The double integral flux is -72π.
We can parameterize the cone as follows:
x = r cosθ
y = r sinθ
z = z
where r is the distance from the z-axis and θ is the angle of rotation around the z-axis.
Then we can calculate the normal vector as follows:
n = (∂x/∂r × ∂y/∂θ)i + (∂y/∂r × ∂x/∂θ)j + (∂z/∂r × ∂z/∂θ)k
= (-r cosθ)i + (-r sinθ)j + (6r/(2√(x^2+y^2)))k
= -r(cosθ i + sinθ j) + 3k/√(x^2+y^2)
Taking the dot product of F with n, we get:
F · n = (5xy)i - 2zk · [-r(cosθ i + sinθ j) + 3k/√(x^2+y^2)]
= -2z(3/√(x^2+y^2)) = -6z/r
Then the flux integral becomes:
double integral_S F · n dS = ∫∫(-6z/r) r dr dθ dz
where the limits of integration are
0 ≤ θ ≤ 2π
0 ≤ z ≤ 6
0 ≤ r ≤ 6√(z^2/36 - 1)
Evaluating the integral, we get:
∫∫(-6z/r) r dr dθ dz = -72π
Therefore, the flux is -72π.
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Using the binomial series formula. The first four terms of the MacLaurin series for 7√(1 + x) are:
7 + (7/2)x - (7/16)x^2 + (21/256)x^3
(a) Using the binomial series formula, we have:
1/(1 + x)^8 = (1 + x)^(-8)
= 1 + (-8)x + (-8)(-9)/2! x^2 + (-8)(-9)(-10)/3! x^3 + ...
Therefore, the first four terms of the MacLaurin series for 1/(1 + x)^8 are:
1 - 8x + 36x^2 - 56x^3
(b) Using the binomial series formula, we have:
7√(1 + x) = 7(1 + x)^(1/2)
= 7(1 + (1/2)x + (-1/8)x^2 + (1/16)x^3 + ...)
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HELP PLEASE !! URGENT !!
What is 631.051 as a fraction
sorry if that doesnt make sense.
Answer:
631 and 51/1000
Step-by-step explanation:
Josie makes invitations for her aunt's paper company. Of all the invitations Josie makes, 15/21 are children's party invitations. Of those invitations, 3/5 have an animal on them. What fraction of the invitations Josie makes are children's party invitations with an animal on them?
Answer:
the fraction of the invitations considered to be an animal on them is [tex]\frac{3}{7}[/tex]
Step-by-step explanation:
The computation of the fraction of the invitations considered to be an animal on them is shown below:
= Children party invitations × animal on them
[tex]= \frac{15}{21} \times \frac{3}{5}\\\\= \frac{3}{7}[/tex]
Hence, the fraction of the invitations considered to be an animal on them is [tex]\frac{3}{7}[/tex]
Christine has her own dog -walking business. She Charges her customers $20 per day to walk their day
Answer:
y= money made
x = amount of dogs walked
equation- y = 20x
for the table name # of dogs walked on the right and money earned on the left.
for the left put 1 2 3 4 5 6 7 and 8
1 goes with 20
2 goes with 40
3 with 60
4 with 80
5 with 100
6 with 120
7 with 140 and
8 with 160
Step-by-step explanation:
Sally measured the height of a flower growing in her garden. The flower was 3.25 inches tall. Over the next week, the flower grew h inches and measured 4.125 inches tall. How many inches did the flower grow during the week? Round to the nearest hundredth.
Answer: The flower grew 0.88 inches during the week
Step-by-step explanation:
Height of flower in the previous week = 3.25 inches
Height of flower the next week = 4.125inches
height the flower added during the week = 4.125 inches - 3.25inches
=0.875 inches
Rounding to the nearest hundredths becomes 0.88 inches
Can someone please tell me what is the solution
Answer:
[tex] \frac{1}{4} \tan {}^{4}(x) + c[/tex]
Delia takes out a loan to buy a car for $18,000 with an interest rate of 6.5%. The amount of interest Delia will have to pay is $4,680. Write and solve an equation to determine the number of months her loan is for. Show all of your work and explain how you got your number of months.
Answer:
Delia pays $4,680 in 4 months
Step-by-step explanation:
Equation:
18,000 * 6.5% = 1170
4680 ÷ 4 = 1170
So, the answer is 4 months this is the equation.
Hope this helps! :)
tysmmmmmmmmmmmmmmmmmmmmmm
Answer:
The answer is 10
Step-by-step explanation:
To get this you will make the improper fraction into a fraction and then turn that into decimal form
[tex]4 \frac{1}{8} = 4[/tex]
and
[tex]5 \frac{6}{10} = 6[/tex]
That is how you find the estimated answer
Hope this Helped
can someone please help me u can just do 5 and explain please
¿Puede alguien ayudarme? Puedes hacer 5 y explicar por favor.
Answer:
i only can explain until number 7
i am sorry
maybe that help you
The altitude of an airplane is decreasing at a rate of 40 feet per second. What is the change in altitude of the airplane over a period of 20 seconds?
Answer:
Step-by-step explanation:
-40t
-40(20)
-800 ft
10.
Write a rule for the linear function in the graph.
A. y = 4/5x + 2
B. y = -5x - 2
C. y = 5/4x - 2
D. y = -4/5x + 2
Answer:
D. y = -4/5x + 2
Step-by-step explanation:
Graph the line using the slope and y-intercept, or two points.
Slope:
−
4
5
y-intercept:
(
0
,
2
)
x
y
0
2
5
2
0
a quadratic polynomial the sum of whose zeros is -3 and product is -10
Answer:
2 and -5 i think
Step-by-step explanation:
Please help me 15 points it’s worth it please help me on this question
Answer:
last answer
Step-by-step explanation:
What scale factor was applied to the first rectangle to get the resulting image?
Answer: Another way to look at it is that the rectangle was reduced in a factor of 5 (1/0.2=5)
don't forget to drop a heart hope it helped
Step-by-step explanation:
Answer: 1/0.2=5
Step-by-step explanation:
I hope this helps if you guys need a reach out to me :)
Solve by elimination:
9x + 4y = 97
9x + 6y = 123
14
15'
B (5, 13)
(13,5)
D (1, 22)
Answer:
B (5, 13)
Step-by-step explanation:
9x + 4y = 97
9x + 6y = 123
To solve by elimination, we want to eliminate a variable. To do this, we must make one variable cancel out.
First, we can see that both equations have 9x. To cancel out x, we must make one of the 9x's negative. To do this, multiply each term in the equation by -1.
-1(9x + 6y = 123)
-9x - 6y = -123
This is one of your equations. Set it up with your other given equation.
9x + 4y = 97
-9x - 6y = -123
Imagine this is one equation. Since every term is negative, you will be subtracting each term.
9x + 4y = 97
-9x - 6y = -123
___________
0x -2y = -26
-2y = -26
To isolate y further, divide both sides by -2.
y = 13
Now, to find x, plug y back into one of the original equations.
9x + 4(13) = 97
Multiply.
9x + 52 = 97
Subtract.
9x = 45
Divide.
x = 5
Check your answer by plugging both variables into the equation you have not used yet.
-9(5) - 6(13) = -123
-45 - 78 = -123
-123 = -123
Your answer is correct!
(5, 13)
Hope this helps!
que volumen ocupará 600 g de agua?
Answer:
Step-by-step explanation:
600 ml
2x + 5xy + 9x + 3 what is the solution to this problem?
Answer:
5xy + 11x + 3
Step-by-step explanation:
We have the expression 2x + 5xy + 9x + 3 and are asked the solution.
This is different from most standard addition problems, we have an influx of variables, since we do. We follow the like term rules, which is that we can only add the numbers that have the same variable endings, in this case, only 2x and 9x are like terms, so we add them.
2x + 9x
11x
Therefore :
5xy + 11x + 3
Please help! image is shown below
Answer:
I think 3 maybe since 5 times 3 is 15
Step-by-step explanation:
Answer:
z=10
Step-by-step explanation:
60/40=1.5
15/1.5=10
find the sum of series of multiple of 5 from 5 to 100 inclusive
Answer:
let me think
Step-by-step explanation:
If 95% of students are coming to school tomorrow, what is the complement?
Question 5 options:
A. 95%
B. 100%
C. 1%
D. 5%
Answer:
d
Step-by-step explanation:
can you help me with this question According to Frost in his poem "The Road Not Taken," what kind of difference did taking one road over another road make? A. It made a good difference, B. It made a bad diference, c. Frost does not say
Answer:
the answer is d
Step-by-step explanation:
it only takes 5% to get to 100%
How do you solve for x and y?
Answer:
x = 100, y = 50
Step-by-step explanation:
Make a system of equations:
First, you know that x + y degrees and 30 degrees are on a line together, they add up to 180 degrees:
x + y + 30 = 180
x + y = 150
Next, the interior angles of a triangle always add up to 180 degrees, and since 2y, x/2, and 30 are all the angles in a triangle, you have:
2y + x/2 + 30 = 180
x/2 + 2y = 150
Now, all you have to do is solve the system of equations.
To start, multiply the second equation by 2 to get rid of the fraction:
x + 4y = 300
Then, you can subtract the two equations:
x + 4y = 300
- (x + y = 150)
3y = 150
divide both sides by 3
y = 50
substitute y = 50 into the equation x + y = 150:
x + 50 = 150
x = 100
Well I need the help in this last question I will mark brain list if you got it right
Answer:
6x−11y+15
Step-by-step explanation:
Distribute the Negative Sign:
=5x−6y+7+−1(−x+5y−8)
=5x+−6y+7+−1(−x)+−1(5y)+(−1)(−8)
=5x+−6y+7+x+−5y+8
Combine Like Terms:
=5x+−6y+7+x+−5y+8
=(5x+x)+(−6y+−5y)+(7+8)
=6x+−11y+15
Answer:
6x−11y+15
I hope I helped!!
what expressions are equivalent to -2(4-3x)+(5x-2)
Answer:
11x-10
Step-by-step explanation:
1.Rearrange terms
-2(4-3x)+(5x-2)
-2(-3x+4)+(5x-2)
2.Distribute
-2(3x+4)+(5x-2)
6x-8+(5x-2)
3.Eleminate redundant parentheses
6x-8+(5x-2)
6x-8+5x-2
4.subtract the numbers
6x-8+5x-2
6x-10+5x
5.Combine like terms
6x-10+5x
11x-10
•solution
11x-10
PLEASE I NEWD HELP ON THIS
Answer:
5. Inequality form: n ≥ 3
Interval notation: [3, ∞)
6. Inequality form: x < 4
Interval notation: (- ∞, 4)
11. Inequality form: x > 50
Interval notation: (50, ∞)
12. Inequality form: y [tex]\geq[/tex] 8
Interval notation: [8, ∞)
15. Inequality form: z < 8
Interval notation: (- ∞, 8)
16. Inequality form: y [tex]\geq[/tex] 4
Interval notation: [4, ∞)
Step-by-step explanation:
I tried to graph them as best as I could, I hope this helps!
Please help it’s due in 20 mins would it be A B C or D
Answer:
C ) x < 1
Step-by-step explanation:
The open circle on a number line means: less than or greater than. The arrow is pointing to the left, towards the negatives, so x would be less than 1.
Find the area of parallelogram ABCD given m∠A = 30° and the following measures. AD = in.; AB = 8 in. A=
32 in.²
32√3 in.²
16√3 in.²'
Answer: Given that a parallelogram ABCD has sides AB= 6 ft and AX = 3√3
Angle A =30
To find the area of the parallelogram
We have area of parallelogram = base x height
Here base can be taken as side AB = 6 ft
Height = perpendicular distance of AB from vertex X
= AX sin A
= 3√3sin30
=1.5√3
Hence area =6(1.5√3)=9√3ft^2
MARK ME BRAINLIST
HOPE IT IS HELPFUL
Answer:
16√3 in.²'
Step-by-step explanation:
Hope this helps, sorry for answering late.
GIVING BRAINLIEST!!!
Answer:
i think its 78.5 but the answers not on there the closest one there to it is 76.5 so just put that one
Step-by-step explanation:
Find (3x+1)(x+4) using the table of products. Write your answer in standard form.
Step-by-step explanation:
just multiply both the values and get the quadratic solution.
The standard form of the (3x+1)(x+4) is 3x^2+13x+4=0.
We have given that,
(3x+1)(x+4) using the table of products.
We have to determine the standard form.
What is the formula of the standard form?
The quadratic function f(x) = a(x - h)2 + k, a not equal to zero, is said to be in standard form. If a is positive, the graph opens upward, and if a is negative, then it opens downward. The line of symmetry is the vertical line x = h, and the vertex is the point (h,k).
ax^2+bx+C=0
[tex]=3xx+3x\cdot \:4+1\cdot \:x+1\cdot \:4[/tex]
[tex]=3x^2+13x+4[/tex]
Therefore the standard form is 3x^2+13x+4=0.
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What is the scientific notation for .000472
Answer:
The scientific notation for 0.000472 is 4.72 * [tex]10^{-4}[/tex].
4. Six numbers are shown.
1.25, -1.5, -0.75,
34,
2 6/8,
5/4
Place each number in its correct location on the number line.
Step-by-step explanation:
sorry i couldn't solve the last and the last second one
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