The area of R can be calculated using the definite integral of the function y = 2x^2 -6x +4 and between g(x ) = cos1/4 and x = 4.
The integral expression is ∫(2x^2)-6x+4dx = ∫e^u du = e^u + C = e^(2x-x^2) + C. Evaluating the integral between x = 0 and x = 1 gives the area of R as e^2 - 1.
(b) The area of S can be calculated using the definite integral of the function y = e^(2x-x^2) between x = 0 and x = 1, minus the integral of the function y = 1 between x = 0 and x = 1. The integral expression for S is ∫e^(2x-x^2)dx - ∫1dx = ∫e^u du - x = e^u + C - x = e^(2x-x^2) + C - x. Evaluating the integral between x = 0 and x = 1 gives the area of S as e^2 - 1 - 1.
(c) The volume of the solid generated when R is rotated about the horizontal line y = 1 can be found using the integral expression ∫2πx(e^(2x-x^2) - 1)dx. This expression represents the area of the circular cross-sections of the solid multiplied by 2πx, which is the circumference of the circle. When evaluated between x = 0 and x = 1, this integral gives the volume of the solid generated when R is rotated about the horizontal line y = 1.
Learn more about integral here:
brainly.com/question/29974649
#SPJ4
If a fair die is rolled 3 times, what is the probability, to the nearest thousandth, of getting exactly 1 three?
The probability of getting exactly 1 three, to the nearest thousandth is 0.347.
What is Binomial Distribution?Binomial distribution is the distribution of a random variable X for which there are only two possibilities. The probability p for the success and the probability of 1-p for the failure, which consist of n trials.
The binomial distribution has the formula,
P(x) = ⁿCₓ pˣ (1-p)ⁿ⁻ˣ
where x : number of times for a specific outcome within n trials
p : probability of success in each trial
n : number of trials
Given that a fair die is rolled 3 times.
Here, n = 3, x = 1
p = probability of getting three for 1 trial = 1/6
1 - p = 1 - 1/6 = 5/6
P(1) = ³C₁ (1/6)¹ (5/6)³⁻¹
= 0.347
Hence the probability of getting exactly 1 three is 0.347.
Learn more about Binomial Distribution here :
https://brainly.com/question/14565246
#SPJ1
Color Number of Stickers Brown 86 Green 24 Yellow 32 Orange 21 Red 21 Blue 30 How is the histogram for the stickers from the large package distributed?
(Algebra 2 Normal Distribution)
The distribution of the histogram for the large packages colors is given as follows:
Right skewed.
How to obtain the distribution of the histogram?The distribution depends on whichever of the mean or the median is greater, as follows:
Hence the distribution is defined as follows:
Mean greater than median: Positively(right) skewedMean less than the median: Negatively(left) skewedThe ordered data-set is given as follows:
21, 21, 24, 30, 32, 86.
The median is the mean of the two-middle values, hence:
Median = (24 + 30)/2
Median = 27.
The mean is the sum of all the observations divided by the number of observations, hence:
Mean = (21 + 21 + 24 + 30 + 32 + 86)/6
Mean = 35.67.
Mean > median, hence the distribution is right skewed.
More can be learned about distributions at brainly.com/question/25800303
#SPJ1
Find the x intercept of the graph of the equation .
2x - 4y = 9
To find the x-intercept of the graph of the equation 2x - 4y = 9, we need to find the value of x when y = 0.
We can solve for x as follows:
2x - 4y = 9
2x - 4(0) = 9 (substitute y = 0)
2x = 9
x = 9/2
Therefore, the x-intercept of the graph of the equation 2x - 4y = 9 is (9/2, 0).
Asap please
Which one is correct
Answer: D. The distance from A to C
Step-by-step explanation:
This formula can be used to find the distance between two points on a three-dimensional coordinate system:
D(x, y, z) = [tex]\sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2} + (z_{2} - z_{1})^{2} }[/tex]
If you apply the formula for all options, you will find the distance from A to C is equal to [tex]\sqrt{5}[/tex]. The other distances are:
A. [tex]\sqrt{17}[/tex]
B. [tex]\sqrt{45}[/tex]
C. [tex]\sqrt{44}[/tex]
So, the answer is D.
If an arrow is shot upward on Mars with a speed of 52 m/s, its height in meters t seconds later is given by y = 52t − 1.86t2. (Round your answers to two decimal places.)
(a) Find the average speed over the given time intervals. (i) [1, 2] m/s (ii) [1, 1.5] m/s (iii) [1, 1.1] m/s (iv) [1, 1.01] m/s (v) [1, 1.001] m/s
(b) Estimate the speed when t = 1. m/s
48.28 m/s is the speed .
What is the definition of a velocity simple?
The speed at which a body or object is moving determines its direction of motion. Most of the time, speed is a scalar quantity. Velocity is fundamentally a vector quantity.
The rate at which distance changes is what it is. It measures the displacement's rate of change.
Height, y = 52t - 1.86t²
Velocity = ∆y/∆t = 52 - 1.86 * 2t = 52- 3.72t
A. Average velocity = (v1 + v2)/2
(i) At t = 1, 2
Average velocity = (52 - 3.72*1 + 52 -3.72*2)/2 = 46.42 m/s
(ii) At t = 1,1.5
Average velocity = (52 - 3.72*1 + 52 - 3.72*1.5)/2 = 47.35 m/s
(iii) At t = 1,1.1
Average velocity = (52 - 3.72*1 + 52 -3.72*1.1)/2 = 48.09m/s
(iv) At to = 1, 1.01
Average velocity = (52 - 3.72*1 + 52 - 3.72*1.01)/2 = 48.26 m/s
(iv) At t = (1, 1.001)s
Average velocity = (52 - 3.72*1 + 52 - 3.72*1.001)/2 = 48.28 m/s
B. Speed at t = 1s
Velocity = 52 - 3.72 * 1 = 48.28 m/s
Learn more about Velocity
brainly.com/question/18084516
#SPJ4
when you represent a three-dimensional object graphi- cally in the plane (on paper, the blackboard, or a com- puter screen), you have to transform spatial coordinates,
The simplest choice is a linear transformation, for example, the one given by the
matrix [tex]\left[\begin{array}{ccc}-1/2&1&0\\-1/2&0&1\end{array}\right][/tex]
What is spatial coordinates and plane coordinates?When compared to pixel coordinates, spatial coordinates provide for a finer level of image position specification. The pixel coordinate system, for example, treats a pixel as a discrete unit that is uniquely recognized by an integer row and column pair, such as (3,4). The pixel coordinates are the default way that spatial coordinates of a picture are related. In row 5, column 3, for instance, the center of the pixel has spatial coordinates of x = 3 and y = 5, for example. The coordinates are inverted, so keep that in mind.When you represent a three-dimensional object graphically in the plane con paper, the blackboard, or a computer screen), you have to transform spatial coordinates,
[tex]$\mathrm{x} 1$ & \\[/tex]
[tex]$\mathrm{x} 2$[/tex] & into plane coordinates
[tex]$\mathrm{x} 3$[/tex]& [tex]$\mathrm{y} 1$[/tex]& [tex]$\mid$ \\[/tex]
[tex]$\mathrm{x}$[/tex] &[tex]$\mathrm{y} 2$[/tex] &
The simplest choice is a linear transformation, for example, the one given by the
matrix [tex]\left[\begin{array}{ccc}-1/2&1&0\\-1/2&0&1\end{array}\right][/tex]
The complete question is,
When you represent a three-dimensional object graphically in the plane (on paper, the blackboard, or a computer screen), you have to transform spatial coordinates | x 1 | | x 2 | into plane coordinates | y 1 |. | x 3 | | y 2 | The simplest choice is a linear transformation, for example, the one given by the matrix | -1/2 1 0 0 | 1 |.
To learn more about spatial coordinates refer to
https://brainly.com/question/24289673
#SPJ4
Find three sets of points that are on the line y=5/3x-2
Note that these points are not different from each other and are on the same line y = 5/3x - 2.
Any point on this line will have the coordinates (x, y) such that y = 5/3x - 2.
What are the points on a line?Generally, A point on a line is any place along that line that is represented by a set of coordinates in either two- or three-dimensional space, denoted by the letters x, y, or x, y, z, respectively.
An equation, such as y = mx + b, may be used to define a line in a mathematical context. In this equation, m refers to the slope, while b refers to the y-intercept.
Any point that can be made to fit into this equation is up for grabs.
Read more about points on a line
https://brainly.com/question/7158994
#SPJ1
the dot product of two vectors with magnitudes of 10 and 6 is equal to 30. What is the angle formed by the vectors
If the magnitude of two vectors is 10 and 6 and their dot product is 30, then the angle between the vectors is 60°.
What is a vector?
A vector in mathematics is a quantity that not only expresses magnitude but also motion or position of an object in relation to another point or object. Euclidean vector, geometric vector, and spatial vector are other names for it.
There are two ways to define a dot product: algebraically and geometrically. The sum of the products of the matching entries of the two number sequences is the definition of the dot product in algebra. Geometrically, it is the sum of the cosine of the angle formed by the two vectors and their Euclidean magnitudes.
The magnitude of the vector 1 is, |a| = 10
The magnitude of the vector 2 is, |b| = 6
The dot product of the two vectors is, a·b = 30.
The formula for dot product of vectors is -
a·b = |a| |b| cos θ
Solve the equation to get the angle -
30 = (10 × 6) cos θ
30 = 60 cos θ
cos θ = 30/60
cos θ = 1/2
θ = cos^-1 (1/2)
θ = 60°
Therefore, the angle is obtained as 60°.
To learn more about vector from the given link
https://brainly.com/question/25705666
#SPJ1
A car owner pays for new brakes that cost $756.25, with a credit card that has an annual rate of 24.5%. Determine the total amount paid, if the car owner pays $100 a month, until the balance is paid off.
The total amount paid with a monthly payment of $100 for a credit of $756.25 at an annual rate of 24.5% is $871.69.
What is a periodic payment?The periodic payment is the amount the car owner pays monthly to offset the balance on the credit card for purchasing new brakes.
The periodic payment is determined using an online finance calculator as follows:
N (# of periods) = 1 year
I/Y (Interest per year) = 24.5%
PV (Present Value) = $756.25
PMT (Monthly Payment) = $100
Results:
Sum of all periodic payments = $871.69
Total Interest = $115.44
Thus the total payment made by the car owner is $871.69 with an interest of $115.44.
Learn more about periodic payments at https://brainly.com/question/24244579
#SPJ1
Answer:
$830.52
Step-by-step explanation:
I got it right on the test :)
Have great day
question 1 fill in the blank: data aggregation involves creating a ____collection of data that originally came from multiple sources.
Data aggregation involves creating a unified collection of data that originally came from multiple sources.
It is the process of combining data from multiple sources into one file, report or summary. Data aggregation can be done using a variety of methods, such as mathematical formulas, grouping, filtering and sorting. For example, a mathematical formula can be used to calculate the average of a set of numbers. Grouping data can be used to divide data into categories and subcategories, such as by country or by product. Filtering data involves removing unnecessary or unwanted data, such as outliers or irrelevant information. Finally, sorting data can be used to organize data in a specific order, such as alphabetically or numerically. Data aggregation is a useful tool for making sense of large datasets and providing greater insight into the data.
Learn more about Data aggregation here:
https://brainly.com/question/14893265
#SPJ4
Solve using the following equation and the listed values for the variables. Round your final answer to 2 decimal places A+B)/2) (a+b)/2) Where A = 21, B = 20,X = 19, Y = 20.
The average of two numbers, A and B, is calculated by adding them together and then dividing by two. In this case, A = 21, B = 20, X = 19, and Y = 20. When we calculate (A + B) / 2, we get 20.00.
1. Add A and B together: 21 + 20 = 41
2. Divide the sum by 2: 41 ÷ 2 = 20.50
3. Round the answer to two decimal places: 20.50 → 20.00
The average of two numbers, A and B, is calculated by adding them together and then dividing by two. This formula is expressed as (A + B) / 2. In this problem, we were given the values A = 21, B = 20, X = 19, and Y = 20. To solve for the average, we first need to add A and B together and get 41. Then we divide this sum by two and get 20.50. To get the final answer, we need to round this value to two decimal places, which results in the answer 20.00. This answer indicates that the average of 21 and 20 is 20.00.
Learn more about average here
https://brainly.com/question/24057012
#SPJ4
Teachers in a district have been teaching for a mean of 8 years with a standard deviation of 3 years, and the distribution of years teaching is strongly skewed to the right. Suppose we took random samples of 30 teachers from this district and calculated x as the sample mean of how long each group of teachers had been teaching. We can assume that the teachers in each sample are independent.
Answer:C. Approx. Normal
Step-by-step explanation:
please answer this timed question
Answer:
50
Step-by-step explanation:
140/x = 168/60
x = 60*140/168 = 50
Answer:
50
Step-by-step explanation:
168/60=2.8
140/2.8=50
A ball is thrown straight downward from the top of a tall building. The initial speed of the ball is10 m/s. It strikes the ground with a speed of60 m/s. How tall is the building? 28. A baseball is thrown straight downward with an initial speed of40ft/sfrom the top of the Washington Monument (555fthigh). How long does it take to reach the ground, and with what speed does the baseball strike the ground?
The tall of the building is 175m and the baseball strikes the ground in 4.53 seconds, 195 ft/s.
Assume that the acceleration due to gravity is 10m/s2.
The equation for the ball’s velocity in the downward direction is
v(t) = at + v₀.
Here
v₀=10m/s a=10m/s² v(t)=60m/s
Solving this for t we get the:
[tex]t =\frac{60m/s-10m/s}{10m/s^2}\\ \\t=\frac{50m/s}{10m/s^2}\\[/tex]
t=5s
The total distance traveled will be
[tex]x(t)=\frac{1}{2} at^2+v_{0} +x_{0}[/tex]
Here x₀ = 0 and we get:
[tex]x(t)=\frac{1}{2} (10m/s^2)(5s)^2+(10m/s)(5s)[/tex]
x=125m+50m
x=175m
The given values are:
u = 50 ft/s
h = 555 ft
g = 32 ft/s²
Let the time taken by the ball to reach the ground be t and the velocity of the ball as it hits the ground be v.
Use the third equation of motion
v²=u²+2as
v²=50²+2*32*555
v = 195 ft /s
Thus, the ball strikes the ground with a velocity of 195 ft/s.
Use the first equation of motion
v = u + at
195 = 50 + 32 t
32 t = 145
t = 4.53 second
Thus, the ball reaches the ground in 4.53 seconds.
To know more about equations of motion:
https://brainly.com/question/13246412
#SPJ4
The doctor orders 500,000 Unlts of penicillin for the patient: The capsules avallable are 200,OOUnits and 100,000 Units Wlth the fwest capsules how many capsules would be given per dosc? (____) 200,000 mo capsuics (____) 100,000 ma capsulcs
Patient needs to 500,000 unit of penicillin, then according to capsule availability we shall provide the 2 capsules of 200,000 unit and 1 capsule of 100,000 unit.
The doctor orders 500,000 unit of penicillin for the patient. the capsule available are 200,000 unit and 100,000 units.
we have to find out the number of capsules required for 500,000 unit,
let's see,
we have 200,000 unit of penicillin and 100,000 units of penicillin available,
patient need of 500,000 unit of penicillin,
so we shall provide the 2 capsule of 200,000 units of penicillin and 1 capsule of penicillin 100,000 unit to the patient,
learn more about capsule.
https://brainly.com/question/13020190
#SPJ4
P=C+MC solve for C?
All terms should be shifted to the left and set to zero. After that, make each factor equal to zero. [tex]C=\frac{P}{1+M}$$[/tex]
What is the solution of the term P=C+MC for C ?P=C+M C
As C + M C = P, rewrite the equation.
C+M C=P
Add C to the equation on both sides. .MC=P−C
Simplify M C = P C by dividing each term by C.
Divide each phrase into [tex]$M C|=| \boldsymbol{P}-\boldsymbol{C}$[/tex] by C
[tex]\frac{M C}{C C} \equiv \frac{P}{C}+\frac{-C}{C}$$[/tex]
C's common factor should be cancelled.
[tex]$M=\frac{P}{C}+\frac{-C}{C}$[/tex]
M=PC−1
An equation that is mostly made up of letters is said to be literal. Literal equations include those found in formulas. Each variable acts as a "literal" representation of an essential element of the overall relationship that the equation expresses. For instance, P = 2L + 2W is a formula for expressing a rectangle's perimeter.
To learn more about solving refer to :
https://brainly.com/question/504117
#SPJ1
What is the greatest number of consecutive integers
that sum to –11? PLS NOW
Answer:
It is not possible for the sum of consecutive integers to be -11. The sum of n consecutive integers is n times the average of the first and last integers. The average of any two integers is a fraction, which when multiplied by n, will always yield a fraction, which cannot equal -11. Therefore it is not possible to have n consecutive integers that sum to -11.
Calculate the Scale Factor given the points A( 12, 4) and A' (9, 3).
The Scale Factor is 0.75, or 3/4
What is scale Factor?Scale factor is a ratio of two related lengths, areas, volumes, or other quantities. It is used to describe how a figure is enlarged or reduced in size. For example, when a figure is enlarged, the scale factor is greater than one, and when a figure is reduced, the scale factor is less than one. Scale factors can be used to calculate the lengths of sides and areas of figures when one side or area is known.
The Scale Factor is calculated by dividing the coordinates of point A' (9, 3) by the coordinates of point A (12, 4). Therefore, the Scale Factor is 0.75, or 3/4.
To know more about scale factor click-
https://brainly.com/question/2826496
#SPJ1
The following inequalities form a system. y is greater than or equal to two-thirds times x plus 1 y is less than negative one-fourth times x plus 2 Which ordered pair is included in the solution to this system? (−6, 3.5) (−6, −3) (−4, 3) (−4, 4)
The ordered pair that is included in the solution to this system of inequalities is: B. (−6, −3)
How to determine the required ordered pair?In order to determine the ordered pair is included in the solution to this system of linear inequalities, we would first of all translate the word problem into an algebraic equation as follows;
y is greater than or equal to two-thirds times x plus 1 ⇒ y ≥ 2x/3 + 1.
y is less than negative one-fourth times x plus 2 ⇒ y < -x/4 + 2.
Next, we would use an online graphing calculator to graphically solve the system of linear inequalities. Therefore, the required solution for the given system of linear inequalities is the shaded area below the solid line, which is given by the ordered pair (−6, −3).
Read more on inequality here: brainly.com/question/12952773
#SPJ1
before the announcement of a three for one stock split, the selling price for a share of a stock in fossil oil refineries was 150 per share. immdeiatley afteyr the stock split, the propable price per share is
The price of the share of stock in fossil oil refineries after the three-for-one split is $50.
A stock split is an event in the stock market when the company declares split of stock into multiple parts to decrease the cost per share and make it easier to purchase.
Given,
The selling price of a stock in fossil fuel before split = $150
After one year the stock split into three parts
∴ Probable prices per share = Price before split/3
= $150/3
= $50
Learn more about the selling prices:
https://brainly.com/question/28017453
#SPJ4
What is the cost of 6 pencils at 60 cents a dozen
To determine the cost of 6 pencils at 60 cents a dozen, we need to convert the price per dozen to the price per pencil. We know that a dozen is equal to 12, so we can use the following formula:
Price per pencil = (Price per dozen) / (Number of items per dozen)
So, in this case:
Price per pencil = (60 cents) / (12 pencils)
To convert cents to dollars, we divide by 100.
Price per pencil = (60/100) $ = 0.6 $
To find the total cost for 6 pencils we multiply the price per pencil by the number of pencils
Cost of 6 pencils = 6 * 0.6 = 3.6 $
So the cost of 6 pencils at 60 cents a dozen is 3.6 $.
Gombak Mega Store is having its Year-End-Sales. Ten percent, five percent and twenty percent discounts were given on shoes, handbags and watches respectively if two or more units of each item were bought. Noor bought three pairs of shoes, two units of handbag and one unit of watch. If the price (per unit) of shoes, handbag and watch is RM150, RM200 and RM250 respectively, how much money does Noor has to pay?
Answer:
$963.00
Step-by-step explanation:
.9(3x150) + .95(2x200) + 250
.9(450) + .95(400) + 250
405 + 308 + 250 = 963
If we are taking 10% off, that is like leaving 90% (.9) on.
If we are taking 5% off, that is like leaving 95% ( .95) on.
No discount for the watch because she only bought one.
Each of 12 refrigerators of a certain type has been returned to a distributor because of the presence of a high-pitched oscillating noise when the refrigerator is running. Suppose that 5 of these 12 have defective compressors and the other 7 have less serious problems. If they are examined in random order, let X = the number among the first 6 examined that have a defective compressor. Compute the following:
(i) P(X = 1)
(ii) P(X ≥ 4)
(iii) P(1≤X ≤3)
(a) .1136, .1212 and 0.7955 respectively.
(b) .1136, .1212 and 0.1136 respectively.
(c) .1136, .1212 and 0.8712 respectively.
(d) .1136, .039 and 0.7955 respectively. (e) .1136, .039 and 0.8712 respectively.
The probability of one defective compressor among the first 6 examined, the probability of four or more defective compressors among the first 6 examined, and the probability of 1 to 3 defective compressors among the first 6 examined are 0.1136, 0.1212, and 0.7955 respectively.
(a) .1136, .1212 and 0.7955 respectively.
(i) P(X=1) = C(5,1) / C(12,6) = 5/66 = 0.1136
(ii) P(X ≥ 4) = P(X = 4) + P(X = 5) + P(X = 6) = C(5,4) / C(12,6) + C(5,5) / C(12,6) + C(5,6) / C(12,6) = .1212
(iii) P(1≤X ≤3) = P(X = 1) + P(X = 2) + P(X = 3) = C(5,1) / C(12,6) + C(5,2) / C(12,6) + C(5,3) / C(12,6) = 0.7955
The probability of one defective compressor among the first 6 examined is P(X = 1) = C(5,1) / C(12,6) = 5/66 = 0.1136. The probability of four or more defective compressors among the first 6 examined is P(X ≥ 4) = P(X = 4) + P(X = 5) + P(X = 6) = C(5,4) / C(12,6) + C(5,5) / C(12,6) + C(5,6) / C(12,6) = .1212. The probability of 1 to 3 defective compressors among the first 6 examined is P(1≤X ≤3) = P(X = 1) + P(X = 2) + P(X = 3) = C(5,1) / C(12,6) + C(5,2) / C(12,6) + C(5,3) / C(12,6) = 0.7955.
Therefore, the probability of one defective compressor among the first 6 examined, the probability of four or more defective compressors among the first 6 examined, and the probability of 1 to 3 defective compressors among the first 6 examined are 0.1136, 0.1212, and 0.7955 respectively.
Learn more about probability here
https://brainly.com/question/11234923
#SPJ4
Use the ALEKS calculator to evaluate each expression.
Round your answers to the nearest thousandth.
Do not round any intermediate computations.
log√7 =
Log 23/6=
Exponential growth is a type of growth that occurs when the rate of increase is proportional to the current amount.
Logarithmic evaluationLog√7 = 1.659Log 23/6 = 0.862It is a rapid increase in the quantity of something over a period of time. Exponential growth can be seen in populations, investments, and other areas.It is characterized by a doubling or tripling of the original amount within a specified period of time.This type of growth is often caused by compounding, where gains from one period are reinvested in the next period, leading to a rapid increase in the overall amount.Exponential growth is often seen in the early stage of a business, when it is experiencing rapid growth due to investments or other factors.However, exponential growth can also lead to rapid decline if not managed properly.This is called logarithmic evaluation, which involves using logarithms to simplify complex expressions.To learn more about logarithmic evaluation refer to:
https://brainly.com/question/29168400
#SPJ1
The volume of a cylinder is 282.6 cubic yards. The radius measures 3 yards. What is the height of the cylinder rounded to the nearest yard? Use 3.14 for π. PLEASE HELP WANTED TTYY!!!
Answer:
10 yards
Step-by-step explanation:
You want the height of a cylinder of radius 3 yards that has a volume of 282.6 cubic yards, using pi = 3.14.
VolumeThe volume of a cylinder is given by ...
V = πr²h
Using the given values, this is ...
282.6 yd³ = 3.14(3 yd)²·h = 28.26h yd²
Dividing by the coefficient of h, we find it to be ...
h = (282.6 yd³)/(28.26 yd²) = 10 yd
The height of the cylinder is 10 yards.
Consider a continuous-time random process, X(t), obtained as the result of a sample-and-hold operation on a noise voltage V(t). IT can be expressed analytically asX(t) = \sum_{n = - \infty }^{\infty} V(nT)h(t- nT)where T is the sampling period and h(t) is the holding pulse,h(t) = 1 \: \: \: \: \: \: 0\leq t \leq Tandh(t) = 0 \: \: \: \: \: \: otherwise
Assume that V(nT) is zero-mean for all n.
Assume that V(nT) has variance\sigma _{v}^{2}for all n.
Assume that T is large enough to render V(nT) and V([n+k]T) statistically independent for all n and for all k\neq0.
A. Find the autocorrelation of X(t).
The holding pulse is nonzero only for[tex]0 \leq t \leq T[/tex], the autocorrelation of X(t) is given by\begin{align}
[tex]R_{xx}(t,t+\tau) =[/tex]
[tex]\begin{cases}\sigma_v^2 \sum_{n=-\infty}^{\infty}\sum_{m=-\infty}^{\infty}h(t-nT)h(t+\tau-mT) & 0 \leq \tau \leq T \\0 & \text{otherwise}.\end{cases}\end{align}[/tex]
The autocorrelation of X(t) is defined as[tex]R_{xx}(t,t+\tau) = E[X(t)X(t+\tau)][/tex]where E[.] is the expectation operator. Since V(nT) has zero mean and is statistically independent, we can write
[tex]R_{xx}(t,t+\tau) &= E[X(t)X(t+\tau)]\\ &= E\left[\sum_{n=-\infty}^{\infty}V(nT)h(t-nT)\sum_{m=-\infty}^{\infty}V(mT)h(t+\tau-mT)\right]\\&= \sum_{n=-\infty}^{\infty}\sum_{m=-\infty}^{\infty}E[V(nT)V(mT)]h(t-nT)h(t+\tau-mT)\\&= \sigma_v^2 \sum_{n=-\infty}^{\infty}\sum_{m=-\infty}^{\infty}h(t-nT)h(t+\tau-mT)\end{align}[/tex]
Since the holding pulse is nonzero only for[tex]0 \leq t \leq T[/tex], the autocorrelation of X(t) is given by\begin{align}
[tex]R_{xx}(t,t+\tau) =[/tex]
[tex]\begin{cases}\sigma_v^2 \sum_{n=-\infty}^{\infty}\sum_{m=-\infty}^{\infty}h(t-nT)h(t+\tau-mT) & 0 \leq \tau \leq T \\0 & \text{otherwise}.\end{cases}\end{align}[/tex]
Learn more about autocorrelation here:
https://brainly.com/question/29342466
#SPJ4
2.87 x 7.8
eeeeeeeeeeeeeee
Answer:
22.386
Step-by-step explanation:
Find the mistake: Explain what the person did incorrectly while solving the problem or how you would solve it.
5x + 8 = 2x + 20
5x + 8 = 2x + 20
-2x -2x
3x + 8 = 20
-8 -8
3x = 12
times each side by 3
x = 36
region r is the base of a solid. for this solid, each cross section perpendicular to the x-axis is an isosceles right triangle with a leg in r. find the volume of the solid.
Without the equation of the graph of the region R, it is not possible to determine the volume of the solid defined by a region R, an isosceles right triangle cross-section, and a line y=k.
The question describes a solid where the base is a region R in the first quadrant, bounded by the graph of y, the x-axis, and the line y = k.
It is also mentioned that each cross section perpendicular to the y-axis is an isosceles right triangle with the right angle on the x-axis and one leg in the XY-plane.
However, the equation of the graph of the region R is not given, which makes it impossible to determine the range of y over which the solid is defined and therefore, calculate the volume of the solid. It's very important to have the equation of the graph of the region R to find the volume of the solid.
To learn more about the volume of the solid at
https://brainly.com/question/12649605?referrer=searchResults
#SPJ4
The question is -
Let R be the region In the first quadrant bounded by the "graph of y the !-axis, and the line y The region R Is the base of a solid For the solid, each cross section perpendicular [tex]t_0[/tex] to the y-axis Is an isosceles right triangle with the right angle on the !-axis and one leg in the 1y-plane What is Ithe volume of the solid?
In the figure below lines A and B are parallel.Find the m<5 if m<1=75 and m <3=40
The unknown angle in the parallel lines is a follows;
m∠5 = 75 degrees
How to find angles in parallel lines?When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate interior angles, alternate exterior angles, linear angles, vertically opposite angles etc.
Therefore, let's use the angle relationships to find the m∠5 in the parallel lines.
The angle m∠1 and m∠5 are corresponding angles.
Corresponding angles are congruent.
Therefore,
m∠1 = m∠5 = 75 degrees.
learn more on angles here: https://brainly.com/question/30172323
#SPJ1
