Given function is { x) = {0, if 0 < x < 1/2, 1, if 1/2 < x < 1}.
Step-by-step explanation: Given function is { x) = {0, if 0 < x < 1/2, 1, if 1/2 < x < 1}.
The function is an even function because the function is symmetric with respect to the y-axis (i.e.) { -x) = {x). So, the Fourier series has only cosine terms. Therefore, the Fourier cosine series of the given function is given by:
f(x) = a0/2 + Σ an cos(nπx/L),
where L is the period of the function.
Since the function is even, the Fourier series reduces to f(x) = a0/2 + Σ an cos(nπx/L) ...(1) , where a0 = 1/L ∫f(x)dx, an = 2/L ∫f(x)cos(nπx/L)dx for n = 1, 2, 3, ..., n. Let L = 1,
then a0 = 1/1 ∫0^1 f(x)dx = 1/2 an = 2/1 ∫0^1 f(x)cos(nπx)dx for n = 1, 2, 3, ..., n.
a1 = 2 ∫1/2^1 cos(nπx)dx = 1/nπ sin(nπx) from 1/2 to 1
= [1/nπ sin(nπ/2) - 1/nπ sin(0)]
= 2/nπ sin(nπ/2)
Hence, the Fourier cosine series is given by f(x) = 1/2 + 2/π ∑[sin(nπ/2)/n] cos(nπx) ...(2)for n = 1, 2, 3, ...Similarly, the Fourier sine series of the given function is given by: f(x) = Σ bn sin(nπx/L)where L is the period of the function. Since the function is even, there are no sine terms in the Fourier series. So, the Fourier sine series is zero, i.e., bn = 0 for n = 1, 2, 3, ....Hence, the full Fourier series is the same as the Fourier cosine series, which is given byf(x) = 1/2 + 2/π ∑[sin(nπ/2)/n] cos(nπx) ...(3)for n = 1, 2, 3, ...The Fourier series converges pointwise to f(x) for x in (0, 1/2) U (1/2, 1).The Fourier series does not converge at x = 0 and x = 1/2 because the function is not continuous at these points.
To know more about Fourier series refer to:
https://brainly.com/question/31472899
#SPJ11
A rancher in Central Califomia has a year-long BLM grazing allotment in the Oak Woodlands that is 5,000 acres in size. Seventy percent of this allotment has loam soils and produces 900 lbs. (DM) of forage per year and the remaining 30% has sandy loam soil and produces 500 lbs. of forage (DM) per year. The allotment is split into large pastures enabling rotational grazing to take place and allowing the producer to practice the "take half, leave half philosophy of grazing. As part of his agreement with BLM, the rancher must account for 30 head of elk (500 lbs.). With the remaining forage, determine how many mature 200 lb. ewes the rancher could run on this allotment.
The rancher can run approximately 19,425 mature 200 lb. ewes. To calculate the number of mature 200 lb. ewes the rancher can run on the remaining forage, we need to find the available forage after accounting for the 30 head of elk.
A rancher in Central California has a 5,000-acre BLM grazing allotment in the Oak Woodlands. Seventy percent of the allotment has loam soils producing 900 lbs. (DM) of forage per year, while the remaining 30% with sandy loam soil produces 500 lbs. of forage (DM) per year. The rancher must also account for 30 head of elk (500 lbs.). We need to determine how many mature 200 lb. ewes can be run on the remaining forage.
The total forage available from the loam soil is 70% of 5,000 acres, which is 3,500 acres. This amounts to 3,500 acres * 900 lbs./acre = 3,150,000 lbs. of forage (DM) per year.
Similarly, the total forage available from the sandy loam soil is 30% of 5,000 acres, which is 1,500 acres. This amounts to 1,500 acres * 500 lbs./acre = 750,000 lbs. of forage (DM) per year.
With the elk accounting for 30 * 500 lbs. = 15,000 lbs. of forage, the remaining available forage is 3,150,000 lbs. + 750,000 lbs. - 15,000 lbs. = 3,885,000 lbs.
Dividing the remaining forage by the weight of a mature ewe (200 lbs.), we get 3,885,000 lbs. / 200 lbs. = 19,425 ewes. Therefore, the rancher can run approximately 19,425 mature 200 lb. ewes on this allotment, considering the given forage production and the presence of elk.
Learn more about percent here:
https://brainly.com/question/31323953
#SPJ11
HURRY!!! ANSWER QUICK!!!
Choose all the equations that have x = 5 as a possible solution.
A. 20 - x = 5
B. x + 2 = 7
C. 3x = 15
D. 5x = 15
E. x- 5 = 0
Answer:
b,c,e
Step-by-step explanation:
Valerie wants to use a PIN to make her purchase more secure. Which method of payment can Valerie use? Credit card , cash, check, or debit card? Question 2: Mr. Juniper uses his debit card to withdraw $10 cash from checking account for football ticket. Which is an advantage of using the debit card? Answers: mr. juniper does not have to remember a number In order to access his checking account, mr juniper debit card can never be lost or stolen, mr juniper will earn rewards such as free hotel stays.
Mr juniper cash will be taken directly from his checking account.
PLS HELP :D I’m low on points but can u help?
Answer: Question 1, debit card because debit cards are used for atms which requires a pin. A positive is that you’re using your own money for a debit card and not from another source, so you don’t have to pay extra frees
Step-by-step explanation:
Draw and identify the coordinates of the image of the figure after a 90° counterclockwise rotation about the origin.
Answer:
5! HOPE I HELPED
Step-by-step explanation:
Can someone please help me no links please
Answer:
x=6
Step-by-step explanation:
3x- 4=14
+4 +4
3x=18
x=6
3. In chemistry, Isaac can mix the correct solution in 20 minutes. Together,
Isaac and Newton can mix the same solution in 11 minutes. How long
does it take Newton to mix the solution when he is working alone
the square root of 279 lies between what two whole nunbers
Answer:
Step-by-step explanation:
The square root of 16 and the square root of 17
Answer:
29 and 34
Step-by-step explanation:
cause
Pleaser help me I’m confused
Answers:
A:section A
B: section B
C: Section C
D: Section D
Answer:
SECTION C (i think)
Please mark as brainliest
Have a great day, be safe and healthy
Thank u
XD
Answer:
section c
it's square root is 4.123......
what’s 3-4?
this definitely wasn’t to give points :) how was your day? did you drink and get enough to eat?
Answer:
yuh, did you bestie
Step-by-step explanation:
≤))≥
_| \_
Answer:
-1 and I hope everyone reading this has a great day!
please help find measure of h.Will mark brainlyist to right answer.No link!
Answer:
∠ H = 59°
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
121° is an exterior angle of the triangle, then
6x - 1 + 5x + 12 = 121 , that is
11x + 11 = 121 ( subtract 11 from both sides )
11x = 110 ( divide both sides by 11 )
x = 10
Then
∠ H = 6x - 1 = 6(10) - 1 = 60 - 1 = 59°
Un muchacho le dijo a otro. "adivina cuántos años tengo si las dos terceras partes de ellos menos 1 es igual a mi edad actual menos 6".
Answer:
The age of the boy is 15 years
Step-by-step explanation:
Let us assume a be the age of the boy
So, two-third of his age is 2 ÷ 3 × a
As the boy said that two-third minus 1 so it would be equivalent to
2 ÷ 3 × to - 1
ANd, his current age is a and now if we deduct 6 so
a - 6
AFter this, two-third minus 1 is equivalent to a minus 6
So,
2 ÷ 3 × a - 1 = a - 6
- 1 + 6 = a - 2 ÷ 3 × a
5 = 1 ÷ 3 × a
a = 3 × 5
= 15
Hence, The age of the boy is 15 years
Helpppppppp pleaseeeeee I will give brainliest if you knowww pleaseeee helpppppppp
Answer:
I think the answer is 1/2 but dont take my word
Solve the equation: log, (a) + log (z - 6) = 2
the solution to the equation log(a) + log(z - 6) = 2 is z = 100/a + 6.
We can simplify the equation using logarithmic properties. The sum of logarithms is equal to the logarithm of the product, so we can rewrite the equation as log(a(z - 6)) = 2.
Next, we can convert the equation to exponential form. In exponential form, the base of the logarithm becomes the base of the exponent and the logarithm value becomes the exponent. Therefore, we have a(z - 6) = 10^2, which simplifies to a(z - 6) = 100.
To solve for z, we need to isolate it. Divide both sides of the equation by a: (z - 6) = 100/a.
Finally, add 6 to both sides to solve for z: z = 100/a + 6.
So, the solution to the equation log(a) + log(z - 6) = 2 is z = 100/a + 6.
Learn more about logarithmic properties here:
https://brainly.com/question/12049968
#SPJ11
student simplifies (6b + 4r) – (2b + r) and says that the result is 4b + 5r. Explain the error and describe the correct steps to simplify the expression.
Answer & explanation:
The student made an error by adding an r after removing the parentheses instead of subtracting an r.
Correct Steps:
(6b + 4r) – (2b + r)
6b + 4r - 2b - r
4b + 3r
Answer:
yo
Step-by-step explanation:
this was the sample response on edge
The student did not distribute the negative when subtracting. Distributing the negative, the expression is equal to 6b + 4r – 2b – r. Then use the commutative property to rewrite it as 6b – 2b + 4r – r. Then you can use the distributive property to write as (6 – 2)b + (4 – 1)r, which simplifies to 4b + 3r.
A turtle can walk 12 miles in 3 miles. What is the average speed of the turtle?
Answer:
4mph
Step-by-step explanation:
What is the theoretical probability of flipping a heads?
answer:
50/50
step-by-step explanation:
hi there!
flip a coin a couple of times, most likely get the same number of heads then you will of tails, since a coin has 2 sides and only two equal sides the probability to flip that very coin and it landing on heads is 50 percent same as landing it on tails, we know its 50 percent because 100 percent is the full amount ( no matter how much the coin is worth ) and dividing that by 2 does indeed equal 50 or 50 percent.
i believe that is one of the reasons why before a lot of sport games start off with a coin toss to chose which team plays first because it is a 50/50 chance for each team, making it fair toss
i hope this helps you! i hope you have a good rest of your day! :)
jemimah went to the market and bought 500g of meat 850g of fish and 900g of eggs. What is the total weight of the items she bought in a kilograms.
Answer:
2.25kg
Step-by-step explanation:
500g+850g+900g=2250
2250/1000=2.25kg
there are 4 red and 8 blue marbles in a bag, Mark draws a blue marble out of the bag and does not replace it. Mark draws a second blue marble out of the bag and does not replace it. what is the probability that the next marble he draws will also be blue,
Answer:3/5
Step-by-step explanation:when he takes one marble it’s 7/11 and when he takes another it’s 6/10 so simplify and you get 3/5
Answer:
Step-by-step explanation:
Answer:3/5
Brandy has 9/10 slices of cake left. She gives her brother 1/5 slices. How much cake does Brandy have left?
Answer:
7/10
Step-by-step explanation:
You make annual deposits of $8,500 into a savings account that pays an annual interest rate of 3.8%, with interest credited to the account annually. If you now have $461, 103.46 in the account, for how many years have you been investing money in this account?
You have been investing money in this account for approximately 15 years.
How long have you been investing money?To determine the number of years you have been investing money in the account, we can use the formula for the future value of an ordinary annuity:
FV = P * [(1 + r)ⁿ- 1] / r
Where:
FV = Future value (final balance in the account) = $461,103.46
P = Annual deposit amount = $8,500
r = Annual interest rate = 3.8% or 0.038 (expressed as a decimal)
n = Number of years
By substituting the given values into the formula and solving for n, we can determine the number of years you have been investing:
$461,103.46 = $8,500 * [(1 + 0.038) ⁿ- 1] / 0.038
54.24 = (1.038 ⁿ - 1) / 0.038
To solve for n, we can rearrange the equation:
1.038 ⁿ- 1 = 54.24 * 0.038
1.038 ⁿ= 2.0632
n = log base 1.038 of 2.0632
Using a logarithmic calculator, we find that n ≈ 14.96. Rounding up, we conclude that you have been investing money in this account for approximately 15 years.
Learn more about: Future value of an ordinary annuity:
brainly.com/question/30587480
#SPJ11
Help help help help help help
Answer: 19 mins
Step-by-step explanation:
hope this helps
in which situation would hydrogen bonding be present?
A. When hydrogen exists as an ion in solution
B. When hydrogen is attached to C, S or P
C. When hydrogen atoms bond together to form H2
D. When hydrogen is attached to N, F or O
Answer:
D
Step-by-step explanation:
lol this is a weird math question
jk
Hydrogen bonds occur only when hydrogen is covalently bonded to one of three elements: fluorine, oxygen, or nitrogen. Anything else isn't considered a hydrogen bond.
escribe con letra 0.00125
Answer:
zero point zero zero one two five
Step-by-step explanation:
natalie has 45 pieces of candy to share with her and her 4 other friends. how many pieces of candy will natalie and all of her friends get?
Answer:
They will each get 9 pieces of candy.
Step-by-step explanation:
if she has 4 friends and she shares with them, she would be sharing with 4 people plus herself, so you would do the problem 45 ÷ 5 = 9.
Suppose This system of linear differential equations can be put in the form y' = P(t)y + g(t). Determine P(t) and g(t). P(t) = 3/1₁ 3/2₂2 g(t) = = t³y₁ + 6y₂ + sec(t), sin(t) y₁ + ty₂ - 4.
The system of linear differential equations is given as y₁' = 3y₁ + 3y₂² and y₂' = 2y₁ + t*y₂ - 4. By comparing it with the general form y' = P(t)y + g(t), we determine that P(t) = [[3, 3y₂²], [2, t]] and g(t) = [0, -4].
To determine the coefficient matrix P(t) and the forcing term g(t), we can compare the given system of linear differential equations with the general form y' = P(t)y + g(t).
The given system is:
y₁' = 3y₁ + 3y₂²
y₂' = 2y₁ + t*y₂ - 4
Comparing the first equation with the general form, we have:
P₁₁ = 3
P₁₂ = 3y₂²
g₁(t) = 0
Comparing the second equation with the general form, we have:
P₂₁ = 2
P₂₂ = t
g₂(t) = -4
Therefore, the coefficient matrix P(t) and the forcing term g(t) for the given system are:
P(t) = [[3, 3y₂²], [2, t]]
g(t) = [0, -4]
Note that the value of y₂ is not provided in the equation for g₂(t), so it remains as y₂ in the expression.
To know more about linear differential:
https://brainly.com/question/30645878
#SPJ11
I need help finding the Diagonals.
Answer:
OE=53 and UH = 53
Step-by-step explanation:
Pythagoras theorem
im need help please!!!
Answer:
The measure of the missing angle is 61
Step-by-step explanation:
Using the Consecutive Interior Angles theorem, you know that the angles are supplementary (meaning both angles combine to a 180* plane). Using that logic, you may subtract 119 from 180, and you get a 61* angle.
Points are plotted at (-2, 2), (-2, -4), and (2, -4). A fourth point is drawn such that the four points can be connected to form a rectangle. What is the area of this rectangle?
Answer:
The area of the rectangle is 24.
Step-by-step explanation:
The given points:
a) (-2, 2)
b) (-2, -4)
c) (2, -4)
To complete the rectangle the other point must be (2, 2), so the rectangle formed has the following dimensions:
x: distance in the x-direction (from -2 to 2):
[tex]x = 2 - (-2) = 4[/tex]
y: distance in the y-direction (from -4 to 2):
[tex]y = 2 - (-4) = 6[/tex]
The area of the rectangle is:
[tex] A = x*y = 4*6 = 24 [/tex]
Therefore, the area of the rectangle is 24.
I hope it helps you!
Read and Complete the Scenario Together (45m) If a person living in the state of Utah, USA gets Covid 19, what is the probability that he or she was vaccinated? There are many variables relating to age, health risks, and behaviors that contribute to getting Covid. However, with those limitations in mind let's see what we can find out. As of May 2021, 41.8% of Utahns had been vaccinated. Utah had a 13.9% rate of Covid before (without) the vaccine. Studies have shown that the Pfizer vaccine is 95% effective in preventing being infected. Using this information, as well as the methods and videos you covered in the pre-group assignment, work with your group to respond the following prompts: C = Got Covid NV = not vaccinated with Pfizer V = Vaccinated with Pfizer 1. If a person is randomly selected from the population of Utah, what is the probability of that person getting Covid? P C)= 2. If a Utah resident gets Covid, what is the probability that he or she was vaccinated with Pfizer? P(VIC) = 3. If a Utah resident gets Covid, what is the probability that he or she was NOT vaccinated with Pfizer? P(NVC) 4. Discuss with your group and then write a paragraph using statistics to support someone choosing to get vaccinated. You may also use other facts but you must reference where you get them. 5. Discuss with your group and then write a second paragraph using statistics to support someone choosing NOT to get vaccinated. You may also use other facts but you must reference where you get them.
The correct probabilities are 0.1017 and 0.2053.
Given:
P(c\NV)=0.139, P(C|V)= 1- 0.95 = 0.05
P(V) = 0.418
P(NV) = 1- 0.418 = 0.582.
(1). The probability of that person getting Covid? P CP(C) = P(C|NV) P(NV)+P(C|V) P(V)
0.139*0.582+0.05*0.418
= 0.1017.
(2). The probability that he or she was vaccinated with P fizer P(V|C).
[tex]P(V|C) = \frac{P(V|C)P(V)}{P(C|NV)P(NV)+P(CV)P(V)}[/tex]
[tex]\frac{0.05\times0.418}{0.139\times0.582+0.05\times0.418} = 0.2053[/tex]
3). P(NV|C) = 1 - P(V|C) = 0.7946.
(4). The chances of Covid is decreased.
(5). A second paragraph using statistics to support someone choosing 0.1017 = 10% got Covid and 0.139 = 13% not vaccinate.
Therefore, the probability of that person getting Covid is 0.1017 and the probability that he or she was vaccinated with Pfizer is 0.2053.
Learn more about probability here:
https://brainly.com/question/29040053
#SPJ4
Suppose the diameter at breast height (in.) of a certain type of tree is distributed normally with a mean of 8.8 and a standard deviation of 2.8.
(a)What is the probability that the diameter of a randomly selected tree will be at least 10 inches? Will exceed 10 inches.
(b) What is the value of c so that the interval (8.8-c, 8.8+c) contains 98% of all diameter values.
Answer:
a. 7% b. 1.4 inches
Step-by-step explanation:
(a)What is the probability that the diameter of a randomly selected tree will be at least 10 inches? Will exceed 10 inches.
Since our mean, x = 8.8 and standard deviation, σ = 2.8, and we want our maximum value to be 10 inches,
So, x + ε = 10 where ε = error between mean and maximum value
So,8.8 + ε = 10
ε = 10 - 8.8 = 1.2
Since σ = 2.8, ε/σ = 1.2/2.8 = 0.43
ε/σ × 100 % = 0.43 × 100 = 43%
Since 50% of our values are in the range x - 3σ to x and 43% of our values are in the range x to x + ε = x + 0.43σ, the probability of finding a value less than 10 inches is thus 50 % + 43% = 93%.
So, the probability of finding a value greater than 10 inches is thus 100 % - 93 % = 7 %.
(b) What is the value of c so that the interval (8.8-c, 8.8+c) contains 98% of all diameter values.
Since 98% of the values range from 8.8-c to 8.8+c, then half of the interval is from 8,8 - c to 8.8 or 8.8 to 8.8 + c. So, the number that range in this half interval is 98%/2 = 49%
So, c/σ × 100 % = 49%
c/σ = 0.49
c = 0.49σ = 0.49 × 2.8 = 1.372 ≅ 1.37 inches = 1.4 inches to 1 d.p