Evaluate iint S sqrt 1+x^ 2 +y^ 2 dS where S is the helicoid: r(u, v) = u * cos (v) * i + u * sin (v) * j + vk with 0 <= u <= 1, 0 <= v <= 2pi
Answers
Given the parameterization
[tex]\vec r(u,v) = u\cos(v) \, \vec\imath + u\sin(v) \,\vec\jmath + v \,\vec k[/tex]
take the normal vector to be
[tex]\vec n = \dfrac{\partial\vec r}{\partial u} \times \dfrac{\partial \vec r}{\partial v} = \sin(v) \,\vec\imath - \cos(v) \,\vec\jmath - u \,\vec k[/tex]
(The order of partial derivatives in the cross product doesn't matter since this a scalar line integral.)
Compute the magnitude of the normal vector.
[tex]\|\vec n\| = \sqrt{\sin^2(v) + (-\cos(v))^2 + (-u)^2} = \sqrt{1+u^2}[/tex]
so that the area element reduces to
[tex]dS = \|\vec n\| \, du\,du = \sqrt{1+u^2}\,du\,du[/tex]
Evaluate the integrand at [tex]\vec r[/tex] to get
[tex]\sqrt{1 + (u\cos(v))^2 + (u\sin(v))^2} = \sqrt{1 + u^2}[/tex]
The surface integral reduces to
[tex]\displaystyle \iint_S \sqrt{1+x^2+y^2} \, dS = \int_0^{2\pi} \int_0^1 (1+u^2) \, du \, dv = 2\pi \int_0^1 (1+u^2) \, du = \boxed{\frac{8\pi}3}[/tex]
Related Questions
Which interval describes where the graph of the function is positive?
Answers
Answer:
D is the correct answer.
Step-by-step explanation:
Find the portion of the graph that is above the x-axis.
Answer:
D
Step-by-step explanation:
Coming in from - inf the graph is positive and remains so until yo get to x = -1 <==== then it is zero and continues to negative values
Turkey sandwiches cost $2.50 and veggie wraps cost $3.50 at a snack stand. Ben has sold no more than $30 worth of turkey sandwiches and veggie wraps in the first hour of business. Let x represent the number of turkey sandwiches and y represent the number of veggie wraps. The inequality 2.50x+3.50y30 represents the food sales in the first hour.
If Ben has sold 4 veggie wraps, what is the maximum number of turkey sandwiches Ben could have sold?
Answers
The maximum number of turkey sandwiches Ben sold is 6.
What is the maximum number of turkey sandwiches Ben sold?Given this equation : 2.50x + 3.50y ≤ $30
If y is 4, take the following steps in order to determine the value of x:
Substitute for y in the above equation:
2.50x + (3.50 x 4) ≤ $30
2.50x + 14 ≤ $30
2.50x ≤ $30 - 14
2.50x ≤ $16
x ≤ 6.4
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Answer:
6
Step-by-step explanation:
f of x is equal to 4x divided by the quantity of x minus 16 end quantity.
Answers
The zero of the equation is 0. Since degree of denominator is greater than degree of numerator, therefore, the horizontal asymptote is y=0
Asymptotes and zeros of a functionThe zero of the function is the point where the function is zero
Given the function below
f(x) = 4x/x-16
For the zeros
0 = 4x/x -16
4x = 0
x = 0
Hence the zero of the equation is 0
The vertical asymptote is the point where the denominator is zero
x - 16 = 0
x = 16
Since degree of denominator is greater than degree of numerator, therefore, the horizontal asymptote is y=0
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helppp im stuck :(
Hope you guys help me
Answers
Answer:
[tex]y=-\dfrac{1}{2}x+2[/tex]
Step-by-step explanation:
Define two points on the line:
[tex]\textsf{let}\:(x_1,y_1)=(0,2)[/tex]
[tex]\textsf{let}\:(x_2,y_2)=(4,0)[/tex]
Use the slope formula and the defined points to find the slope:
[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{0-2}{4-0}=-\dfrac{1}{2}[/tex]
Substitute the found slope and one of the points into the point-slope form of a linear equation:
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-2=-\dfrac{1}{2}(x-0)[/tex]
Simplify:
[tex]\implies y-2=-\dfrac{1}{2}x[/tex]
[tex]\implies y=-\dfrac{1}{2}x+2[/tex]
IN THE GIVEN FIG, FIND THE VALUE OF x.
Answers
The answer is simple
First find the angle measures of first triangle:
statement:
we know that the sum of 45 and 30 sums up to the opposite angle and that is equal to 75, then to find the next remaining angle:
180-(75+20)=85
The you find the supplement of 85:
180-85=95
so x = 95
Hope it helps
1.9^4 × 10 × 2.9 x 10^1
Answers
3779.309 is the answer....
What is the solution to the equation below? Round your answer to two decimal places. 3e2x + 12 = 42
Answers
Answer:
X= 5.52
Step-by-step explanation:
1. Solve the equation:
e×2x + 12= 42
x=15/e
2. Round x=15/e to the required place
x=5.52
Answer:
X=1.15
Step-by-step explanation:
To purchase 13700 worth of restaurant equipment for her business Maria made a down payment of 1500 and took out a business loan for the rest after 3 years of paying monthly payments of 371.16 she finally paid off the loan
What was the total amount Maria ended up paying for the equipment
How much internet did Maria pay on the loan
Answers
The total amount Maria ended up paying for the equipment will be $14,861.76. And The interest of Maria on the loan will be 8.48%.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
To purchase 13700 worth of restaurant equipment for her business.
Maria made a down payment of 1500 and took out a business loan for the rest, after 3 years of paying monthly payments of 371.16 she finally paid off the loan.
The total amount Maria ended up paying for the equipment will be
Total amount = 371.16 × 3 × 12 + 1500
Total amount = $14,861.76
The interest of Maria on the loan will be
Interset = [(14861.76 – 13700) / 13700] x 100
Interset = 8.48%
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¿A qué porcentaje anual se han impuesto Q. 8000.00 que en 32 días han producido Q. 140.00? ¿ A qué porcentaje anual se han impuesto Q. 8000.00 que en 32 días han producido Q. 140.00 ?
Answers
Based on the amount being taxed, the period of taxation, and the tax, the annual percentage of tax is 19.96%.
What is the annual tax percentage?Assuming this rate was x, the following formula would apply:
Annual rate/ 365 days a year x number of days x amount to be taxed = Tax amount
Solving gives:
x/365 x 32 x 8,000 = 140
701.369863x = 140
x = 140 / 701.369863
= 19.96%
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Given f(x)=2x^2-1 and g(x) =3x-5 what is f-g
Answers
[tex]f(x)-g(x)=(2x^{2}-1)-(3x-5)=2x^{2}-1-3x+5=\boxed{2x^{2}-3x+4}[/tex]
Need help with this geometric question
Answers
Answer: QN=19
Step-by-step explanation:
Diagonals of an isosceles trapezoid are congruent, so NQ=PM.
By the segment addition postulate, NQ=QR+RN=3x+7.
So,
[tex]6x-5=3x+7\\\\3x-5=7\\3x=12\\\\x=4[/tex]
So, [tex]QN=3(4)+7=\boxed{19}[/tex]
solve the following inequality:
ALGEBRA 1
Answers
Answer:
[tex]m \leqslant 10 \: or \: m > 4[/tex]
Step-by-step explanation:
[tex] \frac{m - 2}{3} \leqslant - 4 \\ \frac{m - 2}{3} \times 3 \leqslant - 4 \times 3 \\ m - 2 \leqslant - 12 \\ m - 2 + 2 \leqslant - 12 + 2 \\ m \leqslant 10[/tex]
OR
[tex]3m - 8 > 4 \\ 3m - 8 + 8 > 4 + 8 \\ 3m > 12 \\ \frac{3m}{3} > \frac{12}{3} \\ m > 4 [/tex]
What is the volume of a regular pyramid having a base area of 24 inches and height of 6 inches
Answers
Answer:
V= 48 in^2
Step-by-step explanation:
Formula
Since the base has a known area, we do not need the full volume formula. This formula is
V = B * h / 3
B is the area of the base and h is the height measured from the top of the pyramid to the base meeting the base at right angles.
Givens
B = 24 in^2
h = 6 in
Solution
V = B * h / 3
V = 24 * 6/3
V= 48 in^2
Use the five numbers 12, 11, 19, 16, and 12 to complete parts a) through e) below.
a) Compute the mean and standard deviation of the given set of data.
The mean is x = and the standard deviation is s =
(Round to two decimal places as needed.)
Answers
Answer:
mean = 14 and standard deviation = 3.03
Step-by-step explanation:
mean = sum of all numbers ÷ by the numbers available
= (11 + 12 + 12 + 16 + 19) ÷ 5
= 70 ÷ 5
= 14
FOR STANDARD DEVIATION * USE A SCIENTIFIC CALCULATOR THEY WON'T PENALIZE YOU*
follow these steps:
1. press mode then STAT
2. then press 1-VAR
3. put all the numbers on the table in ascending order
4 after press AC
5. press shift then 1
6. you will see many things but we are only interested in standard deviation, press *Var*
7. then select the standard deviation sign and press the equal sign
Indicate the equation of the given line in standard form. Show all of your work for full credit.
The line containing the altitude to the hypotenuse of a right triangle whose vertices are P(-1, 1), Q(3, 5), and R(5, -5).
Answers
Answer: 24 sq units is the area of triangle.
Step-by-step explanation:
Given , (x1 , y1) = (-1, 1), (x2 , y2) = (3, 5) , (x3, y3) = (5, -5)
Using the Formula :
Area of triangle = [tex]\[\frac{1}{2}(x1(y2-y3) + x2(y3-y1) + x3(y1 -y2))\][/tex]
[tex]\[=\frac{1}{2}(-1(5-(-5)) + 3(-5-1) + 5(1-5)) \\=\frac{1}{2}(-10 -1 8 -20) \\=\frac{1}{2}(-48) = -24\][/tex]
Area cannot be negative. We only consider the numerical value of answer. Therefore, area of triangle = 24 sq units.
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Find the value of x.
2x
70
120
Answers
Question 6 of 10
sin 30º = √3/2 and cos 30º = 1/2
O A. True
OB. False
Answers
• sin 30º = 1/2
• cos 30º = √3/2
Question 10: Each tablet in a bottle of 30 costs the pharmacy $4.60. The pharmacy has additional costs including supplies and shipping of $1.40 per pill. If a 12% profit is desired, how much would the pharmacy charge for entire bottle?
Answers
The pharmacy must charge for $201.6 for the entire bottle.
Profit is the financial gain to the seller after selling some commodity
Revenue is the total sale of the seller after selling some commodity
Expenses is the expenditure to the seller before selling the commodity
Profit = Revenue - Expenses
Cost of the tablet = $4.60
Total cost of the bottle=$4.60x30
=$138
Additional cost=$1.40 x 30
= $42
Total expenses=$180
Profit %=125
Revenue= $180 x (1+12/100)
=$180 x (112/100)
=$201.6
Therefore, The pharmacy must charge for $201.6 for the entire bottle for a profit of 12%
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Given: angle 2 and angle 4 are vertical. Prove angle 2 congruent to angle 4
Need help quick!
Answers
The diagram shows that ∠2 and ∠4 are the vertical angles.
What are vertical angles?Vertical angles are the angles that are opposite of each other when two lines cross.
The statements are:
1. < 2 & < 4 are vert. angles
2. Lines M & N intersect at P
3. < 2 & < 3 are a linear pair
4. m < 2 + m < 3 = 180
5. <3 and < 4 are a linear pair
6. m < 3 + m <4 =180
7. m < 2 + m < 3 = m < 3 + m < 4
8. m < 2 = m < 4
9. < 2 =~ <4
Here are the reasons:
1. Given
2. Def of vertical angles.
3. Def of. Linear pair
4. Angle addition postulate
5. Def of a linear pair
6. Angle addition postulate
7. Substitution property
8. Subtraction property
9. Def of =~ angles.
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Answer: View the picture below!
Step-by-step explanation: Just did the assignment!
Graph the equation.
Y= - 3/2x
Answers
Answer:
Step-by-step explanation:
Write a rule to describe each translation
Answers
Answer:
slide - translate
Step-by-step explanation:
you slided them both as neither of the figures changed
Which expression is equivalent to (1−sinβ)(1+sinβ)/cos2β for all values of β for which (1−sinβ)(1+sinβ)/cos2β is defined?
Select the correct answer below:
tan2β
tanβ+secβ
tanβ
sec2β
1
Answers
Work Shown:
[tex]\frac{(1-\sin(\beta))(1+\sin(\beta))}{\cos^2(\beta)}\\\\\frac{1-\sin^2(\beta)}{\cos^2(\beta)}\\\\\frac{\cos^2(\beta)}{\cos^2(\beta)}\\\\1\\\\[/tex]
Therefore, [tex]\frac{(1-\sin(\beta))(1+\sin(\beta))}{\cos^2(\beta)}=1\\\\[/tex] is an identity for all values of β for which the original expression is defined. I used the difference of squares rule for the 2nd step. Then I applied the pythagorean trig identity for the 3rd step.
Denise and Stacey went to a carnival. The admission fee was $6 per person. Each ride at the carnival costs c dollars. The game booths charged g dollars for each game. Both Denise and Stacey went on 7 rides each. Stacey played 3 games, while Denise played 2 games. Which expression represents the total amount of money that Denise and Stacey spent at the carnival?
Answers
The total amount of money that Denise and Stacey spent at the carnival is 12 + 14c + 5g dollars.
What is total amount?
The amount that you get when you add several numbers or things together.
The total amount of money that Denise and Stacey spent at the carnival will be money spent on admission + ride + game.
Total amount = 2 * 6 + 2 ( 7 * c ) + ( 3 * g + 2 * g )
= 2 * 6 + 14 * c + 5 * g
= 12 + 14c + 5g dollars.
Therefore, the total amount of money that Denise and Stacey spent at the carnival is 12 + 14c + 5g dollars.
The questions seems incomplete, its option could be:
12 + 14c + 5g 12 + 14g + 5c 12 + 7g + 5c 12 + 7c + 5g.
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The length of a golden rectangle is 35 cm. Find the width to the nearest centimeter.
17cm
25cm
22cm
29cm
16cm
Answers
Answer:
22 cm
Step-by-step explanation:
First we need to know that The golden number
= (1+√(5))÷2
= 1.61803398875 (in decimal)
………………………………………………
We get the length of a golden rectangle
by multiplying its width by the golden number itself.
Then
The width = 35÷ 1.61803398875
=21.631189606245
Please help !!! I will give 20 points to the correct answer!!
Answers
-2x =31 - 11
-2x = 20
X = 20/2
X = 10
Suppose you want to test the effectiveness of a certain drug for treating a disease that said you wanted to see if using the drug is better the standard treatment used to like 150 patients to give the drug and 150 patients to give the standard treatment name at least five factors you should control for in your samples to make the test more random
Answers
Five factors that should be controlled are the dose of the medicine, the time the patients take this medicine, their diet, the stage of this disease and medicine composition.
Why should some factors be controlled?This is done to avoid bias or imprecise results.
What factors should be controlled?Factors related to the medicine itself and factors that can affect the results should be controlled. This includes:
The dose given to the patients.The stage of the disease that should be similar for all patients.The medicine compositon and manufacturer.The number of day patients take the medicine.The patients' diet.Learn more about medicine in:https://brainly.com/question/21486381
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x + 4 = x2? Assume x greater-than 0
Answers
Answer:
The value comes out to be
[tex]x=\frac{1}{2}+\frac{\sqrt{17}}{2}[/tex]
Step-by-step explanation:
The quadratic equation is an equation containing a single variable of degree [tex]2[/tex]. Its general form is [tex]ax^{2} +bx + c=0[/tex].
The discriminant is the part of the quadratic formula underneath the square root symbol: b²- 4ac. The discriminant tells us whether there are two solutions, one solution, or no solutions.
The equation we are given is :[tex]x+4=x^{2} \\x^{2} -x-4=0\\[/tex]
We know the formula as :
[tex]x=[-b[/tex]±[tex]\sqrt{b^{2}-4ac}][/tex] ×[tex]\frac{1}{2a}[/tex]
[tex]x=[-(-1)[/tex]±[tex]\sqrt{(-1)^{2} -4(1)(-4)}][/tex]×[tex]\frac{1}{2(1)}[/tex]
[tex]x=\frac{1}{2}[/tex] ±[tex]\frac{\sqrt{17} }{2} }[/tex]
Since [tex]x[/tex]≥[tex]0[/tex]
Other negative option is neglected
[tex]x=\frac{1}{2}+\frac{\sqrt{17}}{2}[/tex]
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Which of the following polynomials is in standard form?
A. F(x)=-3x+6x²-1+7x
B. F(x)=7x+6x² -1-3x4
C. F(x)=-3x4 -1+6x² +7x
D. F(x)=-3x +6x² +7x-1
Answers
Answer:
d
Step-by-step explanation:
What is the equation, in point-slope form, of the line that is parallel to the given line and passes through the point (−3, 1)?
y – 1=-3/2(x + 3)
y – 1=-2/3(x + 3)
y – 1=2/3(x + 3)
y – 1=3/2(x + 3)
Answers
The equation of the line parallel to given line and passing through (-3, 1) will be y – 1 = (3/2)(x + 3). Then the correct option is D.
What is the equation of line?The equation of line is given as
y = mx + c
Where m is the slope and c is the y-intercept.
The slope of the parallel lines are equal.
m = (2 + 4) / (2 + 2)
m = 6/4
m = 3/2
Then the equation of the line will be
y = (3/2)x + c
The line is passing through (-3, 1). Then the value of c will be
1 = (3/2)(-3) + c
c = 9/2 + 1
Then the equation will be
y = (3/2)x + 9/2 + 1
y – 1 = (3/2)(x + 3)
Then the correct option is D.
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Evaluate 3a-5b when a=-3 and b=-2
Answers
Answer: 1
Step-by-step explanation:
Substituting in the given values,
3a-5b=3(-3)-5(-2)=-9+10=
