let be the cube with side length 2, faces parallel to the coordinate planes, and centered at the origin. (a) calculate the total flux of the constant vector field out of by computing the flux through each face separately. flux through the face at : -5 flux through the face at : flux through the face at : flux through the face at : flux through the face at : flux through the face at : thus the total flux is flux
Answers
The total flux of the constant vector field out of by computing the flux through each face separately is 0.
S is the surface of a cube centered at the origin with a side length 2.
The surface S is oriented outwards with its face parallel to the coordinate plane.
Let S1 & S2 be the faces of the cube parallel to the xz- plane.
S3 & S4 be the faces of the cube parallel to the yz- plane.
S5 & S6 be the faces of the cube parallel to the xy- plane.
The parallel faces of the cube are oriented opposite in sense and since all the faces are parallel to one the coordinate plane, their unit normal are the same as the parallel coordinate plane.
j is the unit normal for the face S1 which is parallel to the xz- plane. Since S2 is oriented in the opposite direction, its unit normal is -j
S3 has a unit normal i and S4 has a unit normal -i
S5 has a unit normal k and S6 has a unit normal -k
Therefore, the flux integral is evaluated as:
\(\int\int\limit_s {v}. \, ndS = \int\int\limit_{s_1} {v}. \, ndS+\int\int\limit_{s_2} {v}. \, ndS+\int\int\limit_{s_3} {v}. \, ndS+\int\int\limit_{s_4} {v}. \, ndS+\int\int\limit_{s_5} {v}. \, ndS+\int\int\limit_{s_6} {v}. \, ndS\)\(= \int\int\limit_{s_1} (-3,1,5).jdS+\int\int\limit_{s_2} (-3,1,5).jdS+\int\int\limit_{s_3} (-3,1,5).idS+\int\int\limit_{s_4} (-3,1,5).idS+\int\int\limit_{s_5} (-3,1,5).kdS+\int\int\limit_{s_6} (-3,1,5).kdS\)\(=\int\int\limit_{s_1} 1dS+\int\int\limit_{s_2} -1dS+\int\int\limit_{s_3} -3dS+\int\int\limit_{s_4} 3dS+\int\int\limit_{s_5} 5dS+\int\int\limit_{s_6} -5dS\)
= [Area of S1 - Area of S2] + 3[Area of S4 - Area of S3] + 5[Area of S5 - Area of S6]
Therefore Total Flux = 0 ..... (all the faces have the same area)
Hence the answer is the total flux of the constant vector field out of by computing the flux through each face separately is 0.
To learn more about Flux click here https://brainly.com/question/10736183
#SPJ4
Related Questions
Convert the following: 2 liters is equivalent to ounces (rounded to the nearest hundredth)
Answers
Answer:
67.63 oz
Step-by-step explanation:
1 liter = 33.814 oz
2 litres = 2 x 33.814 oz = 67.628 oz
what is the remainder when 5x-3 is divided by x-4
Answers
Answer:
The answer is 4
answer mine
A company manufactures two types of cabinets, type 1 and type 2. It produces 110 total cabinets each week. Last week, the number of type 2 cabinets produced exceeded twice the number of type 1 cabinets produced by 20. If x is the number of type 1 cabinets produced and y is the number of type 2 cabinets produced, the system of equations that represents this situation is x + y = 110 and y = 2x + 20.
Answers
X for type 1 cabinets = 30
Y for type 2 cabinets = 80
And that proven that type 2 cabinets (Y) produced exceeded more than twice the number of type 1 cabinets (X)
As per the equations stated
X + Y = 110 ……….. (1)
Y = 2x + 20 …...... (2)
We substitute Y at equation (1) with equation (2), to find X
X + Y = 110
X + (2X + 20) = 110
3X + 20 = 110
3X = 110 – 20
3X = 90
X = 90 / 3
X = 30
Then, We substitute value X at equation (1 ) with the value that we have discovered before
X + Y = 110
30 + Y = 110
Y = 110 – 30
Y = 80
More about The equations here
https://brainly.com/question/29657983
#SPJ4
answer, please!!!!!!!
Answers
Answer:
C goes to the first one B second one A goes to third one D last one
Step-by-step explanation:
6. segments r4p and bp have the same length. if the coordinates of a and p are (-1, 0) and (4,l2), respectively, which could be the coordinates of b?
Answers
(9,24) and (-8,7) could be the coordinate of B. Hence, the option B is correct.
From the given question,
The segments AP and BP have the same length.
The coordinates of A=(-1, 0) and P=(4,l2).
We have to find the coordinates of B.
let the coordinate of B=(x,y)
So as given:
AP=BP
\(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}\)
Putting the values
\(\sqrt{(4-(-1))^2+(12-0)^2}=\sqrt{(x-4)^2+(y-12)^2}\)
Simplifying
\(\sqrt{(4+1)^2+(12)^2}=\sqrt{(x-4)^2+(y-12)^2}\)
\(\sqrt{(5)^2+(12)^2}=\sqrt{(x-4)^2+(y-12)^2}\)
\(\sqrt{25+144}=\sqrt{(x-4)^2+(y-12)^2}\)
\(\sqrt{169}=\sqrt{(x-4)^2+(y-12)^2}\)
Square on both side, we get
(x-4)^2+(y-12)^2=169
Now put (3/2,6)
(3/2-4)^2+(6-12)^2=169
{(3-8)/2}^2+(-6)^2=169
(-5/2)^2+36=169
6.25+36=169
42.25=169(false)
Now put (9,24)
(9-4)^2+(24-12)^2=169
(5)^2+(12)^2=169
25+144=169
169=169(True)
Now put (-8,7)
(-8-4)^2+(7-12)^2=169
(-12)^2+(-5)^2=169
144+25=169
169=169(True)
So, (9,24) and (-8,7) could be the coordinate of B.
Hence, the option B is correct.
To learn more about distance formula link is here
brainly.com/question/1633033
#SPJ4
The right question is:
Segments AP and BP have the same lengh. If the coordinates of A and P are (-1,0) and (4,12), respectively, which could be the coordinates of B ?
I. (3/2,6) II. (9,24) III. (-8,7)
(A) I and II only
(B) II and III only
(C) II only
(D) III only
i think its six but you know points for u
Answers
Answer:
6 makes the most sense
Step-by-step explanation:
UwU
You are correct
evaluate the line integral, where c is the given space curve. xeyz ds, c is the line segment from (0, 0, 0) to (3, 2, 4)
Answers
Evaluating the line integral, where c is the given space curve. xeyz ds, c is the line segment from (0, 0, 0) to (3, 2, 4) is; 30008.8
How to evaluate the Line Integral?We need the derivative of position vector to solve this integral. The first step will be to evaluate the value of the function F(x,y,z) in terms of the given parametric curve r(t) then multiply it with the magnitude of its derivative i.e. |r'(t)| and then integrate it with the given limits of t.
f(x, y, z) = xe^(yz)
Now the integral;. \(\int\limits^._c {f(x,y.z)} \, ds = \int\{f(rt)} \, * |r'(t)| dt\)
As C is line passing through (0,0,0) and (3,2,4) vector for parametrization is;⟨3 − 0, 2 − 0, 4 − 0⟩v = ⟨3, 2,4⟩
Parametrization is;x = 0 + 3t, y = 0 + 2t,z = 0 + 4t
Thus;r(t) = ⟨3t, 2t, 4t⟩taking the derivative r′(t) = ⟨3, 2 ,4⟩ |r'(t)| = √(9 + 4 + 16) |r'(t)| =√29f(r(t)) = 3te^(8t²)
Integrating with this formula . \(\int\limits^._c {f(x,y.z)} \, ds = \int\{f(rt)} \, * |r'(t)| dt\)
Using online derivative calculator gives us;
\(\int\limits^._c {f( xe^{yz})} \, ds
= 30008.8\)
Read more about Evaluating Line Integral at; https://brainly.com/question/13898754
#SPJ1
Evaluate the definite integral.
2 e 1/x5 x6 1 dx
Answers
The definite integral given is 2e1/x5 x6 dx.
To solve this integral, we need to use integration by parts. We will use u = 2e1/x5 and dv = x6 dx. Using integration by parts, we have:
∫ udv = uv - ∫vdu
Therefore, we have:
∫ 2e1/x5 x6 dx = 2e1/x5 x7/7 - (7/7) ∫e1/x5 dx
We can solve this last integral by using the substitution x5 = u. Doing so, we have:
∫ e1/x5 dx = (1/5) ∫ eudu
Using integration by parts, we have:
∫ eu du = eu u - ∫ ueu du
Therefore, we have:
∫ e1/x5 dx = (1/5) [eu u - ∫ ueu du] = (1/5) [eu u - u2 eu/2]
Substituting x5 = u, we have:
∫ e1/x5 dx = (1/5) [ex5 x5 - x10 ex5/2]
Finally, we can substitute this result into the original integral and get the answer:
∫ 2e1/x5 x6 dx = 2e1/x5 x7/7 - (7/7) [(1/5) [ex5 x5 - x10 ex5/2]]
To know more about definite integral refer here:
https://brainly.com/question/29974649
#SPJ11
Help plssssssssbssssssss
Answers
Answer:
i think its C or B im not really positive, sorry :(
Step-by-step explanation:
3^2x+1=9^2x-1 solve the equation
Answers
2 = 72x
X=36
6x+1 = 18x-1
-18x = -18x
-12x +1= -1
-12x -2
-2/-12= 1/6
x=1/6 or 0.16
In a regression study, a 95% confidence interval for β1 was given as: (-5.65, 2.61). What would a test for H0: β1=0 vs Ha: β1 ≠0 conclude? Select one:a. fail to reject the null hypothesis at null=0.05 and all larger nullb. reject the null hypothesis at null=0.05 and all smaller nullc. fail to reject the null hypothesis at null=0.05 and all smaller nulld. reject the null hypothesis at null=0.05 and all larger null
Answers
The correct answer is (a). fail to reject the null hypothesis at null= 0.05 and all larger null.
The null hypothesis (H0) in this case is that β1=0, meaning that there is no relationship between the independent and dependent variables in the regression study.
The alternative hypothesis (Ha) is that β1≠0, meaning that there is a relationship between the independent and dependent variables.
The 95% confidence interval for β1 is (-5.65, 2.61). This means that we are 95% confident that the true value of β1 falls within this range. Since the range includes 0, we cannot reject the null hypothesis that β1=0.
Therefore, we fail to reject the null hypothesis at a significance level of 0.05 (null=0.05) and all larger significance levels.
In other words, there is not enough evidence to suggest that there is a relationship between the independent and dependent variables in the regression study, so we cannot reject the null hypothesis.
Hence, fail to reject the null hypothesis at null=0.05 and all larger null is the correct answer, i.e., option (a)
To know more about the null hypothesis, refer here:
https://brainly.com/question/17018373#
#SPJ11
What is the slope-intercept equation for the line below?
(5, 4)
(0, 2)
Answers
Answer:
=
2/5x +2
Step-by-step explanation:
let me know if im wrong
hope it helps :)
Answer:
A. y=2/5x +2
step-by-step explanation:
hope this helped :-)
Helpppp pleaseee :]]
![Helpppp pleaseee :]]](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/V7kUT9z4dce5DROCSHFc0QEMIOmtZzCt.png)
Answers
the temperature at 7 am is what the -5 represents
PLEASE HELP WILL GIVE BRAINLY AND 5.0 RATING
Answers
Answer:
(2,-1)Step-by-step explanation:
(-5,-1)
+7 in the x-axis
(2,-1)
Answer:
(2, -1)
Step-by-step explanation:
Moving to the right means add to the x coordinate
(-5+7,-1)
(2, -1)
Solve the quadratic equation for the solutions.
f(x) = 2x^2 - 6x + 10
Answers
Suppose that we have two events, A and B, with P(A) = 0.50, P(B) = 0.60, and P(A ∩ B) = 0.45. If needed, round your answer to three decimal digits.
Find P(A | B)
Find P(B | A
Are A and B independent? Why or why not?
Answers
The probability of event A given event B, denoted as P(A | B), is 0.750. The probability of event B given event A, denoted as P(B | A), is 0.900. A and B are not independent events because the conditional probabilities P(A | B) and P(B | A) are not equal to the marginal probabilities P(A) and P(B), respectively.
To find P(A | B), we use the formula:
P(A | B) = P(A ∩ B) / P(B)
In this case, P(A ∩ B) = 0.45 and P(B) = 0.60.
Plugging these values into the formula, we get
P(A | B) = 0.45 / 0.60 = 0.750.
To find P(B | A), we use the formula:
P(B | A) = P(A ∩ B) / P(A)
Here, P(A ∩ B) = 0.45 and P(A) = 0.50.
Substituting the values, we find
P(B | A) = 0.45 / 0.50 = 0.900.
A and B are not independent because the probabilities of A and B are affected by each other. If A and B were independent, then P(A | B) would be equal to P(A), and P(B | A) would be equal to P(B). However, in this case, both P(A | B) and P(B | A) differ from their respective marginal probabilities. Therefore, A and B are dependent events.
To learn more about probability refer:
https://brainly.com/question/25839839
#SPJ11
Need help ASAP!! Convert this rational number
to its decimal form and round
to the nearest thousandth.
Answers
Answer:
0.167
Step-by-step explanation:
Converting it to decimal form would be :0.16666667
Rounding it to the nearest thousands would be the 3rd decimal place. Round it up to be 0.167
A medical test has a 95% accuracy of detecting a Condition Z if the person has it. It also has a 97% chance to indicate that the person does not have the condition if they really don't have it. If the incidence rate of this disease is 10 out of every 100: What is the probability that a person chosen at random will both test positive and actually have the disease (i.e., get a true positive)
Answers
Answer:
0.77
Step-by-step explanation:
According to the Question,
Let, We have 10000 patients & If the incidence rate is 10 out of 100, then 1000 people will have the disease.
Given, A medical test has a 95% accuracy of detecting Condition Z if the person has it. Thus, Out of those 1000, 950 will test positive.And, It also has a 97% chance to indicate that the person does not have the condition if they really don't have itSo, Out of the 9000 people who don't have the disease, 3%
that is, 270 People, will get a false positive.
Thus, the probability that a person is chosen at random will both test positive and actually have the disease is \(\frac{950}{950+270}\) .
\(\frac{950}{1220}\) ⇒ 0.7786 ≈ 0.77is the square root of 224 a rational or irrational number
Answers
Answer:
It is irrational
Step-by-step explanation:
It is not a perfect square
The diagram Shows a square of side 8 cm and four congruent triangles of height Calculate the areanof one triangle.
Answers
The area of one triangle is 28 cm².
From the question, we have
area = 1/2*base*height
= 1/2*8*7
=28 cm².
Multiplication:
In mathematics, multiplying the numbers is used to find the product of two or more numbers. We carry out one of the basic mathematical operations on a regular basis. The main application that is obvious is using multiplication tables. Mathematicians use the multiplication of two integers to express the repeated addition of one number to another. These numbers can be natural numbers, fractions, integers, whole numbers, etc. M is either added to itself 'n' times or subtracted from itself when m is multiplied by n.
To learn more about multiplication visit: https://brainly.com/question/5992872
#SPJ9
Enter the correct answer in the box. the function f(x) = 7x 1 is transformed to function g through a horizontal compression by a factor of . what is the equation of function g? substitute a numerical value for k into the function equation.
Answers
The equation for function g is given by using translational ideas:
g(x) = 7x/3 + 1.
What does translation mean?According to operations like multiplication or sum/subtraction either in its definition or in its domain, a translation is represented by a change in the function graph. Examples include shifting to the left or right or up or down, compressing or stretching vertically or horizontally, and reflecting over the x- or y-axis.
Given that f(x) exists, obtaining f is equal to compressing horizontally by a factor of a. (ax).
The function in this issue is as follows:
f(x) = 7x + 1.
We have the following for a horizontal compression of 1/3:
g(x) = f(1/3x) = 7x/3 + 1.
To know more about translation visit:
https://brainly.com/question/28159610
#SPJ4
In the diagram above, ∠1=135° . Find the measure of ∠2.
Answers
Answer:
Angle 2 = 45 degrees
Step-by-step explanation:
Angle 1 = Angle D because they are alternate interior angles.
Angle 3 = Angle A because they are alternate exterior angles.
Angle 1 = 135 degrees
Therefore, Angle D = 135 degrees
180 - Angle D = Angle 2
Angle 2 = 180 - 135
Angle 2 = 45 degrees
10. Find the slope of the line.
Answers
Answer: y = 1.75x - 1
Step-by-step explanation: The slope of the line is 1.75
can someone help me with this?
Answers
Answer:
12.1 cm
Step-by-step explanation:
A woman rides her bike 16 miles with the wind in the same time she travels 10 miles against the wind. If the speed of the wind is 3 mph, find the speed of the cyclist in still air.
Answers
The speed of the cyclist in still air is 13 mph
How to find the speed of the cyclist in still airLet the speed of the cyclist in still air be x mph
when she rides with the wind her speed = (x + 3) mph
when she rides against the wind her speed = (x - 3) mph.
Mathematically we can represent the problem as:
16 / (x + 3) = 10 / (x - 3)
cross multiplying and simplifying
16 (x - 3) = 10 (x + 3)
16x - 48 = 10x + 30
6x = 78
x = 13
Learn more about speed of the wind at
https://brainly.com/question/29801913
#SPJ1
Mr. Smith has an online cooking show. Before he films an episode about baking the perfect pound cake, he prepares his ingredients. His recipe calls for 2 1/2 cups of sugar for the cake and 1 1/4 cups of sugar for the vanilla glaze. How many 1/4 cup scoops of sugar does he need?
Answers
Help Exit This Box-and-Whisker Plot displays the distribution of scores of a recent physics test. What is the median number of this set of physics test scores? Physics Test Scores
Answers
Answer: A) 87
The median value is the second quartile (Q₂), which is 87.
Answer:
A: 87
Step-by-step explanation:
Sorry for this very late response. But if anyone is not sure if answer A is correct, it is. I can confirm this because I just took the test. I hope I could help! (:
Need help with this three questions, i will post the other one’s please help me !
Answers
Answer:
5 is the leading coefficient.
find the radius if the circumference is 32 inches
Answers
Answer:
5.1 inches------------------
Use circumference formula:
C = 2πrFind the radius by rearranging the formula and substituting 32 for C:
r = C/(2π)r = 32/(2*3.14)r = 5.10 inches (rounded)Answer:
5.09 in
Step-by-step explanation:
We know that the formula to find the circumference of a circle is:
C = 2πr
Here,
C → Circumference → 32 in
r → radius
Let us find the radius of the circle by substituting the given values.
\(\sf C = 2\pi r\\\\\sf 32 = 2\pi r\\\\Divide\:both\:sides\:by\:2 \pi \:and\:make\:r\:the \:subject\\\\\dfrac{32}{2 \pi} =\dfrac{2 \pi r}{2 \pi} \\\\\red{5.09 \:in=r}\)
A doctor is using a treadmill to assess the strenght of a patient's heart. He sets the 48-inch long treadmil at an incline of 10⁰,how high is the end of the treadmill raised
Answers
The end of the 48-inch long treadmill is raised approximately 8.36 inches.
The incline of the treadmill is given as 10 degrees.
We can use trigonometry to calculate the height of the end of the treadmill.
The height (h) can be found using the formula h = l * sin(θ), where l is the length of the treadmill and θ is the angle of inclination.
Substitute the values into the formula:
h = 48 inches * sin(10 degrees)
Calculate the sine of 10 degrees using a calculator:
sin(10 degrees) ≈ 0.1736
Multiply the length of the treadmill by the sine of the angle:
h = 48 inches * 0.1736 ≈ 8.36 inches
The end of the 48-inch long treadmill is raised approximately 8.36 inches when set at an incline of 10 degrees.
To know more about angle of inclination, visit
https://brainly.com/question/31329503
#SPJ11