evaluate f*ds where f = <3xy^2,3x^2y,z^3> and m is the surface of the sphere of radius 5 centered at the origin

Answers

Answer 1

The value of f.ds = 20π.

What is Flux?

The quantity of electric or magnetic field lines that flow across a surface in a specific period of time is known as flux. Field lines offer a way to visualise the size and direction of the field under study.

Given:

f = <3xy²,3x²y,z³>

Using Divergence Theorem

P= 3xy²

Q= 3x²y

R = z³

So, dP/ dx= 3y²

dQ/ dy = 3x²

dQ/ dz = 3z²

So, [tex]\int\limits\int\limits\int\limits dV[/tex]= [tex]\int\limits\int\limits\int\limits (dP/ dx + dQ/dy+ dR/dz)[/tex]

= [tex]\int\limits\int\limits\int\limits[/tex] (3y² + 3x² + 3z²)

= [tex]\int\limits\int\limits\int\limits[/tex] 3 (y² + x² + z²)

Since the radius is 5.

= [tex]\int\limits\int\limits\int\limits[/tex] 3(5)

= 15 [tex]\int\limits\int\limits\int\limits[/tex] dV

= 15 (4/3)π

= 20π

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Related Questions

What is the equation of this graphed line?
Enter your answer in slope-intercept form in the box.

Answers

Answer:

y = -1/3x - 5

Introduction:

The slope intercept form of a line is y = mx + b. Now, let's start out by solving the slope.

Step-by step explanation:

=> Slope = rise/run = [tex]\frac{y_{2} - y_{1} }{x_{2}-x_{1} }[/tex]=> Slope = [tex]\frac{-3- (-7) }{-6-6 }[/tex]=> Slope = [tex]\frac{4}{-12}[/tex]=> Slope = [tex]\frac{-1}{3}[/tex]

Since we have found the slope, let's find the y-intercept to create our equation.

=> y-intercept = -5

Conclusion:

Therefore, our new equation is y = -1/3x - 5

Hoped this helped.

[tex]BrainiacUser1357[/tex]

How to solve the function problem for this one?

Answers

Answer:

a. f(12) = - 1

b. x = 27 when f(x) = 4

Step-by-step explanation:

We are given that [tex]f(x)=\frac{1}{3} x-5[/tex] and we want to find f(12) and f(x) = 4

To find f(12) we simply plug in 12 into x and evaluate it

[tex]f(x)=\frac{1}{3} x-5[/tex]

plug in 12

[tex]f(12)=\frac{1}{3} (12)-5[/tex]

multiply 12 and 1/3 to get 4

[tex]f(12)=4-5[/tex]

subtract 5 from 4 to get -1

[tex]f(12)=-1[/tex]

Now we want to find the value of x when f(x) = 4

To do this we substitute 4 for f(x) and solve for x

[tex]f(x)=\frac{1}{3} x-5[/tex]

substitute 4 for f(x) and solve for x

[tex]4=\frac{1}{3}x -5[/tex]

add 5 to both sides

[tex]9=\frac{1}{3} x[/tex]

multiply both sides by 3

27 = x

And we are done.

So f(12) = -1 and x = 27 when f(x) = 4

For a plug in 12 for x:

f(12) = 1/3(12)-5

f(12) = 4-5

f(12) = -1

For b plug in 4 for x:

f(4) = 1/3(4)-5

f(4) = 4/3 -5

f(4) = 0.75-5

f(4)= -4.25

there are nine children and Kenneth preschool class three of them chose to play at the sand table based on past data is 12 preschoolers are at school today how many should you expect to play at the sand table​

Answers

Answer:

4 are playing at the sand table

Step-by-step explanation:

There were 9 kids at Kenneth's preschool and 3 were playing, thats one third of the kids(3x3=9). One third of 12 is 4(3x4=12) Basically since there were 9 total kids, and 3 at the sand table, they are divided equally in groups of three so you just divide 12 by 3 too and thats how you get 4

plzzzzz help!! 20 points
Eric's dog gets 34.7 grams of protein in each meal. How much protein does the dog get in 4 meals?

Answers

Answer:

242.9 grams

Step-by-step explanation:

Erics dog get 34.7 grams each meal, When He gets 4x the amount all you are doing is 34.7x4 which equals 138.8 grams

Please help I’ll give brainliest ASAP

Answers

Answer:

1 I don't know if those are questions but try if they are try the first one a

Will give thank,brainly and 5 stars!

Answers

The second and last one.

The second one multiplies the cost of each type of ticket by two, therefore saying that you wanted to buy two of each type of ticket.

The last one multiplies the cost of a single ticket of all three types and multiplies it by 2.

Answer:

The second and last one

Step-by-step explanation:

Hope this helps and have a good day!

WILL GIVE BRAINLIESTTT!!!!!!!!!
Find the solution of the system of equations.
6x+y=30
-2x-5y=18

Answers

Answer:

x-y=12 or x=12+y??????

Step-by-step explanation:

6x+y=30

-2x-5y=18

Add the equations up: 4x-4y=48

Divide by 4

x-4y=12

Divide by 4 again

x-y=12

+y on both sides

x=12+y

(I might be wrong)

Answer:

[tex]x=6; y=-6[/tex]

Step-by-step explanation:

Unless you're required to use any particular method, let's add the first to twice the second to eliminate x:

[tex]6x+y-6x-15y=30+54 \rightarrow -14y=54 \rightarrow y=-6[/tex]

At this point let's plug this value of y in the first equation and find x:

[tex]6x+(-6)=30 \rightarrow x-1=5 \rightarrow x=6[/tex]

What is the answer
(x+8)+4x=(7x-16)

Answers

[tex](x+8)+4x = 7x -16\\\\\implies 5x +8 = 7x -16\\\\\implies 7x -5x = 8+16 \\\\\implies 2x = 24\\\\\implies x = \dfrac{24}2\\\\\implies x= 12[/tex]

A hot-air balloon is tied to the ground with two taut ropes. One rope is directly under the balloon and makes a right angle with the ground. The other rope forms an angle of 60º with the ground. Which statements are correct?
A) d ≈ 60 ft.
B) d ≈ 66 ft.
C) h ≈ 104 ft.
D) h ≈ 108 ft.
E) angle of depression = 30°

Answers

Answer:

d ≈ 60 ft., h ≈ 104 ft.

Step-by-step explanation:

Additionally: angle of depression = 60°

The angle of elevation and the angle of depression are congruent.

PLEASE HELP!! With explanation/solution please!!

Answers

Step-by-step explanation:

Just sum the number of cows and buffaloes:

2p^2 - p + 4 + p^2 + p + 1 = 3p^2 +5 animals.

Answer:

Step-by-step explanation:

here is an explanation:

2p²-p+4+p²+p+1=3p²+5

You can add 2p² and p² because they are both squared (²). -p+p=0, because the first p is negative (-). Lastly, you can add 4+1=5. Hope this helped! Lmkp if you are still confused  :) <3

How do I find the equation of the line?

Answers

Answer:

1.Identify the slope.

2.Identify the point.

4.Substitute the values into the point-slope form, y − y 1 = m ( x − x 1 ) .

5.Write the equation in slope-intercept form.

Step-by-step explanation:

Answer:

y=-\frac{2}{3}x+3

Step-by-step explanation:

[tex]y=mx+b[/tex]

There are 4 variables in this equation, and 3 of them are already given. We already have the slope and the (x, y) of a known point. Plug those 3 into the equation and solve for b:

[tex]7=-\frac{2}{3}(-6)+b\\7=4+b\\b=3[/tex]

Now, with the slope and the y-intercept, you can write the equation of the line:

[tex]y=mx+b\\\\y=-\frac{2}{3}x+3[/tex]

$765. 13 is deposited at the end of each month for 2 years in an account paying 12% interest compounded monthly. Find the amount of the account. Round your answer to the nearest cent. A. $18,911. 18 b. $19,873. 08 c. $20,638. 21 d. $21,403. 34.

Answers

The amount of the account which is also the principal is = $3,188

The formula for calculating the simple interest (I) of an account is = P × T × R / 100

Making P the subject of formula, P = 100 × I / T×R

Where,

T = 2 years

R = 12%

I = $765. 13

[tex]p = \frac{100 \times 765.13}{2 \times 12} [/tex]

[tex]p = \frac{76513}{24} [/tex]

p = $3,188

Therefore, the amount of the account which is also the principal is = $3,188

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What is 2log5(5x^3)+1/3log5(x^2+6)

Answers

Answer:

Ill help you if you come help me with mine c:

Step-by-step explanation:

here is mine:

The values of f(x) and g(x) are shown for selected values of x in the table below.

x f(x) g(x)

0 0 1

1 3 2

2 6 4

3 9 8

4 12 16

Of these two functions, one is exponential and the other is linear. Determine which of the functions is linear, and explain why this must be the case.

ASAP HELP PLEASE SHOW ALL WORK
*Find the value of x. Show all the work

Answers

The line of length 48 is passing through the midpoint of traingle so it's half of base

[tex]\\ \sf\longmapsto \dfrac{3x}{2}=48[/tex]

[tex]\\ \sf\longmapsto 3x=96[/tex]

[tex]\\ \sf\longmapsto x=32[/tex]

Fill in the blanks with the answer to each question based on information provided.Two toy robots are having a race. Robot A can go 14 meter in 15 seconds. Robot B can go 1 meter in 50 seconds.1) If Robot A continues at that same speed, how long will it take to go 1 meter? Remember units! __________2) How long for Robot A to go 4 meters at that speed? Remember units! _________

Answers

Answer:

1 1/14 seconds4 2/7 seconds

Step-by-step explanation:

We are being asked for times, so we can express the rate in terms of seconds per meter.

  (15 seconds)/(14 meters) = (15/14) seconds per meter = 1 1/14 seconds/meter

__

1) It will take Robot A 1 1/14 seconds to go 1 meter.

2) it will take Robot A 4 2/7 seconds to go 4 meters. (4 times as long)

The Wilson family invited 100 relatives to their Christmas party. 90 guests had Dutch heritage, 80 had German heritage and 75 had English heritage. What is the minimum number of people who claimed ancestry from all three heritages? What is the formula i use to find out the answer of the question? and how do i find out the answer?

Answers

Answer:

Out off 100

Step-by-step explanation:

10 don't have dutch heritage.

20 don't have German heritage.

25 don't have English heritage.

100 - 55

At minimum, 45 people have all three heritages.

NAME THE PARTS OF THE CIRRCLR​

Answers

a) Point O

b) [tex]\overline{OB}[/tex]

c) [tex]\overline{AB}[/tex]

4) arc DE (m)

5) [tex]\overline{DE}[/tex]

6) Semicircle AEB

help please
The serving size for a toddler’s daily vitamin C is 4/5 cup of orange juice. If there are 3 1/4 cups of orange juice, how many servings of vitamin C are there for a toddler? Show your work

Answers

Answer:

3

Step-by-step explanation:

First you change 2 1/4 into an improper which is 9/4. Then you do KFC(Keep Change Flip)  9/4 x  4/3=36/12.  THEN YOU SIMPLIFY=9/3,that can still be simplified so the final answer is 3.Its 3 because there are 3 wholes in 9/3.

what is the value of the expression 5 + 6 x (5 - 2) + 9

Answers

i believe its 18x + 14

the function f(x)= (x-8) (x+2) (x+3) has which zeros

Answers

Answer:

(8, 0)

(-2, 0)

(-3, 0)

Step-by-step explanation:

x - 8 = 0

x = 8

x + 2 = 0

x = -2

x + 3 = 0

x = -3

[tex](x-8)(x+2)(x+3) =0\\\\\implies x -8 =0~~~ \text{or}~~~x+2 =0 ~~~ \text{or}~~~x+3 = 0\\\\\implies x = 8 ~~~~~~~~ \text{or}~~~~~~x = -2 ~~~ \text{or}~~~ x = -3\\\\\\\text{Hence the roots are}~ 8, -2 ~\text{and} ~-3[/tex]

Trey will be splitting 2 3/4 pies with himself and 5 friends. how much pie will each person get?

Answers

11/20 of the pie each person
hope this helps!

Answer: 11/24

Step-by-step explanation:I turned 2 and 3/4 into an improper fraction which got me 11/4.

There are 5 friends and him so that's 6 people.

So we can't do 11/4 divided by 6 so we must put 6 over 1.

So 11/4 divided by 6/1

Then we do "Keep Change Flip"

We keep 11/4

We change the division sign to multiplication

Then we flip 6/1 to 1/6

Then the problem is re wrote as:

11/4 times 1/6

And that equals 11/24 as your answer

So each person gets 11/24 of the pies.

Zero is a solution for which inequality?
4.1m > -16.4
4.1m > 16.4
-4.1m > 16.4
4.1m < -16.4

Answers

Since 0 is greater than -4 in the expression 4.1m >-16.4, hence zero is a solution to this inequality

Given the following inequality, we are to check which of them has zero as a solution.

For the expression

4.1m >-16.4

m > -16.4/4.1

m > -4

Since 0 is greater than -4, hence zero is a solution to this inequality

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Which rule describes the composition of
transformations that maps AABC to AA"B"C"?
R0, 9000rx-axis(x, y)
Orx-axis Ro, 900(x, y)
RO, 1800 orx - axis(x, y)
Orx-axis Ro, 1800(x, y)

Answers

Answer:

The second one: r x-axis. R 90(x,y)

Step-by-step explanation:

You can see that from ABC to A'B'C', it's rotated a positive 90 degrees. then, from A'B'C' to A"B"C", reflected across x-axis. and when writing the transformation, it goes by last to first. that's why the R 90 comes first.

The rule which describes the composition of transformations that maps ΔABC to ΔA"B"C" is,

⇒ r _ x-axis. R _ 90(x, y)

What is Translation?

A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.

Given that;

To find the rule which describes the composition of transformations that maps ΔABC to ΔA"B"C".

Now, You can see that from ABC to A'B'C',

it's rotated a positive 90 degrees.

And, Then, from A'B'C' to A"B"C", reflected across x-axis.

Now, when writing the transformation, it goes by last to first. that's why the R 90 comes first.

Thus, The rule which describes the composition of transformations that maps ΔABC to ΔA"B"C" is,

⇒ r _ x-axis. R _ 90(x, y)

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Find the value of r in the isosceles triangle shown below.
8
8
6

Answers

Answer:

r = 6

.....................

23 base 10+1011 base 2=​

Answers

Answer:

10111

Step-by-step explanation:

10111

During crawfish season, Xavier sells crawfish for $62. 50 per sack and charges a $20. 00 delivery fee. Write an equation that could be used to determine y, the total cost of x sacks of crawfish delivered to a customer.

Answers

The equation that could be used to determine y, the total cost of x sacks of crawfish delivered to a customer is y = 20 + 62.50x

Given:

cost per sack of crayfish = $62. 50

Delivery fee = $20. 00

y = Total cost

x = sacks of crawfish

The equation:

Total cost = Delivery fee + cost per sack of crayfish(sacks of crawfish)

y = 20 + 62.50x

Therefore, the equation that could be used to determine y, the total cost of x sacks of crawfish delivered to a customer is y = 20 + 62.50x

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Solve this system of equations, then determine what y equals.
x + 5y= 7
2x + 4y = -4
A y=-18
B y=3
C y=8
D y=-8

Answers

2+2=4 and 4+4=8 and 8+8=16

[tex]x+5y = 7~~~....(i)\\\\\\2x+4y = -4~~~.....(ii)\\\\\\\text{Multiply equation (i) by 2,}\\\\\\2x+10y = 14~~~.....(iii)\\\\\\(iii) - (ii):\\\\2x+10y-2x-4y = 14-(-4)\\\\\implies 6y = 14+4\\\\\implies 6y = 18\\\\\implies y = \dfrac{18}6\\\\\implies y = 3[/tex]

Please help!!!! :) thank you!

Answers

Answer:x-3

Step-by-step explanation:

f(-3)

f(x)= 3 to the power of x

Answers

1/27
See attached picture

HI CAN YOU PLEASE HELP ME

Answers

Answer:

11 C

12 D

13 B

14 E

15 A

Step-by-step explanation:

pure definition case. there is nothing to solve, and not really anything to explain in addition to the assigned texts.

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