Answers
Answer:
Step-by-step explanation:
the distance between the two points are 11.
the slope is m=0
Answer:
11 units
Step-by-step explanation:
[tex]Solution,\\\\Let,\\\\(x_1,y_1)=(-7,-6)\\\\(x_2,y_2)=(4,-6)\\\\Now,\\\\Using\:distance\:formula,\\\\\hookrightarrow d=\sqrt{(x_2-x_1)^{2} +(y_2-y_1)^{2} } \\\\\hookrightarrow d=\sqrt{(4-(-7))^{2} +(-6-(-6))^{2} } \\\\\hookrightarrow d=\sqrt{(11)^{2} +(0)^{2} }\\\\\hookrightarrow d=\sqrt{121} \\\\\hookrightarrow d=11\: units[/tex]
Can someone help me with my homework need to divide fractions
Answers
Answer:
yeah sure
Step-by-step explanation:
What role do plants play in the nitrogen cycle?
Answers
Answer:
Plants absorb nitrates from nearby soils to create proteins. Fertilizer also helps because it makes the soil even richer, allowing for more nitrates, which means more proteins.
a motorist left home at 10 a.m. to travel to a cityof a distance of 260 km he reckoned hecould average 80km/ h at what time would he arrive at the city
Answers
Answer:
He would get there at 1:15 (I did this in my head, may be wrong)
Step by step solution:
We know the motorist left home at 10. We can divide the 260/80 and we get 3 hrs, we still have 20 km left over, keep on dividing and you get 1:15 p.m.
PLEASE HELP I WILL GIVE BRAINLIEST
Answers
Answer:
V=72
Step-by-step explanation:
4x6=24
24x3=72
WxBxH=V
B=6
W=3
H=4