Problem 4. (10 points) Evaluate the line integral [(32³y + 4y) ds, where C is the portion of the circle x² + y² = 4 that joins the point A = (2,0) to the point B = (-√√2, √2) counterclockwise
Answers
The value of the line integral ∫C (32³y + 4y) ds, where C is the portion of the circle x² + y² = 4 that joins the point A = (2,0) to the point B = (-√√2, √2) counterclockwise, is 288.
To evaluate the line integral ∫C (32³y + 4y) ds, where C is the portion of the circle x² + y² = 4 that joins the point A = (2,0) to the point B = (-√√2, √2) counterclockwise, we need to parametrize the curve C and compute the integral along the parametrization.
The given circle has the equation x² + y² = 4, which represents a circle centered at the origin with radius 2. We can parametrize this circle by letting x = 2cos(t) and y = 2sin(t), where t ranges from 0 to π.
Parametrizing the line segment AB, we can let x = 2 - t√2 and y = t, where t ranges from 0 to √2.
Now, let's compute the line integral:
∫C (32³y + 4y) ds = ∫C [(32³y + 4y) √(dx² + dy²)]
For the circle portion, we have:
∫C (32³y + 4y) ds = ∫₀^π [(32³(2sin(t)) + 4(2sin(t))) √((-2sin(t))² + (2cos(t))²)] dt
Simplifying this integral, we have:
∫C (32³y + 4y) ds = ∫₀^π 64sin(t) + 8sin(t) dt = 144∫₀^π sin(t) dt
Using the properties of the definite integral and evaluating, we find:
∫C (32³y + 4y) ds = 144[-cos(t)]₀^π = 144[1 - (-1)] = 288
To learn more about integral click here
brainly.com/question/30094386
#SPJ11
Related Questions
hElP- please.
:) points!
Answers
Help me plz plz I’ll give brainlist just plz plz help plz !!!!!!
Answers
Answer: 2 and 10/21
Step-by-step explanation:
I JUST DID THE WORK.!!
Answer:
answer is 52 /21 or 2 10/21 ....
plz mark my answer as brainlist plzzzz
What is the quotient and remainder of 21÷6
Answers
Answer:
3 remainder 3
Step-by-step explanation:
Suppose we are interested in studying serum cholesterol values in undergraduate men, which has a mean of 190 and a standard deviation of 40 . If we take a random sample of 200 undergraduate men, what is the probability of getting a sample mean that is less than 182? 0.9977 0.0023 0.4207 0.0196
Answers
The probability of getting a sample mean less than 182 is 0.0023, or 0.23%. This can be calculated using the standard normal distribution.
The probability of obtaining a sample mean less than 182 from a random sample of 200 undergraduate men with a population mean of 190 and a standard deviation of 40 can be calculated using the standard normal distribution.
To calculate the probability, we need to standardize the sample mean using the formula for the standard error of the mean. The standard error of the mean (SE) is equal to the population standard deviation (σ) divided by the square root of the sample size (n).
SE = σ / \(\sqrt{(n)}\)
SE = 40 / \(\sqrt{(200)}\)
SE = 40 / 14.14
SE ≈ 2.83
Next, we calculate the z-score using the formula:
z = (x - μ) / SE
z = (182 - 190) / 2.83
z ≈ -2.83
Now, we can find the probability using the standard normal distribution table or a calculator. The probability of obtaining a z-score less than -2.83 is approximately 0.0023.
Therefore, the correct answer is 0.0023, which indicates that the probability of getting a sample mean less than 182 is 0.0023, or 0.23%.
Learn more about probability here:
https://brainly.com/question/32117953
#SPJ11
ill give u brainliest plz help :3 if u can ofc take ur time
Answers
Answer: 1. no
2. yes
3. no
4. if they are talking about the repeating number in -5/6, then yes the repeating number is 3.
5. no
I'm not 100% sure abt these answers but since nobody is answering so far here's my opinion :D I really don't want you to lose 100 points so pls b careful!!
layton's sales of the garner book totaled $300,000 for the last half of 20x6. in its 20x6 income statement, layton should report royalty expense of:
Answers
Answer:
Layton should report royalty expense of: $85,000.
Step-by-step explanation:
Under the cash basis of accounting, sales equals cash collections. Layton's sales of the Garner book totaled $300,000 for the last half of 20X6. In its 20X6 Income Statement.
12
The absolute value function, f(x) = x + 21, is shown.
3
Mark this and return
1-
--5-4-3-2-1₁- 1 2 3 4 5
-2-
-3-
H
If the graph is reflected over the x-axis, what is the
domain of the function?
TIME REMAINING
52:51
all real numbers
all real numbers greater than or equal to 0
O all real numbers greater than or equal to-2
all real numbers less than or equal to -2
Save and Exit
Next
Submit
Answers
To determine the domain of the function after reflecting the graph of f(x) = x + 21 over the x-axis, we need to consider the effect of the reflection on the original domain.
The original domain of the function f(x) = x + 21 is all real numbers since there are no restrictions or limitations on the values that x can take.
When we reflect a graph over the x-axis, the y-values of the points change their signs, while the x-values remain the same. In other words, for each point (x, y) on the original graph, the reflected point will have the coordinates (x, -y).
Since the original domain consists of all real numbers, reflecting the graph over the x-axis does not affect the x-values. Therefore, the reflected function will still have the same domain as the original function, which is all real numbers.
Thus, the correct answer is: "all real numbers" (OA).
The reflection over the x-axis only affects the range of the function by changing the sign of the y-values. In this case, the original range is also all real numbers, and after the reflection, it becomes all real numbers but with the opposite sign. However, the domain remains unchanged.
For more such questions on domain.
https://brainly.com/question/26098895
#SPJ8
To answer the question, consider the following numbers. 38 152 570 76 190 342 57 4788 57 19 285 171 Which of the above are divisible by 4?
Answers
Based on the given numbers, the number that is divisible by 4 are: 152, 76, and 4,788.
What numbers are divisible by 4?The numbers that are divisible by four need to meet certain requirements and the first one is that they should end in an even number.
The numbers divisible by 4 are:
= 152/4 = 38
= 76 / 4 = 19
= 4,788 / 4
= 1,197
This shows that these numbers are divisible by 4.
In conclusion, the numbers that are divisible by 4 are 152, 76, and 4,788.
Find out more on numbers divisible by 4 at https://brainly.com/question/207338
#SPJ1
Let us consider the following system of linear equations.
x+3y+2z=19x+3y+2z=19, 2x+y+z=132x+y+z=13 and
4x+2y+3z=314x+2y+3z=31.
[a] Write the above system in matrix form, �
Answers
The above matrix form of the given system of linear equations is called the Augmented Matrix form of the given system.
The given system of linear equations are as follows:x + 3y + 2z = 19 .......... (1)2x + y + z = 13 ........... (2)4x + 2y + 3z = 31 ....... (3)Now, we can write the above system of linear equations into the matrix form as follows : [x + 3y + 2z = 19] [2x + y + z = 13] [4x + 2y + 3z = 31]
On rearranging, the above matrix form can be written as follows
\(:$$\left[ \begin{matrix} 1 & 3 & 2 \\ 2 & 1 & 1 \\ 4 & 2 & 3 \end{matrix} \right] \left[ \begin{matrix} x \\ y \\ z \end{matrix} \right] = \left[ \begin{matrix} 19 \\ 13 \\ 31 \end{matrix} \right]$$\)
The above matrix form of the given system of linear equations is called the Augmented Matrix form of the given system.
we can write the above system of linear equations into the matrix form as follows : [x + 3y + 2z = 19] [2x + y + z = 13] [4x + 2y + 3z = 31] On rearranging, the above matrix form can be written as follows
\(:$$\left[ \begin{matrix} 1 & 3 & 2 \\ 2 & 1 & 1 \\ 4 & 2 & 3 \end{matrix} \right] \left[ \begin{matrix} x \\ y \\ z \end{matrix} \right] = \left[ \begin{matrix} 19 \\ 13 \\ 31 \end{matrix} \right]$$\)
To know more about matrix visit:-
https://brainly.com/question/29132693
3SPJ11
write 10 rational numbers between -1/3 and 1/3
Answers
Step-by-step explanation:
-1/4, -1/5, -1/6, -1/7, -1/8, 1/8, 1/7, 1/6, 1/5, 1/4
Felicia ran a 4-mile race in 28 minutes. Complete the table to represent Felicia’s average rate of speed during the race.
Answers
Answer:
she runs an average 1mile every 7 minutes
Step-by-step explanation:
sorry if this does not help if this is not what u r looking for maybe clarify
hope this helps also i don't see where the chart is for the question
According to a weather report, there is a 28% chance it will rain tomorrow. What is the
probability that it WILL NOT rain tomorrow? (two decimal answer approximation)
Answers
Answer:
wouldnt it be 72%?
Step-by-step explanation:
the percent is out of 100. if the probability of rain is 28% and you subtract that from 100% you are left with 72%
100%-28%
=72%
sketch the vector field f by drawing a diagram like this figure. f(x, y) = yi − xj x2 + y2
Answers
The length vector is 1. So the sketch vector field f is given below. So the option a is correct.
In the given question, the vector field F by drawing a diagram like this figure.
The given vector field F is:
F(x, y) = (yi + xj)/√(x^2 + y^2)
We can write the vector field as:
F(x, y) = yi/√(x^2 + y^2) + xj/√(x^2 + y^2)
Here
F(x, y) = [y/√(x^2 + y^2)]^2 + [x/√(x^2 + y^2)]^2
F(x, y) = y^2/(x^2 + y^2) + x^2/(x^2 + y^2)
F(x, y) = (y^2+ x^2)/(x^2 + y^2)
F(x, y) = 1
F(0, y) = y/|y| = ±1
F(x, 0) = x/|x| = ±1
So the length vector is 1.
So the sketch vector field f is given below:
To learn more about vector field link is here
brainly.com/question/24332269
#SPJ4
The complete question is:
Sketch the vector field F by drawing a diagram like this figure.
F(x, y) = (yi + xj)/√(x^2 + y^2)
I need help with the sample standard deviation and the sample variance
Answers
ANSWER:
The sample standard deviation is 29.3
The sample variance is 859.2
STEP-BY-STEP EXPLANATION:
We have the following data set:
\(77,\:68,\:32,\:26,\:47,\:6,\:34,\:99,\:27,\:15,\:72\)To determine the sample standard deviation and the sample variance we must first calculate the mean of the data, like so:
\(\begin{gathered} \bar{x}=\frac{1}{n}\sum_{i=1}^na_i\: \\ \\ n=11 \\ \\ \sum_{i=1}^na_i=77+68+32+26+47+6+34+99+27+15+72=503 \\ \\ \bar{x}=\frac{1}{11}(503) \\ \\ \bar{x}=45.7 \end{gathered}\)Now we proceed to calculate the sample standard deviation and the sample variance:
Select the equivalent expression.
(3^4 / 7^3)^3 =?
Answers
The equivalent expression is (3⁴/7³)³ = 3¹²/7⁹
Define Power Rule for Exponents
The Power Rule for Exponents: (aⁿ)ˣ= aⁿ*ˣ .
To raise a number with an exponent to a power, multiply the exponent times the power.
Negative Exponent Rule: x⁻ⁿ = 1/xⁿ.
Given expression is,
(3⁴/7³)³
We need to find equivalent expression,
⇒ (3⁴/7³)³
first, split up exponent 3 to both Numerator and denominator as ,
⇒ (3⁴)³ / (7³)³
Now, power of a power can be done as product as,
⇒ 3¹² / 7⁹
Hence,the equivalent expression is (3⁴/7³)³ = 3¹²/7⁹
To read more about Exponents.
https://brainly.com/question/11975096
#SPJ1
If point C is not located between points A and B then AC+CB__ AB
Answers
Answer:
\(\neq\)
Step-by-step explanation:
If Point C was located between A & B, then:
\(AC+CB=AB\)
However, we are told Point C is not; therefore:
\(AC+AB\neq AB\)
b+2/2≤–1
please help me, and give me A C T U A L answers
Answers
Answer:
i need more info to help
Step-by-step explanation:
If x and b are the roots of ax^2 - bx + c then calculate x + b
Answers
Answer:
Step-by-step explanation:
10) Mr. Stowe wants to bulld a doll house for his daughter that is proportional to their actual house.
The iving room in their house has a with of 16 feet and dr lenati or 20 reet: What will be the width and length of the living room in the doll house in feet if he uses a scale factor of 1/8
Answers
Step-by-step explanation:
To find the dimensions of the living room in the dollhouse, we need to scale down the dimensions of the actual living room by a factor of 1/8.
Width of living room in dollhouse = (Width of living room in actual house) x (scale factor)
= 16 feet x (1/8) = 2 feet
Length of living room in dollhouse = (Length of living room in actual house) x (scale factor)
= 20 feet x (1/8) = 2.5 feet
Therefore, the width of the living room in the dollhouse will be 2 feet and the length will be 2.5 feet.
Please help me with this
Answers
B R= 6
Can I get a Brainly
A boat can travel 2 000 km in one-half day. How many kilometers can it travel in 30 h?
PLS I NEED HELP
Answers
The distance (in Km) the boat can travel in 30 h is 5000 km
Determination of the speed of the boat
From the question given above, the following data were obtained:
Distance = 2000 kmTime = one-half day = ½ × 24 = 12 hSpeed =?Speed = distance / time
Speed = 2000 / 12
Speed = 166.67 km/h
How to determine the distance travelled in 30 hSpeed = 166.67 km/hTime = 30 hDistance =?Speed = distance / time
166.67 = distance / 30
Cross multiply
Distance = 166.67 × 30
Distance ≈ 5000 km
Learn more about speed:
https://brainly.com/question/680492
SOMEBODY PLEASE HELP ! I WILL GIVE BRAINLIEST TO THE CORRECT ANSWER
Answers
Answer:
3n-7=2n+5
Step-by-step explanation:
The equation is : 3n-7=2n+5
3n-2n=12
n=12
Hope I helped!
solve 3 please be fast
Answers
Answer:
3
Step-by-step explanation:
all you have to do is solve it:)
hope this helps have a great day lol :)
What is the quotient of (x^2+6x+8)÷(x+4)x + 4
x + 2
5x + 2
5x + 4
Answers
solve quadratic equation 3x^2+2x-4=0
Answers
Answer:
x1=\(\frac{-1-13}{3}\), x2=\(\frac{-1+13}{3}\)
Step-by-step explanation:
Sabrina is tracking the growth rates of a colony of ants and of a bee hive. From her research, she has developed a function to represent the population growth of each type of insect, where y represents the population and x represents the number of weeks since Sabrina began her research.What is this function written in vertex form?
Answers
Answer:
A
Step-by-step explanation:
i think
The function that represent the growth rate of the population where y represents the population and x represents the numbers of weeks since Sabrina began her research is \(y=3.8^{x}\) (for ant colony) \(y=3.8x\) (for bee hive growth)
What is function?"A function is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable)."
What is research?"Research is creative and systematic work undertaken to increase the stock of knowledge."
What is growth rate?"The growth rate of change of population size, for a given country, territory, or geographic area, during a specified period."
As we know that we have to check the growth of the population. According to the given data, the rate of growth for ant colony is \(y=3.8^{x}\) and also the growth rate of bee hive is \(y=3.8x\)
Hence, the growth rate of ant colony is \(y=3.8^{x}\) and the growth rate of bee hive is \(y=3.8x\)
To know more about growth rate of population here
https://brainly.com/question/15133607
#SPJ2
Please help!
How are 3(3x+5) and -9x-15 equivalent to 9x+15?
Answers
How many elementary events are in the sample space of the experiment of rolling three fair coins? 2 9 8 6
Answers
When we roll three fair coins, there are two possible outcomes for each coin - either it lands heads up or tails up. There are 8 elementary events in the sample space of the experiment of rolling three fair coins.
The sample space of this experiment consists of all possible combinations of three outcomes, which can be calculated by multiplying the number of outcomes for each coin: 2 x 2 x 2 = 8.
Each of these combinations is called an elementary event, which means that there are 8 elementary events in the sample space of the experiment of rolling three fair coins. We can list them as follows:
1. HHH (all three coins land heads up)
2. HHT (two coins land heads up, one lands tails up)
3. HTH (two coins land heads up, one lands tails up)
4. THH (two coins land heads up, one lands tails up)
5. HTT (one coin lands heads up, two land tails up)
6. THT (one coin lands heads up, two land tails up)
7. TTH (one coin lands heads up, two land tails up)
8. TTT (all three coins land tails up)
To learn more about possible outcomes, refer:-
https://brainly.com/question/27292589
#SPJ11
4. The branch of mathematics that analyzes situations in which players must make decisions andthen receive payoffs most often used by economists isA. oligopoly collusion.B. prisoner's dilemma.C. game theory.D. collusion theory
Answers
The branch of mathematics that analyzes situations in which players must make decisions and then receive payoffs most often used by economists is "game theory". So, option C is the correct answeer.
Game theory is a branch of mathematics that studies how people or organizations interact in situations where there are choices to be made and where the outcome of each choice depends on the choices made by others. It is often used in economics to model the behavior of firms and consumers in markets, and to analyze strategic interactions between competitors in oligopolistic industries.
One of the most famous examples of game theory is the prisoner's dilemma, which is a simple model that illustrates how two individuals might not cooperate, even if it appears that it is in their best interest to do so.
Learn more about game theory :
https://brainly.com/question/29217169
#SPJ4
Sketch the region bounded by the curves x=3y3,x=3, and y=0 then find the volume of the solid generated by revolving this region about the y-axis.
a) 82π7
b) 68π7
c) 54π7
d) 61π7
e) 75π7
Answers
Thus, the volume of solid generated by revolving this region about the y-axis is given as: 54π/7. The correct option is c.
To sketch the region, we first plot the curves on the coordinate plane.
The curve x=3y^3 is a parabola that opens to the right and passes through the origin. The curve x=3 is a vertical line that intersects the parabola at y=∛(1/3).
The curve y=0 is just the x-axis.
Now, to find the volume of the solid generated by revolving this region about the y-axis, we use the method of cylindrical shells.
We integrate from y=0 to y=∛(1/3) because those are the limits of integration for the region we are revolving.
The radius of each cylindrical shell is just the value of x at that y-coordinate, which is x=3y^3. The height of each cylindrical shell is the length of the curve, which is just 3 (the length of the vertical line).
Thus, the volume is given by:
V = ∫0^(∛(1/3)) 2π(3y^3)(3) dy
V = 54π/7
Therefore, the correct option is (c) 54π/7.
Know more about the parabola
https://brainly.com/question/64712
#SPJ11