Evaluate the surface integral.
S(x + y + z) dS, S is the parallelogram with parametric equations
x = u + v, y = u − v, z = 1 + 2u + v, 0 ≤ u ≤ 7, 0 ≤ v ≤ 3.
Answers
Answer:
[tex]\frac{115\sqrt{14} }{2}[/tex]
Step-by-step explanation:
∫∫ ( x + y + z ) ds
where :
x = u + v , y = u - v , z = 1 + 2u + v ,
0 ≤ u ≤ 5,
0 ≤ v ≤ 1
R ( u,v ) = < u+v , u-v , 1 + 2u +v > next we have to differentiate
attached below is a detailed solution
The surface integral S(x + y + z) dS, where S is the parallelogram is [tex]115\sqrt{14} /2[/tex] and this can be determined by integrating the given expression.
Given :
The surface integra S(x + y + z) dS, S is the parallelogram with parametric equations x = u + v, y = u − v, z = 1 + 2u + v, 0 ≤ u ≤ 7, 0 ≤ v ≤ 3.
The following calculation can be used in order to determine the surface integral.
[tex]\rm R_u\times R_v = <3,1,-2>[/tex]
[tex]\rm ||R_u\times R_v|| = \sqrt{14}[/tex]
Now, evaluate the surface integral.
[tex]\rm I = \rm \int\int_s(x+y+z)dr[/tex]
[tex]\rm I = \int^5_{u=0}\int^1_{v=0}(u+v+u-v+1+2u+v)||R_u\times R_v||dA[/tex]
[tex]\rm I = \int^5_{u=0}\int^1_{v=0}(u+v+u-v+1+2u+v)\sqrt{14} \;du\;dv[/tex]
[tex]\rm I = \sqrt{14} \int^5_0(v+4uv+\dfrac{v^2}{2})^1_0\;du[/tex]
[tex]\rm I = \sqrt{14} (\frac{3}{2}u+4\frac{u^2}{2})^5_0[/tex]
Simplify the above expression.
[tex]\rm I = \dfrac{115\sqrt{14} }{2}[/tex]
The surface integral S(x + y + z) dS, where S is the parallelogram is [tex]115\sqrt{14} /2[/tex]
For more information, refer to the link given below:
https://brainly.com/question/22008756
Related Questions
Which three lengths could be the lengths of the sides of a triangle?
A. 6 cm, 23 cm, 11 cm
B. 10cm, 15cm, 24cm
C. 22 cm, 6 cm, 6 cm
D. 15 cm, 9 cm, 24 cm
Answers
Answer:
D. 15 cm, 9 cm, 24 cm
Step-by-step explanation:
The three lengths that could be the lengths of the sides of a triangle, must satisfy the following condition;
---sum of any two smaller sides chosen must be equal to the third side.
Test option A : 6 cm + 11 cm = 17 cm ( 17 cm ≠ 23 cm)
Test option B: 10 cm + 15 cm = 25 cm (25 cm ≠ 24 cm)
Test option C: 6 cm + 6 cm = 12 cm (12 cm ≠ 22 cm)
Test option D: 15 cm + 9 cm = 24 cm (24 cm = 24 cm) ---correct option.
Thus, the three lengths that could be the lengths of the sides of a triangle are 15 cm, 9 cm, and 24 cm
Luisa's restaurant bill comes to $85.50, and she leaves a 18% tip. What is Luisa's total
restaurant bill?
Answers
Answer:
85.50+15.39=100.89 dollars
Step-by-step explanation:
First, you calculate the tip cost, which is 15.39. Then you add that to the bill which gives you your total :D
Simplify 5 (3 1/5 +2 4/5−0.6)
Answers
Step-by-step explanation:
l dont understand your question
is it 3 and a fifth or 31/5
What is an equation of the line that passes through the point (6,3) and is parallel to
the line x + 3y = 24?
Answers
Answer:
x + 3 y = 15
Step-by-step explanation:
line is paralle that means that coefficient next to x mand y must be the same
so the equation of the line will be
x + 3y = a
we have to find a, we know that line passes throgh (6,3) so
6 + 3 * 3 = a
a = 15
the line has an equation
x + 3 y = 15
Profit is the amount of money that remains after all expenses of a project have been paid. The year has just ended, and Ajax Construction's owner is anxious to find out if the company had a profitable year. The company was awarded five contracts totaling $7,435,000. The costs associated with each project were: Project 1: $1,245,000 Project 2: $985,689 Project 3: $1,723,000 Project 4: $2,567,054 Project 5: $633,768 How much profit did the company earn?
Answers
Answer:
the Profit earned by the company is $280,489
Step-by-step explanation:
Total Cost of 5 projects awarded = $7,435,000
Cost of Project 1 = $1,245,000
Cost of Project 2 = $985,689
Cost of Project 3 = $1,723,000
Cost of Project 4 = $2,567,054
Cost of Project 5 = $633,768
We need to find the profit earned by the company.
First we need to find Total cost spent on all 5 projects.
It can be found by adding cost spent on all projects.
Total cost spent on all 5 projects = Cost of Project 1 + Cost of Project 2 + Cost of Project 3 + Cost of Project 4 + Cost of Project 5
Total cost spent on all 5 projects = $1,245,000+ $985,689 + $1,723,000+ $2,567,054 + $633,768
Total cost spent on all 5 projects = $7,154,511
Now we can calculate profit earned using formula:
Profit earned = Total Cost of 5 projects awarded - Total cost spent on all 5 projects
Profit earned = $7,435,000 - $7,154,511
Profit earned = $1,280,489
So, the Profit earned by the company is $280,489
If Mrs. Kliesch’s advanced class is 40% boys, and there are 12 boys, how many students are in her class?
Answers
Answer:
30 students
Step-by-step explanation:
40% boys and 12 boys so 60% is girls
40/100=12/x
x=30
30-12 is 18
so 30 students, 12 boys, and 18 girls.
Need help ASAP!!!The measures of angles of a triangle are shown in the figure below.Solve for x
Answers
Answer:
54
Step-by-step explanation:
90 + 36 = 126
180-126= 54
What is 25% increase of 12
Answers
Answer:
15 or 3
Step-by-step explanation:
multiply 12 by .25 and you will get 3. that is 25% of 12. add 3 you will get 15.
I didn't know if you wanted to know how much it increased or final answer.
The square below represents one whole. Express the shaded area as a fraction, a decimal, and a percent of the whole. Fraction: Decimal: Percent: %
Answers
Answer:
Fraction = [tex]\frac{19}{50}[/tex]
Decimal = 0.38
Percent = 38%
Step-by-step explanation:
Number of shaded rectangles = 38
Total number of rectangles = 100
Fraction represented by the shaded area = [tex]\frac{\text{Number of blocks shaded}}{\text{Total number of blocks}}[/tex]
= [tex]\frac{38}{100}[/tex]
= [tex]\frac{19\times 2}{50\times 2}[/tex]
= [tex]\frac{19}{50}[/tex]
Decimal form of the shaded area = [tex]\frac{38}{100}[/tex] = 0.38
Percent of the shaded area = [tex]\frac{38}{100}[/tex] = 38%
Answer:
Fraction =
Decimal = 0.38
Percent = 38%
Step-by-step explanation:
Number of shaded rectangles = 38
Total number of rectangles = 100
Fraction represented by the shaded area =
=
=
=
The decimal form of the shaded area = = 0.38
Percent of the shaded area = = 38%
There are 60 dogs at a doggie daycare one Friday. If 13 of the dogs are large dogs, 16 of the dogs are medium-sized dogs, and the remaining dogs are small dogs, which statement is true?
A. There are 10 less large dogs than small dogs at the daycare.
B. There are 10 more large dogs than small dogs at the daycare.
C. There are 20 less large dogs than small dogs at the daycare
D. There are 20 more large dogs than small dogs at the daycare.
Answers
Answer:
D there are 20 more large dogs than small dog at the daycare
Answer: The answer is that the small dog amount is 73 so
60 medium sized dogs and 13 big dogs and 73 small dog
in total they are 146.
The U.S. Department of Agriculture claims that the mean consumption of coffee by a person in the United States is 24.2 gallons per year. A random sample of 101 people in the United States shows that the mean coffee consumption is 23.5 gallons per year with a standard deviation of 3.2 gallons. At α=0.05, can you reject the claim? Using a P-value, evaluate the claim. Using Rejection Regions for a z-test, evaluate the claim.
Answers
Answer:
The decision rule is
Reject the null hypothesis
The conclusion is
There is sufficient evidence to reject the claim
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 24.2 \ gallons \ per \ year[/tex]
The sample size is n = 101
The sample mean is [tex]\= x = 23.5 \ gallons\ per\ year[/tex]
The standard deviation is [tex]\sigma = 3.2 \ gallons[/tex]
The null hypothesis is [tex]H_o : \mu = 24.2[/tex]
The alternative hypothesis is [tex]H_a : \mu \ne 24.2[/tex]
Generally the test statistics is mathematically represented as
[tex]z = \frac{ \= x - \mu }{ \frac{\sigma }{ \sqrt{n} } }[/tex]
=> [tex]z = \frac{ 23.5 - 24.2 }{ \frac{ 3.2}{ \sqrt{ 101} } }[/tex]
=> [tex]z = -2.198[/tex]
From the z table the area under the normal curve to the left corresponding to -2.198 is
[tex]P(Z < -2.198 ) = 0.013975[/tex]
Gnerally the p-value is mathematically represented as
[tex]p-value = 0.013975 * 2[/tex]
=> [tex]p-value = 0.02795[/tex]
From the value obtained we have that [tex]p-value \ < \ \alpha[/tex] hence
The decision rule is
Reject the null hypothesis
The conclusion is
There is sufficient evidence to reject the claim
Using the Rejection Regions for a z-test method
Generally from the z table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]z_{critical} = \pm 1.96[/tex]
Not we are using [tex]\frac{\alpha }{2}[/tex] because it is a two - tailed test
Now comparing the critical value and the test statistics we see that the
region covered by the test statistics (i.e [tex]2.198 < z < -2.198[/tex]) is greater than the region covered by the critical value (i.e [tex]1.96 < z < -1.96[/tex])
Hence
The decision rule is
Reject the null hypothesis
The conclusion is
There is sufficient evidence to reject the claim
Dan earns £9.90 per hour. How much will he earn for 4 hours work?
Answers
Answer:
39.60
Step-by-step explanation:
9.90 x 4 = 39.60
And you need to know how much will he make for 4 hours ?
Answer: £9.90x4
Find the value of x 6x+2-2x=3x+14-x
Answers
Step-by-step explanation:
x will equal 6
hope this helps bro if u need the explanation I'll explain to u if needed
6x + 2 - 2x = 3x + 14 - x
6x - 2x + 2 = 3x - x + 14
4x + 2 = 2x + 14
4x - 2x = 14 - 2
2x = 12
x = 12/2
x = 6
Do y’all know the answer ?
Answers
Answer:
700
Step-by-step explanation:
Answer:
the answer is b
Step-by-step explanation:
because it 719,283 so you have to look at the 71 for this equation and sense the 1 is in higher then 5 it stays the same
hope that helps :)
Carl is the beneficiary of a $29,000 trust fund set up for him by his grandparents. Under the terms of the trust, he is to receive the money over a 7-year period in equal installments at the end of each year. If the fund earns interest at the rate of 4%/year compounded annually, what amount will he receive each year?
Answers
Answer:
$8,939.58
Step-by-step explanation:
Let x represent the amount to be received each year
==> x * Present value annuity factor (4%,7yrs) = $29,000
==> x * 3.240 = $29,000
==> x = $29,000/3.244
x = 8939.580764488286
x = $8,939.58
So, $8,939.58 is the amount he will receive each year.
If 3/4 = x/8 then x is equal to what
Answers
Answer:
x is 6
Step-by-step explanation:
3/4 * x/8
3*8=24 then,
divide by 4 which gives you 6.
Also if you simplify 6/8, it will give you 3/4.
Answer:
6 =x
Step-by-step explanation:
100,000,000 sheep are in a field the farmer says there are 36 acres for each sheep how many acres are there in the field
Answers
Answer:
3,600,000,000
Step-by-step explanation:
if i understood this correctly, you just multiply 100,000,000 by 36 and you're done
A cell phone is plugged in to be charged. The table shows the percent of battery power at some times
after it was plugged in.
Time
Percent charged
6:00 pm
2%
6:15 pm
10%
6:35 pm
21%
7:05 pm
38%
At what time will the battery be 100% charged? Use the data to find out and explain or show your
reasoning
Answers
Answer:7:45
Step-by-step explanation:
what is the equation of a line that has a slope of -5 and passes through the point (0,2) a)y= -5x b)y= -5x + 2 c)y = 2x - 5
Answers
Answer:
y=-5x+2
Step-by-step explanation:
desmos
also -5= the slope and 2 was the y intercept aka B you had all Pieces
"what is 3/8 divided by 6? give your answer as a fraction in the simplest form"
Answers
Step-by-step explanation:
[tex]{:}\hookrightarrow\sf \dfrac {3}{\dfrac {8}{6}}[/tex]
[tex]{:}\hookrightarrow\sf \dfrac {3}{8}\times \dfrac {1}{6}[/tex]
[tex]{:}\hookrightarrow\sf \dfrac {3}{8\times 6}[/tex]
[tex]{:}\hookrightarrow\sf \cancel {\dfrac {3}{48}}[/tex]
[tex]{:}\hookrightarrow\sf \dfrac {1}{16}[/tex]
-26=b-13
Plz answer I’m a month late on this test
Answers
Answer:
B = -13
Step-by-step explanation:
Add 13 to both sides
- 13 = b
rename the fraction 2/5 using tenths and hundredths
Answers
Answer:
20/50
Step-by-step explanation:
i think
you spin the spinner twice what is the probability of landing on a 6 and then landing on a number greater than 4
p(6,then>4)=
a)1/4
b)1/6
c)1/8
d)1/10
Answers
-8+12 divided by 2 + (-14)
Answers
Answer:
-16
Step-by-step explanation:
Answer:
the answer is negitive 12 or -12
What is 18 percent of 210?
Answers
Answer:
WN=37.8
Step-by-step explanation:
WN=18%*210
WN=0.18*210
WN=37.8
A soft drink filling machine, when in perfect adjustment, fills the bottles with 12 ounces of soft drink. Any overfilling or underfilling results in the shutdown and readjustment of the machine. To determine whether or not the machine is properly adjusted, the correct set of hypotheses is _____.
Answers
Answer:
[tex]\mathbf{H_o : \mu = 12} \\ \\ \\ \mathbf{H_a: \mu \ne 12}[/tex]
Step-by-step explanation:
Given that:
The population mean μ = 12
By computing the null and alternative hypotheses, the correct set of hypotheses for this test is:
[tex]\mathbf{H_o : \mu = 12} \\ \\ \\ \mathbf{H_a: \mu \ne 12}[/tex]
This is a two-tailed test.
What is the perimeter of the triangle?
unit
Answers
Answer:
36 unitsStep-by-step explanation:
perimeter of the given triangle = 16 + slant (10) + slant (10)
= 36 units
(see image below)
What is the product of(5)(3)
Answers
Answer:
15
Step-by-step explanation:
just cause
You earn 18n dollars. How much do you earn for mowing 3 lawns? 9 lawns?
Answers
Answer:
I am confused but my best guess would be you would earn 54$ for 3 lawns and 162 for 9
Step-by-step explanation:
You multiply 3 x 18 and 9 x 18
Im sorry if im wrong but i dont know what you were asking
Sam mows a ¼ of a lawn in ½ of an hour. At this rate, how long will it take him to finish one lawn?
Answers
Answer:
Two hours
Step-by-step explanation:
1/4 = 1/2
2/4 = 1
3/4 = 1 1/2
4/4 = 2