find the work done by the force field f(x, y) = xi (y 1)j in moving an object along an arch of the cycloid r(t) = (t − sin(t))i (1 − cos(t))j, 0 ≤ t ≤ 2.
Answers
The work done by the force field f(x, y) = xi (y 1)j in moving an object along an arch of the cycloid
r(t) = (t − sin(t))i (1 − cos(t))j, 0 ≤ t ≤ 2 is -4
To find the work done by the force field in moving an object along the arch of the cycloid r(t), we need to compute the line integral of the dot product of the force field with the unit tangent vector of the arch. The cycloid is given by:r(t) = (t - sin(t))i + (1 - cos(t))j, 0 ≤ t ≤ 2.To find the unit tangent vector T(t), we differentiate the cycloid:
r'(t) = (1 - cos(t))i + sin(t)j.
T(t) = r'(t)/|r'(t)|
= (1 - cos(t))/√(2 - 2cos(t)) i + sin(t)/√(2 - 2cos(t)) j. The work done by the force field in moving the object along the arch is given by the line integral:W = ∫C f(r) · T(t) ds,where C is the arch of the cycloid, r is the position vector, T is the unit tangent vector, and ds is the arc length element. We have: f(x, y) = xi(y - 1)j, so f(r(t))
= (t - sin(t))i(1 - cos(t) - 1)j
= (t - sin(t))i(-cos(t))j
= -t cos(t) i + (t sin(t) - t) j.Writing this in terms of the unit tangent vector, we have:f(r) ·
T = (-t cos(t) i + (t sin(t) - t) j) · ((1 - cos(t))/√(2 - 2cos(t)) i + sin(t)/√(2 - 2cos(t)) j)
= -t cos(t) (1 - cos(t))/(2 - 2cos(t)) + (t sin(t) - t) sin(t)/(2 - 2cos(t))
= -t (cos(t) - cos²(t) + sin²(t))/(2 - 2cos(t))
= -t (cos(t) - 1)/(1 - cos(t))
= t (1 - cos(t))/(cos(t) - 1). Therefore, the work done by the force field in moving the object along the arch is:
W = ∫C f(r) · T(t) ds
= ∫0² t(1 - cos(t))/(cos(t) - 1) |r'(t)| dt
= ∫0² t(1 - cos(t))/√(2 - 2cos(t)) dt
= -∫0² t d(cos(t))
= t(cos(t) - 1) |0²
= -4. The work done by the force field in moving the object along the arch of the cycloid is -4.
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Related Questions
g a data analyst is working with the world happiness data in tableau. what tool do they use to select the area on the map representing finland? 1 point radial rectangular lasso pan
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You can select numerous impressions with the Tableau Lasso Selection tool by tracing a freehand shape around them.
How do they choose the region on the map that Tableau uses to represent Finland? You can select numerous impressions with the Tableau Lasso Selection tool by tracing a freehand shape around them.To display only the nations with a World Happiness score of 3.5 or lower, utilize the Filter tool.By tracing a freehand form around several marks with the Lasso tool, you can choose a group of them.When you wish to include only some marks and eliminate others around them, this tool is helpful.Based on the common values, Tableau creates the view of blended data.For instance, Tableau will match data on "Purple" from the main and "Purple" from the secondary if Color is the linking field in both data sources.To learn more about Lasso Selection refer
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On a recent trip, Juan started at an elevation of 1200 feet above sea level. He descended into a valley 20. 4 feet below sea level. Which of the following shows one way to calculate how many feet he descended in all?
A. -20. 4 – (-1200)
B. 1200 – 20. 4
C. -20. 4 + 1600
D. 1200 – (-20. 4)
Answers
Therefore , the solution of the given problem of expression comes out to be (D) 1200 - is the correct response (-20.4).
Describe expression.Multiplying, splitting, adding, and subtracting are important mathematical operations. If you combined them, you'd get the following sentence: A mathematical formula, some data, and an equation A declaration of truth is composed of values, variables, and functions like additions, erasures, multiplications, and divisions. It is possible to evaluate and contrast words and sentences.
Here,
Juan began his descent into a ravine 20.4 feet below sea level from a starting point of 1200 feet above it.
The ravine Juan entered is 20.4 feet above sea level (negative because it is below sea level). The difference between his initial elevation and the valley's elevation is thus:
=> 1200 - (-20.4) = 1200 + 20.4 = 1220.4
Juan then ascended 1220.
All told, 4 feet.
Thus, (D) 1200 - is the correct response (-20.4).
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Suppose each license plate in a certain state has three digits followed by three letters. The digits 4 and 5 are not used. So, there are 26 letters and 8 digits that are used. Assume that the letters and digits can be repeated. How many license plates can be generated using this format?
Answers
The required, there are 8998912 possible license plates that can be generated using this format.
Here, we have,
There are 8 digits that can be used for each of the three digits on the license plate, with two digits (4 and 5) that cannot be used.
Therefore, there are 8 choices for each of the three digits,
giving us 8 x 8 x 8 = 512 possible combinations for the digits.
Similarly, there are 26 letters that can be used for each of the three letters on the license plate.
Therefore, there are 26 choices for each of the three letters, giving us 26 x 26 x 26 = 17576 possible combinations for the letters.
Total number of license plates = number of choices for the digits x number of choices for the letters
= 512 x 17576
= 8998912
Therefore, there are 8998912 possible license plates that can be generated using this format.
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HELP ASAP PLS!!!!! VERY MUCH APPRECIATED
Answers
Answer:
0.3
Step-by-step explanation:
\(y=k\times x\)
passing through (5, 1.5) so the value of x=5 and y=1.5. substituted to equation above
\(1.5=k \times 5\)
\(k=\frac{1.5}{5} \)
\(k=0.3\)
the u shaped curve created by a quadratic equation
Answers
Answer: it is called a parabola
Step-by-step explanation:
The difference of two timber’s is 8. When twice the first number is added to three times the second number, the result is 51. What are the two numbers?
Answers
Answer:
First number:15
Second number: 7
Step-by-step explanation:
To find the 2 numbers, we can use system of equations.
Let's use x for the first number and y for the second number. Our first equation would be:
x-y=8
This equation comes from the first sentence: the difference of the 2 numbers is 8. The second equation would be
2x+3y=51
This equation comes from the second part of the question.
We can use elimination method to find x and y.
x-y=8
2x+3y=51
Let's eliminate x. To do so, the x in both equations must be equal to each other. Since one is x and another is 2x, we must multiply the first equation by 2 to get the same x.
2x-2y=16
2x+3y=51
Now that the x are the same, we can subtract the equations.
-5y=-35
y=7
With our y value, we can find x by plugging y into any of the equations.
x-7=8
x=15
Since we found our x and y, the first number is 15 and the second number is 7.
For questions 8, 9, 10: Note that x² + y² = 1² is the equation of a circle of radius 1. Solving for y we have y = √1-², when y is positive. 8. Compute the length of the curve y-√1-² between x = 0 and x = 1 (part of a circle.)
Answers
To compute the length of the curve y = √(1 - x²) between x = 0 and x = 1, we use the formula for the arc length of a curve. In this case, we can treat y as a function of x and integrate the square root of (1 + (dy/dx)²) over the given interval.
The formula for the arc length of a curve is given by the integral of √(1 + (dy/dx)²) dx. In this case, the equation of the curve is y = √(1 - x²). To find dy/dx, we take the derivative of y with respect to x, which gives dy/dx = -x/√(1 - x²).
Now we can compute the length of the curve between x = 0 and x = 1. Substituting the expression for dy/dx into the formula for arc length, we have ∫√(1 + (-x/√(1 - x²))²) dx from 0 to 1. Evaluating this integral will give us the length of the curve.
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The scores of individual students on the American College Testing (ACT) Program Composite College Entrance Examination have a Normal distribution with mean 18.6 and standard deviation 6.0. A representative sample of 64 students shows up at a test center. What is the shape of the sampling distribution model.
Answers
We can use the Normal distribution to estimate probabilities related to the sample mean.
The Central Limit Theorem (CLT) applies in this case. The theorem states that if the sample size is sufficiently large (n > 30) and the population distribution is not extremely skewed, the sampling distribution of the sample mean can be modeled using the Normal distribution.
In other words, the distribution of the sample means is Normal if the sample size is greater than or equal to 30, regardless of the shape of the population distribution, as long as it is not extremely skewed. Since the sample size is 64 and satisfies the requirements of the CLT, the shape of the sampling distribution model for the ACT scores will be Normal.
For example, we could use the Normal distribution to find the probability that the mean ACT score of a sample of 64 students is greater than a certain value. This is useful in making inferences about the population mean based on the sample mean.
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A flagpole casts a 40-foot shadow. The angle of elevation from the tip of the shadow to the tip of the flagpole is 32 degrees. how tall is the flagpole? round your answer to the nearest foot.
Answers
Apex: 25 feet is the correct answer!
Step-by-step explanation:
Take it or leave it:) Good Luck
The height of the pole is 25 foot (approximate)
What is angle of elevation?The angle of elevation is the angle formed between the horizontal line and a given observer’s line of sight. From its name, the angle of elevation represents the angle formed by the ground or base and the direction or the observer’s line of sight as the observer looks up at an object.
Given,
The shadow of the flagpole = 40 foot,
and the angle from the tip of the shadow to the tip of the flagpole = 32°
Perpendicular is the height of the pole and Base is its shadow.
Tan(x)=(perpendicular)÷(base)
Tan(32°) = 0.624869352
0.624869352 = (height of pole)÷40
0.624869352 x 40 = height of pole
24.9947741 = height of pole
Height of pole = 24.9947741
Height of pole ≈ 25 foot
Hence, tthe height of the pole is 25 foot (approximate)
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consider the probability experiment: a fair, six-sided, die is rolled three times. a. how many outcomes are in the sample space? b. what is the probability that all three flips are 2?
Answers
Given that each roll is independent and that the odds of rolling a 2 are 1/6, the probability of receiving three 2s in a row is 1/216.
a. We can apply the multiplication principle to determine how many outcomes there are overall in the sample space.
There are 666 = 216 possible outcomes in the sample space because there are six outcomes for each die roll and we are rolling the die three times.
b. As each die roll is independent of the others, there is a 1/6 chance that any particular roll will result in a 2.
Therefore, the probability of getting three 2's in a row is (1/6)(1/6)(1/6) = 1/216.
So the probability of all three rolls being 2 is 1/216.
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Angle P and Angle Q form a linear pair. If angle P = (7x - 4)º and
angle Q = (2x - 5), find the measure of each angle.
Answers
Answer:
Angle P = 143º
Angle Q = 37º
Step-by-step explanation:
Linear pair means the angles add up to 180º
So, using this, set up the equation: 7x - 4 + 2x - 5 = 180
Combine Like Terms
9x - 9 = 180
Add on both sides
9x = 189
Divide
189/9 = 21
Substitute 21 for x
Angle P: 7(21) - 4
Angle Q: 2(21) - 5
Answer:
hope you got the answer!
I found this because I had the same question and needed help!
What is the average rate of change of the function F(x)=-3x+5
Answers
The average rate of change of the function F(x) = -3x + 5 is -3.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
F(x) = -3x + 5
x = 1
F(1) = -3 + 5 = 2
F(2) = -6 + 5 = -1
The average rate of change of the function.
= (F(2) - F(1)) / (2 - 1)
= (-1 - 2) / 1
= -3/1
= -3
Thus,
The average rate of change is -3.
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(05.05 MC)
The area of a triangle is 24 square inches. What is the height of the triangle if the base length is 6 inches? (5
points)
Answers
Answer:
h = 8 inches
Step-by-step explanation:
the area (A) of a triangle is calculated as
A = \(\frac{1}{2}\) bh ( b is the base and h the height )
given A = 24 and b = 6 , then
\(\frac{1}{2}\) × 6 × h = 24 , that is
3h = 24 ( divide both sides by 3 )
h = 8 inches
What is the result when the number 38 is increased by 50%?
Answers
Answer:
Step-by-step explanation:
So you've got 38 to which you add 50% of 38 since we're talking about increasing.
You can either use percentage directly in your calculation, or you can see it as 50/100, meaning 1/2.
\(38+38*50/100 = 38 + 38*1/2 = 38 + 19 = 57\\\)
And here you go !
Last month, Brooklyn worked 255 hours for $750 per hour at her job at the store. How much did she earn the last month
Answers
Answer:
191,250
Step-by-step explanation:
Y=750(255)
P, Q and R are points on a circle. A tangent to the circle, RT is also shown. What is the size of angle x? Give a reason for your answer.
PS: I know the answer is 60, but I don't know how to write the reason for it.
Answers
Step-by-step explanation:
x = 60° { the angles formed by a tangent to a circle and a chord drawn from the point of contact are equal to respective angles in alternate segments }
Hope it will help
The value of x is 40.
What is the area and circumference of a circle?The circumference (or) perimeter of a circle = 2πr units. The area of a circle = πr2 square units. Where r is the radius of the circle. The circumference of the circle or the perimeter of the circle is the measurement of the boundary of the circle. Whereas the area of the circle defines the region occupied by the circle.
Given;
A tangent RT to the circumference of the circle at a point R
We know;
A tangent always forms a 90 degree angle with the diameter of the circle
Hence, x+50=90
x=90-50
x=40
Therefore, the value of x in circle will be 40.
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Quadrilateral ABCD is reflected across the x-axis. What are the coordinates of quadrilateral A´B´C´D
Answers
Answer:
D
Step-by-step explanation:
the answer is d because the quadrilateral is in quadrant 3 which is (-,-)
Answer:
D
Step-by-step explanation:
The table below gives input and output values for the function h(x) = a^x.
Answers
Answer:
It's the first one.
hope it helps :)
Step-by-step explanation:
As of April 2006, roughly 50 million .com web domain names were registered (e.g., yahoo.com).
a. How many domain names consisting of just two letters in sequence can be formed? How many domain names of length two are there if digits as well as letters are permitted as characters? [Note: A character length of three or more is now mandated.] b. How many domain names are there consisting of three letters in sequence? How many of this length are there if either letters or digits are permitted? [Note: All are currently taken.] c. Answer the questions posed in (b) for four-character sequences. d. As of April 2006, 97,786 of the four-character sequences using either letters or digits had not yet been claimed. If a four-character name is randomly selected, what is the probability that it is already owned?
Answers
There are 676 two-letter domain names. With digits, there are 1296. For three letters, there are 17576, and with letters or digits, there are 46656. For four letters, there are 456976, and with letters or digits, there are 1679616.
Out of 1679616, 97786 are unclaimed, resulting in a 5.82% probability of randomly selecting an owned four-character name.
(a) There are 26 * 26 = 676 domain names consisting of just two letters in sequence. If digits are also permitted, there are 36 * 36 = 1296 domain names of length two.
(b) There are 26 * 26 * 26 = 17576 domain names consisting of three letters in sequence. If either letters or digits are permitted, there are 36 * 36 * 36 = 46656 domain names of length three.
(c) Similarly, there are 26 * 26 * 26 * 26 = 456976 domain names consisting of four letters in sequence. If either letters or digits are permitted, there are 36 * 36 * 36 * 36 = 1679616 domain names of length four.
(d) The number of four-character sequences using either letters or digits is 36 * 36 * 36 * 36 = 1679616. Given that 97,786 of these sequences have not yet been claimed, the probability of randomly selecting an owned four-character name is 97,786 / 1,679,616 ≈ 0.0582, or approximately 5.82%.
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Hello please helpppp I will mark brainliest
Answers
Answer:
A, D, and B
Step-by-step explanation:
If you see the word sum, it means addition. If you see the word difference, it means subtractions.
Also, if you see the word quotient, it means related to divide.
-kiniwih426
Luis camina 2 kilómetros hacia el sur y luego un cierto número de kilómetros hacia el este. Termina a 5 kilómetros de su posición inicial. ¿Cuántos kilómetros caminó Luis hacia el este?
Answers
Answer:
camino 5 kilometros
Step-by-step explanation:
2-3+5
бw + 3 – 10w = 7w – 8
Solve for w
Answers
\(6w + 3 - 10w = 7w - 8 \\ = > 6w - 10w - 7w = - 8 - 3 \\ = > - 11w = - 11 \\ = > w = \frac{ - 11}{ - 11} \\ = > w = 1\)
Answer1
Hope it helpsray4918 here to help
How to put a starting pay of $500 with 100% increase every month on a graph.
This is the graph I need to use
Answers
Answer:
if boo ygdv
Step-by-step explanation:
f bi igfcnkyf f jurf
(1 point) a kite 50ft above the ground moves horizontally at a speed of 2ft/s. at what rate is the angle between the string and the horizontal decreasing when 200ft of string has been let out? answer (in radians per second):
Answers
Answer:
Step-by-step explanation:yes
Consuelo deposited an amount of money in a savings account that earned 6. 3% simple interest. After 20 years , she had earned $5’922 in interest. What was her initial deposit
Answers
Consuelo deposited an amount of money in a savings account that earned 6. 3% simple interest. After 20 years , she had earned $5’922 in interest then the initial deposit was $4700
Use the simple interest formula
I = P r t
where I = simple interest
P = principal
r= rate of interest
t= number of years
5922=Px6.3%x20
5922=Px1.26
P=5922/1.26
P=4700
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write 16+32 as a product of two factors one the gcf
Answers
Answer:
4 is one factor as gcf
In a factory, there are x technicians and y packers. The technicians are paid $100 per day and the packers are paid $60 per day. The total number of technicians and packers is 120. Their total wages per day is $8400.
(a) Write down an equation to represent the total number of technicians and packers in the factory.
b) Write another equation to represent the total wages of three employees by day.
Answers
Answer:
(a) The total number of technicians and packers in the factory is given to be 120. Therefore, we can write the equation:
x + y = 120
where x represents the number of technicians and y represents the number of packers.
(b) The total wages of three employees - two technicians and one packer - is given by:
2($100) + 1($60) = $260
To find the total wages of all technicians and packers, we can use the fact that the total number of technicians and packers is 120, and their total wages per day is $8400. Therefore, we can write another equation:
2($100) x + 1($60) y = $8400
where 2($100)x represents the total wages of all technicians and 1($60)y represents the total wages of all packers.
Step-by-step explanation:
expand and simpilfy (x+3)(x+5)
GIVING THE BRAINLIEST
Answers
Answer:
x^2+8x+15
Step-by-step explanation:
You can use FOIL method
(x*x)+(x*5)+(3*x)+(3*5)
x^2+5x+3x+15
x^2+8x+15
3 lines are shown. A line with points P, R, N intersects a line with points O, R, M at point R. A line extends from point R to point L in between angle M R P. Marcus states that angle ORP and angle LRP are a linear pair. Which best describes his statement?
Answers
Answer:
Marcus is wrong.
Step-by-step explanation:
As we see from the figure the angles ORP and PRM makes 180 degrees or are supplementary angles.
Marcus is wrong because a linear pair has a sum equal to 180 degrees.
But if we observe carefully the angles ORP and LRP don not together make an angle of 180 degrees. Also these angles do not have opposite rays .
Therefore angles PRM and ORP are linear pair angles but angle ORP and angle LRP are not a linear pair.
These angles do not have opposite arms as uncommon sides .
The linear pair must have
1) 180 degrees
2) opposite rays as uncommon sides
3) common vertex
Answer:
He is incorrect. Ray RO and ray RL are not opposite rays.
Step-by-step explanation:
Marcus is incorrect. In order for angles to be a linear pair, the rays of the angles that don't have a common side point, need to be opposite. This is not true for rays RO and RL, so Marcus's statement is not true.
answer plsss as soon as possible
Answers
Answer:
Step-by-step explanation:
both angles must add up to 180 so
6x+12+3x+63 must =180
= 9x+75
9x+75=180
-75 -75
9x=105
x=11.66
meaning A is approximately 81.96