Find the volume of the given solid.
Bounded by the coordinate planes and the plane
6x + 7y + z = 42

Answers

Answer 1

The volume of the given solid is equal to the triple integral of 1 over the region bounded by the coordinate planes and the plane 6x + 7y + z = 42. This can be written as:

[tex]$\iiint 1\, dV = \iiint 1\, dx\, dy\, dz$[/tex]

The region of integration is bounded by the coordinate planes x = 0, y = 0, and z = 0, and the plane 6x + 7y + z = 42. This is a right triangular prism with vertices (0,0,0), (6,0,0), and (0,6,42). To calculate the volume, we will use the triple integral in cylindrical coordinates, which can be written as:

[tex]$\iiint 1\, dV = \int0^{2\pi}\int0^6\int_0^{42/7} r\, dz\, dr\, d\theta$[/tex]

The volume of the given solid is given by:

[tex]$\frac{504\pi}{7}$[/tex]

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Related Questions

pls helpp i'll give u brainliest

Answers

Answer:

(-5, -1)

Step-by-step explanation:

Equation Form:

x = -5

y = -1

Answer:

Solve the System of Equations

Solve for the first variable in one of the equations, then substitute the result into the other equation.

Point Form:

(−5,−1)

Equation Form:

x= −5, y= −1

Solve for x. The triangles in each pair are similar.

Answers

Apply arithmetic operations on both sides of the equation to move the variable to one side and all other values to the opposite side.

How Do You Solve for x?

Let's begin with a basic equation: x + 2 = 7.

How may x be obtained on its own?

x + 2 - 2 = 7 - 2 x = 5 after deducting 2 from both sides.

Put the solution, x = 5, back into the equation to confirm it. We get 5 + 2= 7.

Since LHS = RHS

In the triangle, find x.

Use triangle properties or the Pythagorean theorem to find the value of x, the unknown side or angle in a triangle.

Let's use an example to better understand how to solve for x in a triangle.

Using the Pythagorean theorem, we obtain AC2 = AB2 + BC2 where x2 = 72 + 242 x = 49 + 576 x = 625 x = 25 units.

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Answers

Answer:

I think a but I'm not sure

Question 1 of 10
How many lines of symmetry are there in the object pictured below?
A. O
B. 1
C. 3
D. 2

Answers

Answer:

B. 1

Because of the shape you can have only one line of symmetry

How do you find the missing side of a right triangle without a calculator?

Answers

The missing side of a right triangle without using a calculator can be found by using the Pythagoras theorem .

What is Pythagoras Theorem ?

The Pythagoras Theorem states that the square of the hypotnuse (longest side) is equal to the sum of the square of the perpendicular and base .

that means : [tex]Hypotnuse^{2} = Perpendicular^{2} + Base^{2}[/tex]  ;

let the missing side of the right triangle  be the hypotnuse ;

So , missing side can written as :  [tex]Hypotnuse = \sqrt{Perpendicular^{2} + Base^{2}}[/tex] .

For Example : Let the right triangle has sides lengths as perpendicular = 6 and hypotnuse = 10

The length of side "base" is unknown.

So ,  to find length of side b, we put the known values into theorem:

[tex]10^{2} = 6^{2} + Base^{2}[/tex] ;

[tex]base^{2} = 100 - 36[/tex] ;

So , the missing side "base" = 8 ;

Therefore , the missing side without using calculator can be found by the Pythagoras Theorem .

The given question is incomplete , the complete question is

How do you find the missing side of a right triangle without a calculator when the other two sides are given ?

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pleaseeee helpppppppppp

Answers

Answer:

A

Step-by-step explanation:

will give brainliest please

Answers

Answer:

Step-by-step explanation:

a. we konw triangle have 180°

b. A straight line have 180°, so

∠abc=180-5x-12=168-5x,

∠bca=180-10x+37=217-10x

∠cab=180-9x-1=179-9x

then  add them all 564 - 24x = 180

c.384=24x, x=16

d.so ∠bca=217-10·16=57.

Answer:

m∠BCA = 57°

-------------------------------------------

Sum of exterior angles is 360°:

9x + 1 + 5x + 12 + 10x - 37 = 36024x  - 24 = 36024x = 384x = 384/24x = 16

The exterior angle at vertex C is:

10x - 37 = 10*16 - 37 = 160 - 37 = 123

The ∠BCA is the linear pair with 123°:

m∠BCA = 180° - 123° = 57°

b) Felipe is deciding how many people to take to the movies. The table below
shows the cost for different sized groups of people.
Number in group
Cost (in dollars)
2
10
3
9
15 45
The cost for each person is not always the same.
O The cost for each person appears to be the same.
Predicted number in group for a cost of $50:

Answers

Answer:The cost for each person is not always the same. It is not a linear relationship between number in group and cost in dollars. Since we have only 4 rows it's difficult to make an accurate prediction for cost of $50, In addition, we don't have any formula or equation that can represent this data set.

The best way to find out how many people will go to movie with $50 is by looking at the table.

So the answer is, We don't have any information that can give us a prediction of number in group for a cost of $50,

Step-by-step explanation:

heyy! i’ll give brainliest please help

Answers

Answer:

Name as a person

Step-by-step explanation:

Answer:

In the name of a person.

Step-by-step explanation:

The seasons are not written with capital letters unless they form part of a name. For example:

I am leaving in the winter.

I live near Winter Mountain River.

el numero decimal 3,1 representa a la fraccion 3 entre 10

Answers

Answer:

ne cheaso le uprenta singil layu ka bts dung lyr

Need help on both plz help me ASAP!

Answers

Answer:

graph 1= 3. graph 2= -3

Step-by-step explanation:

the y-intercept is where it cuts the line

therefore,

graph 1=3

graph 2=-3

Graph 1 is 3 and graph 2 is -3

Which equation shows how to use equivalent fractions to evaluate 7/6-4/5

Answers

Answer:How do you evaluate equivalent fractions?

Summary:

You can make equivalent fractions by multiplying or dividing both top and bottom by the same amount.

You only multiply or divide, never add or subtract, to get an equivalent fraction.

Only divide when the top and bottom stay as whole numbers.

Step-by-step explanation:

Encircle the correct formula in getting the area of the shaded region

Answers

Answer:

1. A=bh/2

2. I don’t know, I‘m sorry :(((( but if I had to guess I’d pick A = s x s

3. A = πr² (might be wrong, i’m so sorry)

Step-by-step explanation:

1.  The formula for area of a triangle is A = bh/2

2. The formula for area of a square is s x s.

3. The formula for area of a circe is A = πr².

The formula used in getting the area of the shaded region is (1/2)bh, s * s and  πr²

What is an area?

An area is the amount of space occupied by a two dimensional shape or object.

1) The area of a triangle = (1/2) * base (b) * height (h) = (1/2)bh

2) Area of square = side (s) * side(s) = s * s

3) Area of circle = π * radius (r)²= πr²

The formula used in getting the area of the shaded region is (1/2)bh, s * s and  πr²

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Suppose m = 2 + 6i, and║m + n║ = 3√10, where n is a complex number.
a. What is the minimum value of the modulus of n?
b. Provide one example of the complex number, n.

Answers

Answer:

the modulus of a complex number z = a + bi is:

Izl= √(a²+b²)

The fact that n is complex does not mean that n doesn't has a real part, so we must write our numbers as:

m = 2 + 6i

n = a + bi

Im + nl = 3√10

√(a² + b²+ 2²+ 6²)= 3√10

√(a^2 + b^2 + 40) = 3√10

squaring both side

a²+b²+40 = 3^2*10 = 9*10 =90

a²+b²= 90 - 40

a²+b²=50

So,

|n|=√(a^2 + b^2) = √50

The modulus of n must be equal to the square root of 50.

now

values a and b such

a^2 + b^2 = 50.

for example, a = 5 and b = 5

5²+5²=25+25= 50

Then a possible value for n is:

n = 5+5i

a) 3.2 ÷ 0.8 = ? please explain how you got it and b) 7.5 ÷ 0.5 also please explain how you got it i'll give the brain thing​

Answers

Answer: To solve a division problem of the form a ÷ b = c, you need to find the value of c that makes the equation true. This means that if you multiply b by c, the result should be equal to a.

a) In the problem 3.2 ÷ 0.8 = ?, we are looking for the value of c that makes the equation true.

To solve this problem, we can multiply 0.8 by c to find the value of c that makes the equation true:

0.8 * c = 3.2

Dividing both sides of the equation by 0.8, we get:

c = 4

Therefore, the value of c that makes the equation 3.2 ÷ 0.8 = ? true is 4.

b) In the problem 7.5 ÷ 0.5 = ?, we are looking for the value of c that makes the equation true.

To solve this problem, we can multiply 0.5 by c to find the value of c that makes the equation true:

0.5 * c = 7.5

Dividing both sides of the equation by 0.5, we get:

c = 15

Therefore, the value of c that makes the equation 7.5 ÷ 0.5 = ? true is 15.

P.S. I don't need a brainliest, i am just happy that I am helping someone

Step-by-step explanation:

If 4, 6 and 8 and 14, 21, and x are the lengths of the corresponding sides of two similar triangles, what is the value of x

Answers

When you add all the numbers up and then divide by two you get the answer

The question is in the picture

Answers

Answer:

For the first line its distributive property
The 2nd is combining like terms

4th is simplifying it

Im not sure about the last one since its just the answer of the problem

Step-by-step explanation:

HELPPPPppPPppPpP MeEEEeEEEE PLEASEEEEeEeeEEe

Answers

Last answer is the correct.
Distance between each hour is the same-13 miles. Good luck.

The length of AB (the minor arc) is 40 cm. What is the circumference of C?

A. 360 cm
B. 120 cm
C. 60 cm
D. 240 cm
E. 6.67 cm
F. 24 cm

Answers

Answer: 240 cm

Explanation : the circumference of C is: 6 X 40=240

A horse walks 4224 feet in 12 minutes at this rate how many yards does a horse walk in twelve minutes.

Answers

Answer:

1408 yards

Step-by-step explanation:

A horse walks 4224 feet in 12 minutes, so to find out how many yards the horse walks in twelve minutes, we need to convert 4224 feet to yards. Since there are 3 feet in a yard, we can divide 4224 by 3 to find the number of yards:

4224 feet / 3 feet/yard = 1408 yards

So a horse walks 1408 yards in 12 minutes.

Seacausus stadium has a seating capacity for 25,000 spectators. The stadium has 25 exits and can be vacated in 20 minutes. The time taken to exit the stadium varies directly with the number of spectators and inversely with the number of exits. Determine the time taken for 21,000 spectators to vacate the stadium, if only 15 exits are functional.

Answers

The time taken for 21,000 spectators to vacate the stadium, if only 15 exits are functional is 28 minutes

How to determine the time taken for 21,000 spectators to vacate the stadium?

A variation is a relation between a set of values of one variable and a set of values of other variables

Let E, N and T represent the number of exits, the number of spectators and the time taken to exit the stadium respectively

We can write the variation as:

T α N/E

T = kN/E  (where k is constant of proportionality)

when N = 25,000, E = 25, T = 20:

T = kN/E

k = TE/N

k = (20×25)/25000 = 0.02

when N = 21,000 and E = 15:

T = kN/E

T = (0.02×21,000)/15 = 28 minutes

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Which expression is not equivalent to logp 36? 1. 6 log 2 2. log 9+ Iog, 4 O 3 2 logb 6 4. log 72 logp 2

Answers

log 30+ log 6 is not equivalent to log 36

What is equivalent expressions?

Equivalent expressions are expressions that perform the same function not with standing their appearance. If two algebraic expressions are equivalent, they have the same value when the same value(s) for the variable are used (s).

The original phrase is as follows

Log 36

Following that, we write the alternatives (a) log 2+ log 18

Apply the logarithmic rule log 2+ log 18 log (218)

Log 2 plus log 18 log (36)

Remove the bracket

Log 2 plus log 18 log36

(a) Log 2+ Log 18 is the same as log 36.

(b) Log 30 plus log 6

Use the logarithms’ law. 30 logs or more 6 logs (30 x 6)

Log 30 plus log 6 Equals log (180)

Remove the bracket

Log 30-plus log 6-log180

Hence,

(c) Log 30+log 6 does not equal log 36.

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Please help me! Urgent, thanks!

The lowest common multiple of 60, 156 and n is 10920. Find the smallest possible value of n.

60 = 2² x 3 x 5
156 = 2² x 3 x 13
10920 = 2³ x 3 x 5 x 7 x 13

Answers

Answer:

2 cube into 3 into 5 into 13 into 7

2 cube into 5 something

find x using the trig ratios please

Answers

Answer:

12.9

Step-by-step explanation:

cos 72 = 4/x

x = 4/cos72

x = 12.9

Find the volume and round to the nearest hundredths place when necessary.

Answers

Answer:

477

Step-by-step explanation:

Answer:

half of 8 is 4

4^4 = 16

16 x 3.14 = 50.24 (area of a circle)

Now we multiply it by the height:

50.24 x 19 = 954.56 rounded to the nearest hundredths place is:

954.56 yd3 is your answer.

2x. 4
Find the measure of the
exterior angle shown.
75°
(13x - 1990

Answers

Answer:

75 hope it helps you

thank you

Factor by gcf 5x + 20 please someone

Answers

Answer:

5 (x + 4)

Step-by-step explanation:

5x = 5 * x

20 = 5 * 4

5 is the only thing thye have in common, so we put 5 in front and add x + 4

5 (x + 4)

5(x+4) is the correct answer



3. ) Copy Center charges $0. 08 a page for machine fed copies and $0. 20 per page for hand-fed copies. I lagan's

bill for 80 copies of his movie script is $13. 00, how many copies of each type were made?

Answers

The number of machine fed copies are 25 and the number of hand fed copies are 55. This is solved forming simultaneous equations.

What are simultaneous equations?

Two or more algebraic equations that share variables, such as x and y, are said to be simultaneous equations. Since the equations are solved simultaneously, they are known as simultaneous equations. These equations alone could have an infinite number of solutions.

Given cost per page of machine fed copies = $0.08

          cost per page of hand fed copies = $0.20

Let,

  number of machine fed copies = x

 number of hand fed copies = y

Given the total number of copies = 80

So we can write the equation as

  x + y = 80  ⇒   (1)

It is also given that the total cost of the movie script is $13

So we can the equation as

0.08x + 0.20y = 13 ⇒ (2)

Solving the simultaneous equations (1) and (2)

From (1),

x = 80 - y

Substituting the above in (2)

0.08(80 - y) + 0.20y = 13

0.12y = 6.6

y = 55

x = 80 - 55 = 25

Therefore the number of machine fed copies are 25 and the number of  hand fed copies are 55.

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What literary device did Oscar Wilde use?

Answers

Oscar Wilde creates a hilarious tone by using puns, situational irony, dramatic irony, satire, and epigrams.

Who is Oscar Wilde?

Oscar Fingal O'Flahertie Wills, an Irish poet, and playwright, lived from 16 October 1854 to 30 November 1900.

He wrote in a variety of genres throughout the 1880s before becoming one of London's most well-known playwrights in the early 1890s.

The Picture of Dorian Gray, his plays and epigrams, as well as the circumstances surrounding his meningitis-related early death at age 46 and criminal conviction for gross indecency for consensual homosexual activities in "one of the earliest celebrity trials," is what people will remember him for most.

Using puns, situational irony, dramatic irony, satire, and epigrams, Oscar Wilde establishes a humorous tone.

Therefore, Oscar Wilde creates a hilarious tone by using puns, situational irony, dramatic irony, satire, and epigrams.

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Fill in the missing number. % of 70 = 63

Answers

90% of 70 = 63 is the answer I believe
90% should mine that Awser I belive
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