question content area top part 1 use a triple integral to find the volume of the solid bounded below by the cone z

Answers

Answer 1

The volume of the solid bounded below by the cone z = √(x^2 + y^2) and bounded above by the sphere x^2 + y^2 + z^2 = 18 is 192π/3 cubic units

To find the volume of the solid bounded below by the cone z = √(x^2 + y^2) and bounded above by the sphere x^2 + y^2 + z^2 = 18, we can use a triple integral.

First, we need to determine the limits of integration. Since the solid is symmetric about the z-axis, we can use cylindrical coordinates.

The cone is given by z = √(x^2 + y^2), which in cylindrical coordinates becomes z = r. The sphere is given by x^2 + y^2 + z^2 = 18, which in cylindrical coordinates becomes r^2 + z^2 = 18.

Thus, the limits of integration are

0 ≤ r ≤ √(18 - z^2)

0 ≤ θ ≤ 2π

0 ≤ z ≤ √(r^2)

The integral to find the volume is

V = ∭ dV = ∫∫∫ dV

Using cylindrical coordinates, dV = r dz dr dθ, so the integral becomes

V = ∫₀²π ∫₀ᵣ√(18 - z²) ∫₀ᵣ r dz dr dθ

We can simplify this integral by first integrating with respect to z:

V = ∫₀²π ∫₀ᵣ√(18 - z²) r dz dr dθ

Using a trigonometric substitution u = z/√(18 - z²), we can simplify this to

V = ∫₀²π ∫₀¹ r√(18 - u²(18)) 18du dr dθ

V = 18∫₀²π ∫₀¹ r√(18(1 - u²)) du dr dθ

Using another substitution u = sin(θ), we can simplify this to:

V = 36∫₀²π ∫₀¹ r√(1 - u²) du dr dθ

This integral can be evaluated using the formula for the volume of a sphere of radius R

V = 36(4/3 π(√2)³)

V = 192π/3 cubic units

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The given question is incomplete, the complete question is:

Use a triple integral to find the volume of the solid bounded below by the cone z = √(x^2 + y^2 ) and bounded above by the sphere x^2 + y^2 + z^2 = 18


Related Questions

I need help , any of u guys have the answer?

I need help , any of u guys have the answer?

Answers

the answer the third choice
(x to the power of 2+1)+(5-x)
first, u keep x to the power of two because there are no like terms, and then you combine the like terms 1 and 5 to get 6, then you subtract x

therefore, the answer is x squared minus x plus 6

which function is a quadratic function?
(x-4)^2+3
(2x+4)^3+3
(-6x-4)^4+3(x+2)^2
-(x-6)+3(x+1)

Answers

Answer:

(-6x-4)^4+3(x+2)^2

Step-by-step explanation:

question is in picture please help

question is in picture please help

Answers

Answer:

\( \sf {a}^{6} \)

Step-by-step explanation:

Given expression

\( \sf \: {a}^{0} \: • \: \: {a}^{6} \)

To find expression solution

power rule

\( \sf \: {a}^{m} \: {a}^{n} = {a}^{m + n} \)

\( \sf {a}^{0} + {a}^{6} = {a}^{0 + 6} \)

\( \sf \therefore \: {a}^{6} \)

\( \: \Large \mathbb{SOLUTION:}\)

\( \: \: \rm{ {a}^{0} \times {a}^{6} }\)

\( \: \: \text{Calculate the power }\)

\( \: \: \underline{\underline{\rm{{a}^{6} }}}\)

What is this I need help don’t mind the room

What is this I need help dont mind the room

Answers

Here’s a picture of my work. The answer is b. Hope this helps :-)
What is this I need help dont mind the room

Any help with this? It's a proof, but not a long one

Any help with this? It's a proof, but not a long one

Answers

Angle NKL is congruent to NJM (given)
KL is congruent to JM (given)
Angle N is congruent to angle N (reflexive)
Triangle JNM is congruent to triangle KNL (AAS)

LN is congruent to MN (CPCTC)

The American Population is living longer. Along with the longevity of life comes additional challenges with both medical and Psychiatric problems. Your patient is about to be discharged from a short-tern rehab center. You overhear the daughter confiding in the nursing student that she cannot handle her mother and will be looking for a Memory care unit to put her mother in. You also hear the student nurse who was raised in a foreign country state, " I would NEVER put my mother in a home. I would take care of her woth my two sisters junti she dies.

what considerations might you make withthis students. Address the cultural differneces in elder care and adress the conself od "Role Strain" in caring for special populations.

Answers

Cultural sensitivity is crucial in elder care. Cultural beliefs impact elderly care. A foreign-raised nursing student desires to care for her mother and sisters until her mother's passing.

What is the cultural Strain?

Consider cultural values: Students from certain backgrounds may see caring for their elderly parents as a moral duty. Respecting elder beliefs is critical in discussing care options. Have open, non-judgmental communication with the nursing student. Show empathy and listen to her perspective.

Educate the nursing student about caring for a loved one with medical and psychiatric problems. Explain physical, emotional, and financial consequences, including effects on relationships and responsibilities.

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help me please thank you it would mean a lot to me y+7=3/4(x+2)

help me please thank you it would mean a lot to me y+7=3/4(x+2)

Answers

Hmmmmmmmmmmmmmmmmmmmmmmmmmmm

The box plots display data collected when two teachers asked their classes how many pencils they lose in a school year.

A box plot uses a number line from 5 to 47 with tick marks every one unit. The box extends from 8 to 14 on the number line. A line in the box is at 11. The lines outside the box end at 7 and 45. The graph is titled Mr. Johnson's Class, and the line is labeled Number Of Pencils.

A box plot uses a number line from 0 to 51 with tick marks every one unit. The box extends from 12 to 21 on the number line. A line in the box is at 14.5. The lines outside the box end at 0 and 50. The graph is titled Mr. Simpson's Class, and the line is labeled Number Of Pencils.

Which class lost the most pencils overall based on the data displayed?

Mr. Simpson's class; it has a larger median value 14.5 pencils
Mr. Johnson's class; it has a larger median of 11 pencils
Mr. Simpson's class; it has a narrow spread in the data
Mr. Johnson's class; it has a wide spread in the data

Answers

Answer:

A)  Mr. Simpson's class; it has a larger median value 14.5 pencils.

Step-by-step explanation:

A box plot is a visual display of the five-number summary:

Minimum value = The value at the end of the left whisker.Lower quartile (Q₁) = The left side of the box.Median (Q₂) = The vertical line inside the box.Upper quartile (Q₃) = The right side of the boxMaximum = The value at the end of the right whisker.

From inspection of the box plots (attached), the measures of central tendency (median) and dispersion (range and IQR) are:

Mr Johnson's class:

Median = 11IQR = Q₃ - Q₁ = 14 - 8 = 6Range = max - min = 45 - 7 = 38

Mr Simpson's class:

Median = 14.5IQR = Q₃ - Q₁ = 21 - 12 = 9Range = max - min = 50 - 0 = 50

In a box plot, the median is a measure of central tendency and tells us the location of the middle value in the dataset. It divides the data into two equal halves, with 50% of the values falling below the median and 50% above it.

The median number of pencils lost in Mr Simpson's class is greater than the median number of pencils lost in Mr Johnson's class. Therefore, Mr. Simpson's class has a larger median value.

The spread of data in a dataset can be measured using both the range and the interquartile range (IQR).

As Mr Simpson's class has a greater IQR and range than Mr Johnson's class, the data in Mr Simpson's class is more spread out than in Mr Johnson's class.

In summary, as Mr Simpson's class has a larger median 14.5 and a wider spread of data, then Mr Simpson's class lost the most pencils overall.

The box plots display data collected when two teachers asked their classes how many pencils they lose

A 799.99 television is selling for 13% off. Find the final price of the television if the sales tax is 6%

Answers

I can’t do that math man…

what is 1/8 as a percentage ?HELP

Answers

Answer:

12.5%

Step-by-step explanation:

Write 18 as a percent. Divide 1 by . Therefore, the fraction 18 is equivalent to 12.5% .

The percent is 12.5%


Write the following numbers in order, putting the largest
first:
a)
31 009
31.53
31. 099
b)
0.007
0.03
0.009

Answers

Answer:

a)

31.53

31.099

31.009 ⬅ (I'm assuming this one is a decimal too)

b)

0.03

0.009

0.007

Explanation:

Here ya go.

Hope this helps :)

Anu was checking her emails she casually told her friend siting next to her the ratio of unread emails in my inbox is 4:1 The total number of emails is 120 what is the number of unread emails in her inbox

Answers

In a case whereby Anu was checking her emails and she casually told her friend siting next to her the ratio of unread emails in my inbox is ratio 4:1 where the total number of emails is 120  then the number of unread emails in her inbox is 96mails.

How can the unread mails be calculated?

The concept that will be used here is ratio. An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls)

The total mails in her box is 120

The we can represent the unread mails  as 4x and read mails be 1x

This can be expressed as :

(4x+1x)=120mails

5x=120mails

x=120/5

x=24

This implies that the uread mails(4×24)

=96mails

Then the number of the read mail =(1×24)=24mails

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If A = (9.18) and B = (1, 12), what is the length of AB?
A. 11 units
B. 9 units
C. 10 units
D. 12 units

Answers

\(d^2=(x_2-d_1)^2+(y_2-y_1)^2\\ \\ d^2=(9-1)^2+(18-12)^2\\ \\ d^2=64+36\\ \\ d=\sqrt{100}\\ \\ d=10\)

The relationship between pressure (P),
volume (V), and temperature (T) for
an ideal gas is stated by the Ideal Gas
Law: PV = nRT, where n is the number
of moles and R is the universal gas
constant. If n is kept constant, which of
these statements is not true according to
the equation?
A Decreased volume at constant
pressure reduces temperature.
B Decreased volume at constant
temperature increases pressure.
C Decreased temperature at constant
volume reduces pressure.
D Decreased temperature at constant
volume increases pressure.

Answers

Answer:

A

Step-by-step explanation:

For an ideal gas : PV=RT

And the internal energy of an ideal gas:

E

in

=

2

3

RT

E

in

=

2

3

PV

V

E

in

=

2

3

P

Energy density (E)=

2

3

P

P=2/3E

4
3
3
2+
-4
-3
-2 -1
1
1
2
3
4
-1+
-2+
-3
-4
What is the slope of the line?

4332+-4-3-2 -111234-1+-2+-3-4What is the slope of the line?

Answers

Answer:

2/3

Step-by-step explanation:

rises 2 units and east 3 units

rise / run = 2 / 3

Find the median and mean of the data set below:
25, 13, 6, 4,2

Answers

Answer: im sorry but there is nothing here to help? may you add a picture? or something file maybe?

Step-by-step explanation:

Natalie is selling fruit at the Saturday market. She has a
otal of 48 pears that she wants to sell. She makes bags of
pears and sells them for $5 per bag. In which equation
oes b represent the number of bags of pears?

Answers

If Natalie puts 4 pears in each bag, she will be able to sell a total of 12 bags of pears at the Saturday market.

To represent the number of bags of pears, b, that Natalie sells at the Saturday market, we can use the following equation:

b = total_number_of_pears / pears_per_bag

In this equation, "total_number_of_pears" represents the total quantity of pears Natalie has, and "pears_per_bag" represents the number of pears she puts in each bag.

Given that Natalie has a total of 48 pears, we can substitute the value into the equation:

b = 48 / pears_per_bag

Now, we need to determine the number of pears she puts in each bag. The information provided states that Natalie sells bags of pears, and each bag is sold for $5. However, the specific number of pears per bag is not given. To proceed, we need this information.

Let's assume that Natalie puts 4 pears in each bag. We can substitute this value into the equation:

b = 48 / 4

Simplifying the equation gives:

b = 12

So, if Natalie puts 4 pears in each bag, she will be able to sell a total of 12 bags of pears at the Saturday market.

It's important to note that the specific value of "pears_per_bag" will affect the final result. If Natalie puts a different number of pears in each bag, the equation will yield a different number of bags sold.

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Which linear function has the same y-intercept as the one that is represented by the graph?

On a coordinate plane, a line goes through points (3, 4) and (5, 0).
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 3, negative 1, 1, 3. Column 2 is labeled y with entries negative 4, 2, 8, 14.
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 4, negative 2, 2, 4. Column 2 is labeled y with entries negative 26, negative 18, negative 2, 6.
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 5, negative 3, 3, 5. Column 2 is labeled y with entries negative 15, negative 11, 1, 5.
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 6, negative 4, 4, 6. Column 2 is lab
eled y with entries negative 26, negative 14, 34, 46.

Answers

The linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

To determine the linear function with the same y-intercept as the graph, we need to find the equation of the line passing through the points (3, 4) and (5, 0).

First, let's find the slope of the line using the formula:

slope (m) = (change in y) / (change in x)

m = (0 - 4) / (5 - 3)

m = -4 / 2

m = -2

Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Using the point (3, 4) as our reference point, we have:

y - 4 = -2(x - 3)

Expanding the equation:

y - 4 = -2x + 6

Simplifying:

y = -2x + 10

Now, let's check the given options to find the linear function with the same y-intercept:

Option 1: The table with x-values (-3, -1, 1, 3) and y-values (-4, 2, 8, 14)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 2: The table with x-values (-4, -2, 2, 4) and y-values (-26, -18, -2, 6)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 3: The table with x-values (-5, -3, 3, 5) and y-values (-15, -11, 1, 5)

The y-intercept is the same as the given line (10). So, this option is correct.

Option 4: The table with x-values (-6, -4, 4, 6) and y-values (-26, -14, 34, 46)

The y-intercept is not the same as the given line. So, this option is not correct.

Therefore, the linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

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Number of Computers
72
60
48
36
24
12
V
1 2 3 4 5 6 7 8 9 10 11 12
Number of Days
The graph shows a proportional relationship between
the number of computers produced at a factory per day.
In three days, 36 computers are produced; 48
computers are produced in 4 days; and 60 computers
are produced in 5 days.
Find the unit rate of computers per day using the graph.
Unit rate:
computers per day

Answers

The unit rate of computers per day using the graph is that 12 computers are made per day.

What is a unit rate?

The unit rate is how many units of quantity correspond to the single unit of another quantity. We say that when the denominator in rate is 1, it is called unit rate. Unit rates is said to be the amount of something in each unit or per unit.

How to find the unit rate of computers per day

To obtain the unit rate of computers sold per day using the graph, we need to obtain the slope of the graph, which is the change in y per change in x

So, it is given by:

\(\text{Slope} = \dfrac{\text{change in y}}{\text{change in x}}\)

\(\text{Slope} = \dfrac{\text{y}_2-\text{y}_1}{\text{x}_2-\text{x}_1}\)

\(\text{y}_2 = 60 , \ \text{y}_1 = 36 , \ \text{x}_2 = 5, \ \text{x}_1 = 3.\)

\(\text{Slope} = \dfrac{(60 - 36)}{(5 - 3)} = \dfrac{24}{2} = 12\)

\(\bold{Slope = 12}\)

Unit rate = 12 computers per day.

The attachment of the graph is given below.

Therefore, the unit rate of computers per day is 12.

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Number of Computers726048362412V1 2 3 4 5 6 7 8 9 10 11 12Number of DaysThe graph shows a proportional

show 2/3 of 4 on the number line.

Answers

The position of the value is shown on the number line attached to this answer.

What is a number line?

A number line is a ray which extends from -∞ to +∞ as its two extreme ends. Thus all number fall within this range such that all directed numbers can be located on the number line.

A directed number is a any number which has either a positive or negative sign. This implies that the position of all numbers can be shown on the line.

Thus, from the question to show 2/3 of 4 on the number line;

2/3 of 4 = 2/3 x 4

             = 8/ 3

             = 2 2/3

The position of 2 2/3 is shown on the number line attached to this answer.

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show 2/3 of 4 on the number line.

What is the maximum value and what is the point the maximum value is at?

What is the maximum value and what is the point the maximum value is at?

Answers

9514 1404 393

Answer:

  z = 47 at (x, y) = (3, 8)

Step-by-step explanation:

In the attached graph, the inequalities are graphed as their opposites, so the feasible solution region is the white area of the graph. The dashed boundary lines are part of the feasible region. The vertex of the feasible region that is farthest from the origin is ...

  (x, y) = (3, 8)

The value of z there is 5·3 +4·8 = 47.

The maximum value of z is 47 at the point (x, y) = (3, 8).

What is the maximum value and what is the point the maximum value is at?

Pregúntales a tus compañeros qué compraron para el almuerzo ayer. Anota las respuestas. Después escribe un resumen de los resultados

Answers

Answer:

"Que compraste para el almuerzo ayer?"

"yo me compre una torta de huevo" = i bought an egg sandwich

"yo no compre nada porque comi cereal en la manana"= I didn't buy anything since i had eaten cereal in the morning

very urgent

A construction worker drew a sketch he will use as he works.
Which statement is not true?
A. The distance from the ground to the pipe is 2.5 feet.
B. The distance between the pipe and the rope is 1 foot.
C. The distance between the ground and the rope is 5 feet.
D. The distance from the ground to the pipe is 1 foot less than the distance from the ground to the rope.

Answers

Answer:

wheres the word problem portion of the question

Step-by-step explanation:

tell me and I'll be happy to answer you

Guided Practice

Type your answer and then click or tap Done.

For the equation y = 3x2 + 12x − 4, what is the minimum value?

Fill in the blank text field 1

Answers

Answer: The vertex is (−2, −16).

Use the formula  x

=

b/

2

a  to find the maximum and minimum.  (

2

,

16

)

Step-by-step explanation:  (-2, -16)    

For the equation  y

=

3

x

^2

+

12

x

4  , what is the minimum value?

The minimum of a quadratic function occurs at  x

=

b

/2

a

. If  a  is positive, the minimum value of the function is  f

(

b

/2

a

)

.

f

minx

=

a

x

^2

+

b

x

+

c  occurs at  x

=

b

/2

a

Find the value of  x

=

b

/2

a

.

Tap for more steps...

x

=

2

Evaluate  f

(

2

)

.

Tap for more steps...

16

Use the  x  and  y  values to find where the minimum occurs.

(

2

,

16

)

image of graph

Guided PracticeType your answer and then click or tap Done.For the equation y = 3x2 + 12x 4, what is

PLEASEEEEEEEEE HELPPP!!!!! IM BEGGIN PLEASE !!!!!(show work)


give explanation (optional)

PLEASEEEEEEEEE HELPPP!!!!! IM BEGGIN PLEASE !!!!!(show work)give explanation (optional)

Answers

Ok so the 1st one as a two decimal is 3520.46 and the second is 81285.48

Please help!
Whoever answers right gets brainliest!!!!

Please help!Whoever answers right gets brainliest!!!!

Answers

Answer:

\(y - 4 = - 3(x - 2)\)

3 Jack walk from Santa Clara to Polo Allo. Il took I hour 25 min to walk from Santa Clot to Los Altos. Than it took 25 minute of wal from los altos to Palo buto. He arrived in Palo alto at 2:45 P.M. of what time die Santa Clara ? he leave Santa clara​

Answers

The time Jack left Santa Clara is 1 : 55 pm

What is word problem?

A word problem in math is a math question written as one sentence or more. These statements are interpreted into mathematical equation or expression.

The time for Jack to walk to lose Altos is 25 min and he uses another 25mins to work to Palo alto.

Therefore, the total time he spent is

25mins + 25 mins = 50 mins

He arrived Palo at 2 :45 pm, therefore the time he left Santa Clare will be ;

2:45 pm = 14 :45

= 14:45 - 50mins

= 13:55

= 1 : 55pm

Therefore he left at 1:55 pm

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A primary credit card holder has a current APR of 15.75%. What is the monthly periodic interest rate, rounded to the nearest hundredth of a percent?
O 15.75%
O 13.13%
O 1.31%
O 0.01%

Answers

the mοnthly periοdic interest rate, rοunded tο the nearest hundredth οf a percent is (C) 1.31%

What dοes mοney interest mean?  

Any lοans and bοrrοwings cοme with interest. the percentage οf a lοan balance that lenders use tο determine interest rates. Cοnsumers can accrue interest thrοugh lending mοney (via a bοnd οr depοsit certificate, fοr example), οr by making a depοsit intο a bank accοunt that pays interest.

We must divide its yearly percentage rate (APR) by 12 tο determine a mοnthly periοdic interest rate (the number οf mοnths in a year).

Hence, the periοdic interest rate fοr each mοnth is:

15.75% / 12 = 1.3125%

The result οf rοunding tο the clοsest hundredth οf such a percent is:

1.31%

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recall that when ab =0, either a or b must be 0. How does this property help you solve quadratic equations

Answers

This type of property helps us to solve quadratic equations by allowing us solve the two linear equations.

What is Quadratic equation?

This is referred to as a type of polynomial which has the highest degree of 2.

In solving for the values in a quadratic equation, there are two linear equations which employs the zero product property which states that that if ab=0, then either a or b is equal to 0.

In a scenario where we have (x-4)(x+3)=0 as the two linear equations of a quadratic equation, we can get the values which would be 4 and -3 respectively.

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If Fran were to paint her living room alone, it would take 6 hours. Her sister Denise could do the job in 8 hours. How many hours would it take them working together? Express your answer as a fraction reduced to lowest terms, if needed.

Answers

It would take Fran and Denise (working together) approximately \(\frac{24}{7}\) hours to paint the living room.

To solve this problem, we can use the concept of "work rates."

Let's find out how much work Fran and Denise can do individually in one hour.

If Fran takes 6 hours to paint the living room alone, her work rate is \(\frac{1}{6}\) of the room per hour \((\frac{1 room}{6 hours } = \frac{1}{6}room/hour )\).

Similarly, if Denise takes 8 hours to paint the living room alone, her work rate is \(\frac{1}{8}\) of the room per hour \((\frac{1 room}{8 hours } =\frac{1}{8}room/hour )\).

When they work together, their work rates are additive.

So, their combined work rate would be:

\(\frac{1}{6} room/hour+\frac{1}{8} room/hour\)

\(=(\frac{4}{24} )room/hour + (\frac{3}{24} )room/hour\)

\(=\frac{7}{24} room/hour\)

This means that working together, Fran and Denise can paint \(\frac{7}{24}\) of the living room in one hour.

To determine the total time required for them to paint the entire room, we can invert their combined work rate:

\(\frac{(1 room) }{(\frac{7}{24}room/hour) } =\frac{24}{7}hour\)

Therefore, it would take Fran and Denise (working together) approximately \(\frac{24}{7}\) hours to paint the living room.

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