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2 years ago

(1 point) Let f be a periodic function of period 10 such that f(x)=x2 for −5≤x<5. Then the Fourier series of f is

Mathematics

1 answer:

ehidna [41]2 years ago

7 0

Answer:

The answer is " $\frac{25}{3}$ ".

Step-by-step explanation:

please find the complete question in the attached file.

$a_0=\frac{1}{10}\int^{5}_{x=-5} x^2 dx\\$

$=\frac{1}{10} (\frac{x^3}{3})^{5}_{-5}\\\\=\frac{1}{30}[5^3+5^3]\\\\=\frac{2}{30}(125)\\\\=\frac{1}{15} \times 125\\\\=\frac{25}{3}$

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Q2) The following travel times were measured for vehicles traversing a 2,000 ft. segment of an arterial: Vehicle Travel Time (s)

adelina 88 [10]

Answer:

TMS = 45.78 m/s

SMS = 45.66 m/s

Step-by-step explanation:

Vehicle Travel Time (s)

1 40.5

2 44.2

3 41.7

4 47.3

5 46.5

6 41.9

7 43.0

8 47.0

9 42.6

10 43.3

Time mean speed and space mean speed are parameters used to express the speed of a group of vehicles in traffic flow.

Time mean speed is given as the average speed of all the cars

The speed for each vehicle is calculated by dividing the (2000 ft) distance by the time taken by each vehicle to complete that segment of the journey.

Let vehicle = V

Travel time = time

Speed = s

V | Time | speed (ft/s)

1 | 40.5 | 49.383

2 | 44.2 | 45.249

3 | 41.7 | 47.962

4 | 47.3 | 42.283

5 | 46.5 | 43.011

6 | 41.9 | 47.733

7 | 43.0 | 46.512

8 | 47.0 | 42.553

9 | 42.6 | 46.948

10| 43.3 | 46.189

TMS = (Σsᵢ)/N

Σsᵢ = (49.383+45.249+47.962+42.283+43.011+47.733+46.512+42.553+46.948+46.189)

Σsᵢ = 457.823

N = number of vehicles = 10

TMS = 457.823 ÷ 10 = 45.7823 = 45.782 m/s

b) Space mean speed is given as

SMS = N ÷ [Σ (1/sᵢ)]

V | Time | speed | (1/sᵢ)

1 | 40.5 | 49.383 | 0.02025

2 | 44.2 | 45.249 | 0.02210

3 | 41.7 | 47.962 | 0.02085

4 | 47.3 | 42.283 | 0.02365

5 | 46.5 | 43.011 | 0.02325

6 | 41.9 | 47.733 | 0.02095

7 | 43.0 | 46.512 | 0.02150

8 | 47.0 | 42.553 | 0.02350

9 | 42.6 | 46.948 | 0.02130

10| 43.3 | 46.189 | 0.02165

Σ (1/sᵢ) = (0.02025+0.02210+0.02085+0.02365+0.02325+0.02095+0.02150+0.02350+0.02130+0.02165)

Σ (1/sᵢ) = 0.219

SMS = 10 ÷ [Σ (1/sᵢ)] = 10 ÷ 0.219

SMS = 45.662 m/s

Hope this Helps!!!

4 0

3 years ago

Write the relation as a set of on rdered pai

kirill115 [55]

The relation as a set of ordered pairs is d. {(–2, 1), (0, -1), (2, -3)}.

Step-by-step explanation:

Step 1:

First, we plot the three points on the given graph.

The coordinates are given in the following form (x coordinate, y coordinate) where the symbol of the coordinates depends on the quadrant on which the point lies.

For the first quadrant, both x and y values are positive.

For the second quadrant, the x value is negative but the y value is positive.

For the third quadrant, both the values of x and y are negative.

For the fourth quadrant, the x value is positive but the y value is negative.

Step 2:

The first point has an x value of 2 and a y value of 1 since it is in the second quadrant, the coordinates are (-2, 1).

The second point has an x value of 0 and a y value of 1 since it is in the third or fourth quadrant, the coordinates are (0, -1).

The third point has an x value of 2 and a y value of 3 since it is in the fourth quadrant, the coordinates are (2, -3).

So the coordinates are {(–2, 1), (0, -1), (2, -3)} which is option d.

6 0

3 years ago

Please helpppppppppp

tekilochka [14]

y = sqrt(x) .... parent function

y = sqrt(x+2) .... replace x with x+2 to shift 2 units to the left

y = sqrt(x+2)+3 ... add on 3 to move 3 units up

y = sqrt(-x+2)+3 ... replace x with -x to reflect over y axis

<h3>Answer: y = sqrt(-x+2)+3</h3>

5 0

2 years ago

What is the probability that both spinners land on red or orange?

yawa3891 [41]

Answer:

A, the probability is 1/9. you get this because you multiply the probabilities

in this example its 1/3 times 1/3 so you get 1/9

Step-by-step explanation:

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3 years ago

Cube-shaped boxes will be loaded into the cargo hold of a truck. The cargo hold of the truck is in the shape of a rectangular pr

Mrrafil [7]

Solve each problem. Volume of a Box A piece of sheet metal is 2.5 times as long as it is wide. It is to be made into a box with an open top by cutting 3 -inch squares from each corner and folding up the sides, as shown at the top of the next page. Let x
represent the width of the original piece of sheet metal. (a) Represent the length of the original piece of sheet metal in terms of x.
(b) What are the restrictions on x?
(c) Determine a function V
that represents the volume of the box in terms of x
(d) For what values of x
(that is, original widths) will the volume of the box be between 600 and 800 cubic inches? Determine the answer graphically, and give values to the nearest tenth of an inch

3 0

2 years ago