Use the following binomial series formula (1 + x)^m = 1 + mx + m(m - 1)/2! x^2 +...... + m(m - 1).....(m - k + 1)/k! x^k + ...| to obtain the MacLaurin series for (a) 1/(1 + x)^8 = sigma^infinity_k = 0| (b) 7 squareroot 1 + x = | + ....| Enter first 4 terms only.

Answers

Answer 1

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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Answer 2

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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Related Questions

Please help! image is shown below

Answers

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

Can someone please tell me what is the solution

Answers

Answer:

[tex] \frac{1}{4} \tan {}^{4}(x) + c[/tex]

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.​

Answers

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

How do you solve for x and y?

Answers

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

2x + 5xy + 9x + 3 what is the solution to this problem?

Answers

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

What is 631.051 as a fraction
sorry if that doesnt make sense.

Answers

Answer:

631 and 51/1000

Step-by-step explanation:

Well I need the help in this last question I will mark brain list if you got it right

Answers

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!!

(5x-6y+7) -(-x +5y -8)
=5x-6y+7+x-5y+8
=6x -11y +15
Hope it helps you (^_^)

find the sum of series of multiple of 5 from 5 to 100 inclusive​

Answers

Answer:

let me think

Step-by-step explanation:

GIVING BRAINLIEST!!!

Answers

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:

What scale factor was applied to the first rectangle to get the resulting image?

Answers

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 :)

Christine has her own dog -walking business. She Charges her customers $20 per day to walk their day

Answers

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:

tysmmmmmmmmmmmmmmmmmmmmmm

Answers

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

what expressions are equivalent to -2(4-3x)+(5x-2)​

Answers

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 help me 15 points it’s worth it please help me on this question

Answers

Answer:

last answer

Step-by-step explanation:

HELP PLEASE !! URGENT !!

Answers

Directions and I am not sure of the other answer sorry :)

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

Answers

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

Find (3x+1)(x+4) using the table of products. Write your answer in standard form.

Answers

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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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'

Answers

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.

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?

Answers

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]

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.

Answers

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! :)

Solve by elimination:
9x + 4y = 97
9x + 6y = 123
14
15'
B (5, 13)
(13,5)
D (1, 22)

Answers

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!

PLEASE I NEWD HELP ON THIS

Answers

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!

que volumen ocupará 600 g de agua?

Answers

Answer:

Step-by-step explanation:

600 ml

Please help it’s due in 20 mins would it be A B C or D

Answers

Option C is correct

x < 1

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.

What is the scientific notation for .000472

Answers

Answer:

The scientific notation for 0.000472 is 4.72 * [tex]10^{-4}[/tex].

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?

Answers

Answer:

Step-by-step explanation:

-40t

-40(20)

-800 ft

If 95% of students are coming to school tomorrow, what is the complement?

Question 5 options:

A. 95%


B. 100%


C. 1%


D. 5%

Answers

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%

a quadratic polynomial the sum of whose zeros is -3 and product is -10​

Answers

Answer:

2 and -5 i think

Step-by-step explanation:

can someone please help me u can just do 5 and explain please


¿Puede alguien ayudarme? Puedes hacer 5 y explicar por favor.

Answers

Answer:

i only can explain until number 7

i am sorry

maybe that help you

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.

Answers

Step-by-step explanation:

sorry i couldn't solve the last and the last second one

Was it helpful?

comment down

If there is any kind of suspicious mistake

then sorry

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