The line integral over the curve c of the function f(x,y) = 3x - 2y is 6.
To evaluate the line integral of the given function over the curve c, we need to parameterize the curve and express the function in terms of the parameter.
The curve c is given by x = sin(t), y = cos(t) for 0 ≤ t ≤ π, which is the top half of the unit circle. To parameterize the curve, we can use the following vector function:
r(t) = (sin(t), cos(t)), 0 ≤ t ≤ π
Then the line integral of the function f(x,y) = 3x - 2y over the curve c can be expressed as:
∫c f(x,y) ds = ∫π₀ (3sin(t) - 2cos(t)) ||r'(t)|| dt
where ||r'(t)|| is the magnitude of the derivative of r(t) with respect to t, which is:
||r'(t)|| = √(cos²(t) + sin²(t)) = 1
Substituting this value, we get:
∫c f(x,y) ds = ∫π₀ (3sin(t) - 2cos(t)) dt
Now, we can integrate the function with respect to t:
∫π₀ (3sin(t) - 2cos(t)) dt = [-3cos(t) - 2sin(t)]π₀
Substituting the limits of integration, we get:
∫c f(x,y) ds = [-3cos(π) - 2sin(π)] - [-3cos(0) - 2sin(0)]= (3 + 0) - (-3 - 0) = 6.
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The intersection of f(x,y) = 3x - 2y on curve c is 6. To evaluate the system of a function on curve c, we need to evaluate the curve and represent the following discordant activities.
The curve c is given by x = sin(t), y = cos(t), where 0 ≤ t ≤ π, this is a semicircle. We can use the following vector function to measure the curve:
r(t) = (sin(t), cos(t)), 0 ≤ t ≤ π
So the function f(x, y) = 3x - 2y on the curve c it can be represented as:
∫c f(x,y) ds = ∫π₀ (3sin(t) - 2cos(t)) r'(t)dt
where r'(t) is the magnitude of the derivative of r(t) with respect to t, for example:
r'(t) = √(cos²(t) + sin²(t)) = 1
This substituting the value we get:
∫c f(x,y) ds = ∫π₀ (3sin(t) - 2cos(t)) dt
Now we can integrate the function t (∫π₀ (3sin(t)) ) - 2cos(t)) t) - 2cos(t)) dt = [-3cos(t) - 2sin(t)]π₀
Substitution at the limit of our shares :
∫c f(x,y) ds = [-3cos( π ) - 2sin(π)] - [-3cos(0) - 2sin(0)] = (3 + 0) - (-3 - 0) = 6.
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Jeremy rides a Ferris wheel. The graph shows h, Jeremy’s height above the ground at any time during the ride.
Which inequality represents the heights shown on the graph?
The inequality that represents the height that is displayed by the graph is: 10 ≤ h ≥ 50.
How to Identify the Inequality of a Graph?In an inequality graph, we the small circle at any end is shaded or full, the inequality sign used is either "less than or equal to" or "greater than or equal to" ("≤" or "≥"). If the circle is empty or not shaded, we use "less than" or "greater than" ("<" or ">").
In the graph showing Jeremy’s height above the ground at any time during the ride, we have a full circle (shaded) starting from 10, and another on the right at 50.
This implies that the range of height is from 10 to 50. Since the circle is full (shaded), then we would use "less than or equal to" and "greater than or equal to" ("≤" and "≥") in writing the inequality that represents the height.
Thus, where h is the height, the inequality would be: 10 ≤ h ≥ 50.
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I need helppppp for this question
Answer:
too small
Step-by-step explanation:
Nozomi works as a waiter and earns $16/h. She also receives 8% of the gratuities earned by all the staff. In one week, she worked 20 hours and the gratuities totalled $1,267.28. What was Nozomi’s gross pay?
Her gross pay is $421.38
What was Nozomi’s gross pay?First, we know that she gets $16 per hour, and she worked 20 hours, then she gets:
20*$16 = $320
Now we also know that she receives a percentage of 8% of the gratuities, and the gratuities totaled $1,267.28
The 8% of $1,267.28 is:
$1,267.28*(8%/100%) = $1,267.28*0.08 = $101.38
Her gross pay is:
P = $101.38 + $320 = $421.38
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Which of the sets of ordered pairs represents a function?
A = {(−5, 5), (−2, 2), (2, −2), (5, −5)}
B = {(4, 2), (3, −2), (9, 4), (11, −3)}
Only A
Only B
Both A and B
Neither A nor B
Answer:
Both A and B
Step-by-step explanation:
A set of ordered pairs is not a function if there is a repeating output (Y value.)
Y values of A= 5, 2, -2, -5.
Y values of B= 2, -2, 4, -3.
There are no repeating outputs.
A bookmark has an area of 18 cm the perimeter is 22 cm what are the dimensions of the bookmark
Answer:369
Step-by-step explanation:
all you have to do is multiply 18 and 22 its easy
18 x 22 = 369.
What is the domain of the quadratic function graphed below?
The domain of the graph is the set of all real values
How to determine the domain?The domain is the set of x values of the graph
From the graph, the x values extend in both directions without end
This means that the x values can accommodate all real values
Hence, the domain of the graph is the set of all real values
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Find the equivalent expression of 20a + 28b.
Answer:
4 (5a + 7b)
Don't worry I helped my brother with this.
A napkin is folded into an isosceles triangle, triangle ABC, and placed on a plate, as shown. The napkin has a perimeter of 38 centimeters.
The area of the plate covered by the napkin is (C) [tex]56cm^{2}[/tex].
What is an area of a triangle?
The area of a triangle is defined as the total region that is enclosed by the three sides of any particular triangle. Basically, it is equal to half of the base times height, i.e. A = 1/2 × b × h. As a result, in order to calculate the area of a triangular polygon, we must first determine its base (b) and height (h).To find the area of the plate covered by the napkin:
Given :
A napkin is folded into an isosceles triangle, triangle ABC, and placed on a plate.The napkin has a perimeter of 38 centimeters.The following steps can be used in order to determine the area of the plate covered by the napkin:
Step 1 - The formula of the perimeter of a triangle is given below:
P = a + b + c --- (1)
where a, b, and c are the length of the sides of the triangle.
Step 2 - According to the given data, the triangle is isosceles.
Therefore, the two sides are similar and the length of the base is 8 cm.
Step 3 - Now, substitute the values of the known terms in the above formula.
38 = 2L + 8
38 - 8 = 2L
L = 15 cm
Step 4 - The area of the plate covered by the napkin is given below:
[tex]A=\frac{1}{2} * 15 * 15 *Sin30[/tex]
Step 5 - Simplify the above expression.
[tex]A=56.25cm^{2}[/tex]
Rounding off to the nearest whole number, which is [tex]56cm^{2}[/tex].
Therefore, the area of the plate covered by the napkin is (C) [tex]56cm^{2}[/tex].
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The question you are looking for is here:
A napkin is folded into an isosceles triangle, triangle ABC, and placed on a plate, as shown. The napkin has a perimeter of 38 centimeters. To the nearest square centimeter, how many square centimeters of the plate is covered by the napkin?
(A) 16 square centimeters
(B) 30 square centimeters
(C) 56 square centimeters
(D) 60 square centimeters
What are the coordinates of the midpoint of the segment whose endpoints are C(−7, −10) and D(3, 9) ?
(−2, −0.5)
(−4, −1)
(−5, −9.5)
(−8.5, 3)
Answer:
(-2, -0.5)
Step-by-step explanation:
1. add the x-coordinates and then either divide by 2 or multiply by 1/2
2. add the y-coordinates and then either divide by 2 or multiply by 1/2
(-7+3)/2 = -2
(-10+9)/2 = -0.5
Have a blessed day!
WILL MAKE BRAINLIEST!!! Find the correct angle measure for angle b in each figure.
_1. 52°
_2. 27°
_3. 32°
_4. 98°
Answer:
98, 27
Step-by-step explanation:
In the first figure, the two angles are supplementary, meaning that their sum would equal 180 degrees, giving the equation: b+82 = 180 --> b=98
In the second figure, the two angles are complementary, meaning that they add up to 90 degrees, giving the equation: b+63 = 90 --> b=27
The standard deviation of the sampling distribution of the sample mean is also called?
The standard deviation of the sampling distribution of the sample mean is also called standard error of the mean.
For the given question,
Standard error is a mathematical tool used in statistics to measure variability. The standard error of the mean (SEM) measures how much discrepancy is likely in a sample's mean compared with the population mean.The SEM takes the SD and divides it by the square root of the sample size. The SEM will always be smaller than the SD.
The standard error of the mean indicates how different the population mean is likely to be from a sample mean. You can decrease the standard error by increasing the sample size.
Standard error of the mean and standard deviation are both measures of variability used to summarize sets of data. It helps you estimate how well your sample data represents the whole population by measuring the accuracy with which the sample data represents a population using standard deviation.
Hence we can conclude that the standard deviation of the sampling distribution of the sample mean is also called standard error of the mean.
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Mamadou drove 168 miles in 8 hours. If he continued at the same rate, how long
would it take to travel 126 miles?
With the given rate Mamadou will take 6 hours to travel 126 miles.
What is Unitary method ?In order to solve a problem for two different values of a quantity, its unit value is first derived. This method is known as unitary method.
Given that,
The distance travelled in 8 hours is 168 miles.
In order to calculate time for 126 miles, unitary method can be used as,
The time for 168 miles is 8 hours.
Then, the time for 1 mile is 8/168 hours.
Thus, the time for 126 mile is 8/168 × 126 = 6 hours.
Hence, the time taken by Mamadou to travel 126 miles is 6 hours.
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Each edge of a graph is colored with one of the four colors red, blue, yellow, or green. How could you represent the edges in this graph using a variation of the adjacency matrix structure
G is the matrix representation of the four colored graph.
According to the statement
we have given that a graph is colored with one of the four colors red, blue, yellow, or green.
And we have to represent the edges of this graph using a variation of the adjacency matrix structure
So, Adjacency Matrix Structure is a way of representing a graph as a matrix of booleans (0's and 1's). A finite graph can be represented in the form of a square matrix on a computer, where the boolean value of the matrix indicates if there is a direct path between two vertices.
And in this graph representation the Adjacency Matrix Structure denoted by a matrix G.
so, there are a four colors used that's why there are 4 into 4 matrix is formed to represent the edges.
G = [tex]\left[\begin{array}{cccc}1&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&1\end{array}\right][/tex]
And this is the matrix representation of the graph which is colored with four graphs.
So, G is the matrix representation of the four colored graph.
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8. For circle A, the circumference is 31.4 ft. What is the area? Use 3.14 for pi
314 ft²
15.7ft²
78.5 ft²
9.9 ft²
Answer:
[tex]\huge\boxed{\sf A = 78.5\ ft\²}[/tex]
Step-by-step explanation:
Circumference = C = 31.4 ft
We know that,
C = 2πrWhere, r is the radius
31.4 = 2(3.14)r
31.4 = 6.28(r)
Divide 6.28 to both sides
31.4/6.28 = r
5 ft. = r
r = 5 ft.Now,
Finding area:A = πr²
A = (3.14)(5)²
A = (3.14)(25)
A = 78.5 ft²[tex]\rule[225]{225}{2}[/tex]
At which angle is sin theta=1
Answer:
second option : π/2 or pi/2
Step-by-step explanation:
sinθ = 1 = 90
π = 180
π/2 = 90
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A music website claims the mean length of their songs is 3.75 minutes. Suppose the length of songs from this website follows a Normal distribution with standard deviation 0.5 minutes. If 7 songs from this website are randomly selected, then there is about a 90% probability that the sample mean will fall in which interval
The confidence interval is from 3.44 to 4.06 minutes.
According to the statement
we have given that the mean length of songs is 3.75 minutes and standard deviation 0.5 minutes and the sample size n is 7. and the confidence interval is 90%
and we have to find the mean interval.
So, We know that the
A confidence interval is defined as the range of values that we observe in our sample and for which we expect to find the value that accurately reflects the population.
And A margin of error is a statistical measurement that accounts for the difference between actual and projected results in a random survey sample.
We know that the z value for 90% confidence interval is 1.64.
so, The formula to calculate margin of error is
MOE = Z*standard deviation/ (n)^1/2
put the values in it
MOE = Z*standard deviation/ (n)^1/2
MOE = 1.64*0.5/ (7)^1/2
MOE = 1.64*0.189
MOE = 0.310
And to find the interval the formula is
Confidence interval = sample mean ± margin of error
Confidence interval = 3.75 ± 0.310
Confidence interval = (4.06,3.44)
So, The confidence interval is from 3.44 to 4.06 minutes.
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A helicopter is flying from Hong Kong to Jakarta. The latitude of Jakarta is -6.20°, and its longitude is 106.80°. The latitude of Hong Kong is 22.27°, and its longitude is 114.15°. What is the helicopter’s net change in latitude and longitude as it travels from Hong Kong to Jakarta?
The net Change in latitude and longitude of the helicopter are; 28.47 and 7.35 respectively.
What is the net Change in latitude and longitude of the helicopter?The net change in latitude of the helicopter can be evaluated as follows;
x = |-6.20° - 22.27°| = |-28.47°|
x = 28.47°
The net change in longitude of the helicopter can be evaluated similarly as follows;
y = |106.80° - 114.15°| = |-7.35°|
x= 7.35°
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Find the distance between the two points.
(-1,1)
(4,-3)
✓ [?]
Enter the number that
goes beneath the
radical symbol.
PLEASE HELP HURRY!!!!!
Jerry makes coffee tables to sell in a furniture shop. The length of each table is n+8 and the width is 1/2n - 4 inches. If n=42, what are the measurements of the length and width of each coffee table?
Answer:
Length= 50
Width=17
Step-by-step explanation:
length= n+8
Since n= 42, Just plug it in. So it would be 42+8 which is 50 for the length
Widith: 1/2n-4
basically since N is given for 42, you do 1/2 multipied by 42 which is 21.
Since you also have to subtract 4 inches it would be 17 for the length
The two dot plots below compare the forearm lengths of two groups of schoolchildren: Two dot plots are shown one below the other. The title for the top dot plot is Forearm Length, Group X and the title for the bottom plot is Forearm Length, Group Y. Below the line for each dot plot is written Length in inches. There are markings from 10 to 13 on each line at intervals of one. For the top line there are 4 dots above the first mark, 4 dots above the second mark, and 2 dots above the third mark. For the bottom line there are 2 dots above the second mark, 2 dots above the third mark, and 6 dots above the fourth mark. Based on the visual inspection of the dot plots, which group appears to have the longer average forearm length? Group X, because no child in the group has a forearm length longer than 12 inches. Group X, because four children in the group have the least forearm length of 10 inches. Group Y, because a child in the group has the least forearm length of 10 inches. Group Y, because six children have a forearm length longer than 12 inches.
The group that have the longer average forearm length is group Y, because six children have a forearm length longer than 12 inches.
Which group has a longer forearm length?
A dot plot is a graph that shows the frequency of a number using dots. The greater the number of dots above a number, the greater its frequency.
In group X, the highest arm length is 12 while in group Y, it is 13. This means that group Y would have longer arm lengths.
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what is the probability that random permutation of n numbers gets sorted after 1 pass of bubble sort
It means the probability of a random permutation of n numbers gets sorted after 1 pass of bubble sort is n!
According to the statement
we have to find the probability of random permutation of the N numbers.
So, according to the definition of A random permutation is a random ordering of a set of objects, that is, a permutation-valued random variable.
In this we order of select the objects randomly.
So, Let There are n−1 comparisons, so 2n−1 possible sequences of actions - swap or don't swap.
To find the permutations, start with 1,2,3,4,5 and undo a sequence.
For example, if let n=5, there are 24=16 out of 5!
which is 5! =120 that end after one round of bubble sort.
So, It means the probability of a random permutation of n numbers gets sorted after 1 pass of bubble sort is n!
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If you had worked on an externship in a prosecutor’s office, and then you moved to another state, which of these legal support positions would be best suited for?
Haven worked on an externship in a prosecutor’s office, the legal support position which you would be best suited for is: paralegal.
What is paralegal?Paralegal can be defined as a person who has been trained in subsidiary legal matters (issues), but not fully qualified to act as an attorney or lawyer.
In this context, we can infer and logically deduce that paralegal is a legal support position which you would be best suited for a person who has worked on an externship in a prosecutor’s office.
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Complete Question:
If you had worked on an externship in a prosecutor’s office, and then you moved to another state, which of these legal support positions would be best suited for?
mediator
paralegal
legal secretary
court reporter
Give the perimeter and the area of a square with sides that measure 9 cm.
Answer:
Perimeter = 36
Area = 81
Step-by-step explanation:
Perimeter of a square is side length * 4.
9*4 = 36
Area of a square is L*L,
9*9 = 81
if the coordinate of p and t are -6 and 4 respectively, what it the length of segment pt?
The length of the segment [tex]pt[/tex]is [tex]10[/tex] if the coordinates of [tex]p[/tex] and [tex]t[/tex] is [tex](-6 )and( 4)[/tex]
How can find the length of the segment ?
The coordinate of [tex]p=-6[/tex]
The coordinate of [tex]t=4[/tex]
We can assume only [tex]x[/tex] coordinates given and [tex]y[/tex] coordinates is [tex]0[/tex]
so coordinate of [tex]p=(-6,0)\\[/tex]
And coordinate of [tex]t=(4,0)[/tex]
So the length of the segment
[tex]pt=x_{2} -x_{1} \\pt=4-(-6)\\pt=4+6\\pt=10[/tex]
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URGENT ASAP Please answer the option b
The solution to the system of inequalities x < 2y + 3 and -2x < y + 1 is the darker region shown in the graph.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Inequality is an expression that shows the non equal comparison of two or more numbers and variables.
The solution to the system of inequalities x < 2y + 3 and -2x < y + 1 is the darker region shown in the graph.
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The system of inequalities x > 2 · y + 3 and - 2 · x < y + 1 includes the point (x, y) = (10, 0).
How to change signs of the inequalities to contain a given point.The solution area of the two inequalities given in the statement does not contain the point (x, y) = (10, 0) as we can see in the first figure.
But if we change the sign "<" for ">" in the first inequality, then the solution area includes the point mentioned above. Please see the second figure for further details.
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Does this graph show a function?
Answer:
I think that is is C
Step-by-step explanation:
The Vertical Line Test determines whether or not a curve on the graph is a function. This one passes the vertical line test because no vertical line can intersect the curve more than once. I hope that helps!
lines L, R, and S are coplanar. Suppose L is perpendicular to R and R is perpendicular to S. Is L perpendicular to S? Explain.
Answer:
No, L and S are parallel.
Step-by-step explanation:
Perpendicular lines go directly opposite from each other, making a + looking arrangement. While parallel lines go in the exact same direction, making a = looking arrangement. The only way both S and L can both be perpendicular to R is if they are both parallel to each other. An illustration by yours truly is placed below to represent it visually.
L |
_______________________________|_____
|
|
| R
|
_______________________________|_____
S |
|
Now, if this were on the outside of a sphere, then it would be totally possible to have three lines all be parallel, because they can curve with the sides of the sphere and create a triangle with all right angles.
Solve the equation algebraically. Calculus section 1.5 of textbook
2^x + 2^-x = 5
The value of x from the given expression is [tex]\frac{5+\sqrt{29}}{2log2} \\[/tex]
Solving quadratic expressionGiven the algebraic expression below;
2^x + 2^-x = 5
This can also be expressed as:
1/2^x+ 1/2^x = 5
Let P = 2^x, such that;
P + 1/P = 5
P²-1/P = 5
P²-1 = 5P
P²-5P-1=0
On factrorizing, then;
P = [tex]\frac{5+\sqrt{29}}{2} \\[/tex]
Since 2^x = P, then;
[tex]2^x=\frac{5+\sqrt{29}}{2} \\\\xlog2=\frac{5+\sqrt{29}}{2} \\\\x=\frac{5+\sqrt{29}}{2log2} \\[/tex]
Hence the value of x from the given expression is [tex]\frac{5+\sqrt{29}}{2log2} \\[/tex]
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The cost in collars, CCC, from an airplane flight given that the average cost of a first class seat is fff dollars and the average cost of an economy seat is eee dollars is given by the equation above if all seats are sold. What is the best interpretation of 88e88e88, e as shown in the above equation
88e interprets the total cost for all the economy class seats, as all seats are sold, where 88 is the number of economy class seats and e dollars is the cost of each economy class seat.
In the question, we are given an equation, C = 24f + 88e, and are informed that the cost, C, in dollars from an airplane flight given that the average cost of a first class seat is f dollars and the average cost of an economy seat is e dollars is given by the equation above if all seats are sold.
We are asked for the interpretation about the 88e as shown in the equation.
The equation given to us is a cost equation.
A cost equation comprises of two parts:
Per unit priceNumber of units.In the given equation, we have two types of quantities:
First class seatsEconomy seatsThus, both these quantities must be having a per unit price, multiplied by the number of units sold.
Now, we are informed that e dollars is the per unit price for an economy class seat.
Thus, 88e interprets the total cost for all the economy class seats, as all seats are sold, where 88 is the number of economy class seats and e dollars is the cost of each economy class seat.
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For complete question, refer to the attachment.
What is the missing reason in the proof?
Given: ∠ABC is a right angle, ∠DBC is a straight angle
Prove: ∠ABC ≅ ∠ABD
A horizontal line has points D, B, C. A line extends vertically from point B to point A. Angle A B C is a right angle.
definition of angle bisector
segment addition property
definition of congruent angles
transitive property
Mark this and return
We can identify that the missing reason in the proof is: Definition of Congruent angles.
How to give proof of a congruent triangle?We know that an angle measure of 90° of ∠ABC in the triangle means that it is a right angle triangle.
We also see that ∠ADB is also a right angle and is equal to 90°.
Now, since they have exactly the same measure, these angles are congruent. Then we can say that the angles are congruent and as such:
∠ABC ≅ ∠ABD
Thus, we can identify that the missing reason is: Definition of Congruent angles.
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