Find the following trigonometric Fourier Series:
(a) Extend the definition of f(x) to make it an even function f*(x),
[tex]f^*(x)=\begin{cases}0&\text{if }-2\le x<-1\\1&\text{if }0\le x\le1\\0&\text{if }1<x\le2\end{cases}[/tex]
and we take f* to be periodic over an interval of length P = 4. We compute the coefficients of the cosine series:
[tex]a_n = \displaystyle\frac2P \int_{-2}^2 f^*(x)\cos\left(\frac{2n\pi}Px\right)\,\mathrm dx = \frac{2\sin\left(\frac{n\pi}2\right)}{n\pi}[/tex]
Note that a₀ = 1 (you can compute the integral again without the cosine, or just take the limit as n -> 0). For all other even integers n, the numerator vanishes, so we split off the odd case for n = 2k - 1 :
[tex]a_{2k-1} = \dfrac{2\sin\left(\frac{(2k-1)\pi}2\right)}{(2k-1)\pi}[/tex]
Then the cosine series of f(x) is
[tex]\displaystyle \frac{a_0}2 + \sum_{k=1}^\infty a_{2k-1}\cos\left(\frac{(2k-1)\pi}2x\right)[/tex]
(b) For the sine series, you instead extend f(x) to an odd function f*(x),
[tex]f^*(x)=\begin{cases}-1&\text{if }-2\le x\le-1\\x&\text{if }-1<x<1\\1&\text{if }1\le x\le2\end{cases}[/tex]
Again, P = 4, and the coefficient of the sine series are given by
[tex]b_n = \displaystyle\frac2P\int_{-2}^2f^*(x)\sin\left(\frac{2n\pi}Px\right)\,\mathrm dx[/tex]
which we can again split into the even/odd cases,
[tex]b_{2k} = -\dfrac1{k\pi}[/tex]
[tex]b_{2k-1} = \dfrac{4(-1)^{k+1}+2(2k-1)\pi}{(2k-1)^2\pi^2}[/tex]
So the sine series is
[tex]\displaystyle \sum_{k=1}^\infty\left(b_{2k}\sin\left(k\pi x\right) + b_{2k-1}\sin\left(\frac{(2k-1)\pi}2x\right)\right)[/tex]
I've attached plots of the extended versions of f(x) along with the corresponding series up to degree 4.
The odds in favor of Frank McKinnis winning a hot dog eating contest are 2:7.
simple
a. Determine the probability that Frank will win the contest.
nas 0.216
b. Determine the probability that Frank will not win the contest.
a. The probability that Frank will win the contest is
b. The probability that Frank will not win the contest
Answer:
the probability of winning & not winning the contest is 2 ÷ 9 and 7 ÷ 9 respectively
Step-by-step explanation:
The computation is shown below
a. The probability of Frank win the contest is
= 2 ÷ 2 + 7
= 2 ÷ 9
b. The probability of Frank that not win the contest is
= 1 - 2 ÷ 9
= 7 ÷ 9
hence, the probability of winning & not winning the contest is 2 ÷ 9 and 7 ÷ 9 respectively
The same would be relevant
Alex and Tim are going to race. Tim gives Alex a 50 meter head start. Alex
walks 2 meters per second. Tim walks 4 meters per second. When will the
two tie?
Answer:
After 3 min
Step-by-step explanation:
So becuase Tim is walking and Tim gave Alex a 50 meter head start so after 3 min they will tie each other.
Word problem will mark brainly
Answer:
A) Replace L with the length of the skid mark:
Speed = √(20(208))
Speed= √(4160)
Speed = 64.5 miles per hour
B) set the equation to the speed and solve for L:
47 = sqrt(20L)
Square both sides:
2209 = 20L
Divide both sides by 20:
L = 110.5 feet
Write an equation of the line that passes through the pair of points. (-2, -3), (4,5)
Answer:
y=4/3x-1/3
Step-by-step explanation:
Which is the distance between the point with the coordinates (-2, 3) and the line with the equation 6x - y = -3?
37
C. 637
a.
37
37
b. 337
d. 1237
37
37
Please select the best answer from the choices provided
ОООО
Oo
Answer:
d. 12√37 / 37
Step-by-step explanation:
standard formula for the distance between a point (x₀,y₀) and a line ax+by+c=0 is |a*x₀ + b*y₀ + c| / √a²+b²
(x₀,y₀) : (-2 , 3)
ax+by+c=0 : 6x - y +3 = 0
x₀ = -2 y₀ = 3 a = 6 b = -1 c = 3
d = | 6*(-2) + (-1)*3 + 3 | / √6²+(-1)²
d = 12 / √37 = 12√37 / 37
Select all the properties of a right triangle.
A. Has a right angle
B. Has one obtuse angle
C. Has parallel lines
D. Has perpendicular lines
E. Has three acute angles
no links!! help please!!
Answer:
A. has a right angle
thats one
Answer:
I think it is A and D. Not 100% sure tho.
PLEASE HELP ASAP!!!!!!!!!!!!!
Answer:
3 + 8 times 3 +27 times 3 + 64 times 3+ 125 times 3 + 216 times 3+ 343 times 3
2352 cubic units^3
Step-by-step explanation:
Need help with this question
Answer:
B. 45
Step-by-step explanation:
we know the sum of both angles is 90 because of the small sqaure in the corner.
90 = 2x+20
70 = 2x
45 = x
Answer:
35
Step-by-step explanation:
Because of the box in the graph, you can tell that this is a 90-degree angle
2x means the next angle will be twice of the answer choice number
because the end product must be 70 the answer must be 35
35 x 2 = 70
Identify the angles (congruent vs supplementary
Answer:
Angles 1 & 2 = supplementary
Angles 1 & 3 = supplementary
Angles 1 & 4 = congruent
Angles 1 & 5 = congruent
Angles 1 & 6 = supplementary
Angles 1 & 7 = supplementary
Angles 1 & 8 = congruent
PLEASE HELP .........!!!!!!!!!!!!!!!!!!!!!!!!’!!!!
It goes in the order 3,1,2,4
A coach recommends that Nathan get 64 minutes of exercise per day. Today Nathan lifts weights for 16 minutes. What percent of his recommended exercise has Nathan completed?
Answer:
25%
Step-by-step explanation:
16 x 100 ÷ 64.
you simply take the minutes that he exercised and thereafter divide it by the recommended exercise that was prescribed by his coach.
What is the Estimate of 296.8
Answer:
The answer is 297
Hey guys I don’t understand this one so can y’all please help me? :))))
Answer:
11) c = 16.1
12) c = 11.4
Step-by-step explanation:
11)
a² + b² = c²
8² + 14² = c²
64 + 196 = c²
c² = 260
[tex]\sqrt{c^2} =\sqrt{260}[/tex]
c = 16.1
12)
a² + b² = c²
7² + 9² = c²
49 + 81 = c²
c² = 130
[tex]\sqrt{c^2} =\sqrt{130}[/tex]
c = 11.4
• Question 1 :-
We see that in a right angled triangle two sides are 8cm and 14cm . We can find the third side using Pythagoras Theorem .
[tex]\tt \to Hypotenuse^2 = Perpendicular^2+Base^2\\\\\tt \to h^2 = (8)^2+(14) \\\\\to \tt h^2 = 64 + 196 \\\\\tt \to h^2 = 260 \\\\\tt \to h=\sqrt{260} \\\\\tt \to \boxed{\orange{\tt h = 16.12 }}[/tex]
____________________________
• Question 2 :-
[tex]\tt \to Hypotenuse^2 = Perpendicular^2+Base^2\\\\\tt \to h^2 = (9)^2+(7)^2 \\\\\to\tt h^2 = 81 + 49 \\\\\tt \to h^2 = 130 \\\\\tt \to h=\sqrt{130} \\\\\tt \to \boxed{\orange{\tt h = 11.40}}[/tex]
What is the solution to the equation Vn= 3n-3+1?
On=-4, n = -1
O n=-1
n=1
n= 1, n = 4
Answer:
C
Step-by-step explanation:
Help me please!!!!
10. The table shows the change in your hair length over a year.
January
February
August
September
December
Month
Change in hair
length (inches)
2
-1
3
4
3
a. What is the total change in your hair length at the end of the year?
b. Is your hair longer in January or December? Explain your reasoning.
c. When is your hair the longest? Explain your reasoning.
Answer:
3
December. total change in December is greater than change in January. 3 is greater than 2
August. the total change in hair growth is 4.
Step-by-step explanation:
total change in hair length = 2 - 1 + 3 - 4 + 3 = 3
My hair is longer in January .
total change in hair length in February = 2 -1 = 1
total change in hair length in August = 1 + 3 = 4
total change in hair length in September = 4 - 4 = 0
total change in hair length in December = 0 + 3 = 3
My hair is the longest in August because that is the month that has the highest change in hair length
do you add or multiply when you do area
Answer:
either one will work.
you can either multiply length times width or you can add all the sides together.
Step-by-step explanation:
hope this helps
have a good day
Answer:
mulitpy
Step-by-step explanation:
area= L x W
(Length x Width = Area)
ok so i need help and fast!!!!!
Answer:
With what?
Step-by-step explanation:
Find the 97th of the arithmetic sequence 25, 29, 33, ...
Answer:
434
Step-by-step explanation:
hello :
note : the n th term of an arithmetic sequence is :
An =A1+(n-1)d ....a common difference is : d and A1 the first term
in this exercice : d = 33-29 =29-25= 4 A1 = 25
when : n =97 you have the 97rd term A97
so : A97 =25 +(97-1)(4)
A97 = 434
The width of a rectangle is 4 feet and the diagonal length of the rectangle is 13 feet. Which measurement is closer to the length of this rectangle in feet?
A. 12.4 ft
B 13. 6ft
C 9ft
D 17 ft
I’m not sure which answer this is
Jamie purchases a new pair of shoes for $35. She has a coupon for 15%
off the price of the shoes. What is the cost of Jamie's shoes after using
the coupon?
Answer:
Ewan di ko alam e sorry I didn't understand e
My teacher says the answer is not 140 or 90
Answer:
150
Step-by-step explanation:
Area of A:
A = bh
A = 10(10)
A = 100
Area of B:
A = 1/2bh
A = 1/2(10)(10)
A = 5(10)
A = 50
Combined:
100 + 50
150
Answer:
150
Step-by-step explanation:
My math genius friend told meh the answer bc I'm not smart at math.
Connor wants to solve the equation 4" = 26. How could he use graphs to solve this
equation?
Drag statements into order to complete an explanation.
Answer:
graph the curve that models the expression is the first on, I don’t know the rest
Step-by-step explanation:
If 3=7k and 7= m/2 then mk=
Answer:
Step-by-step explanation:
3=7k
Meaning k = 3/7
7=m/2
Meaning m = 7*2 = 14
Therefore mk = 3/7*14 = 6
The product of m and k i.e. mk is 6.
Algebraic terms usually consist of two or more variables with their arithmetic operations.
From the parameters given:
3 = 7k ---- (1)
7 = m/2 ---- (2)
We are to determine mkFrom equation (1), let's make (k) the subject, we have:
k = 3/7
From equation (2), let's make (m) the subject, we have:
m = 7 × 2
m = 14
The product of m and k which is mk will now be:
= 14 × 3/7
= 2 × 3
= 6
Learn more about algebraic terms here:
https://brainly.com/question/1451099
Assume that 3-month Treasury bills totaling $12 billion were sold in $10,000 denominations at a discount rate of 3.605%
In addition, the Treasury Department sold 6 month bills totaling $10 billion dollars at a discount rate of 3.55%.
What is the discount amount for the three-month bills?
What is the discount amount for the six-month bills?
Answer: 55,000,000
this might not be right but hear
Let f(x) = – x-1 and g(x) = x² – 4.
Find (f o g)(3).
Then (f o g)(3) =
Answer:
answer is -6
Step-by-step explanation:
hope it helped!!!
1) The endpoints of AB are A(-3, 8) and B(4,5). If AB is
dilated by a scale factor or 2, what is the slope and length
of A'B?
The original length of AB is 7.62. If we dilate it with the scale factor 2, the length will be 15.23.
The slope of the line remains the same even if we dilate it, so it will remain 0.43.
(y2-y1/x2-x1)
Explanation: The answers are taken from by solving on the graph
Each scatter plot below shows the same data. Which scatter plot has the most reasonable line of best fit?
Answer:
The second one where line go through more points
Step-by-step explanation:
What is the value of m in mn= 12?
A) m= 12-n
B) m = 14
C) m= 12n
D) m = 12 + n
Answer: There is no choice available for the answer.
Step-by-step explanation:
The question is asking for the value of m in terms of n, so we need to isolate m to one side.
Given
mn=12
Divide n on both sides
mn/n=12/n
m=12/n
Hope this helps!! :)
Please let me know if you have any questions
In the polyhedron above x=5 mm, y=9 mm, and z=4 mm. The volume of the polyhedron is _____ mm3. Round your answer to the tenths place.
Answer:
180 mm³
Step-by-step explanation:
The polyhedron is an oblique rectangular prism
Area of the oblique rectangular prism = base area * height
height = z = 4 mm
Base area = L*W
L = y = 9 mm
W = x = 5 mm
Base area = 9*5 = 45 mm²
Area of the oblique rectangular prism = 45*4 = 180 mm³
