1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Arturiano [62]
3 years ago
9

Find the volume of the following solid. The solid between the cylinder ​f(x,y)equals=e Superscript negative xe−x and the region

Requals=StartSet left parenthesis x comma y right parenthesis : 0 less than or equals x less than or equals ln 6 comma negative 6 less than or equals y less than or equals 6 EndSet{(x,y) : 0≤x≤ln6, −6≤y≤6}. An x y z coordinate system has a positive x-axis with a tick mark at ln 6, a y-axis with tick marks at negative 6 and 6, and a positive z-axis. A surface labeled f left parenthesis x comma y right parenthesis equals e Superscript negative x has a rectangular projection in the x y plane that extends between x-coordinates 0 and ln 6 and between y-coordinates negative 6 and 6. All cross sections of the surface parallel to the x z plane are identical curves that fall at a decreasing rate from x-coordinate 0 to a x-coordinate ln 6, with a z-coordinate greater than 0 at x-coordinate ln 6. ln 6ln6 66 66 The volume of the solid is
Mathematics
1 answer:
PilotLPTM [1.2K]3 years ago
7 0

It is hard to comprehend your question. As far as I understand:

f(x,y) = e^(-x)

Find the volume over region R = {(x,y): 0<=x<=ln(6), -6<=y <= 6}.

That is all I understood. It would be easier to understand with a picture or some kind of visual aid.

Anyways, to find the volume between the surface and your rectangular region R, we must evaluate a double integral of f on the region R.

\iint_{R}^{ } e^{-x}dA=\int_{-6}^{6} \int_{0}^{ln(6)} e^{-x}dx dy

Now evaluate,

\int_{0}^{ln(6)}e^{-x}dx

which evaluates to,  5/6 if I did the math correct. Correct me if I am wrong.

Now integrate this w.r.t. y:

\int_{-6}^{6}\frac{5}{6}dy = 10

So,

\iint_{R}^{ } e^{-x}dA=\int_{-6}^{6} \int_{0}^{ln(6)} e^{-x}dx dy = 10

You might be interested in
When Mr. Gree bought a used car he made a
Ilya [14]

Answer:

2750

Step-by-step explanation:

825/30=27.5

27.5X100=2750

7 0
3 years ago
What happened that caused Brian to lose his shelter and all of his belongings? (picture in link) helpp pls fast!
Lilit [14]

Answer:

Step-by-step explanation:

Can I have the rest of the question(picture)?

3 0
3 years ago
Read 2 more answers
Please helpppp
Zarrin [17]

Answer:

|(15,055) is the number of pages in a book with

15,055 words.

Step-by-step explanation:

becuz the no of pages is a function to the words ..

8 0
3 years ago
The sum of two non-zero numbers a and b equals the sum of their reciprocals. If a+b≠0, what is the product of the two numbers?
Vadim26 [7]

Answer:

ab = 1

Step-by-step explanation:

A Reciprocal of a number is a number which when multiplied by the original number yields the multiplicative number, 1.

So the reciprocal of x would be x⁻¹ or ¹⁄ₓ

The information we are given states that the sum of the two non-zero numbers a and b equals the sum of their reciprocals.

So we can write this into an equation and solve,

(See image)

Once we solve, we get the equation (ab-1)(a+b) = 0

We are given info that a+b≠0

So for the above equation to be true, ab-1 has to equal 0

For <em>this</em> to be true, the product ab must equal 1

7 0
3 years ago
What is the value of x in the equation 5(4x-10)+10x=4(2x-3)+2(x-4) ?
MrRissso [65]
5(4x - 10) + 10x = 4(2x - 3) + 2(x - 4)
20x - 50 + 10x = 8x - 12 + 2x - 8
30x - 50 = 10x - 20
30x - 10x = -20 + 50
20x = 30
x = 3/2 <==
6 0
4 years ago
Read 2 more answers
Other questions:
  • Maurice has made 13 litres of nutritious toothpaste soup which he plan to share equally between himself and his four best friend
    5·1 answer
  • Order the set of numbers from least to greatest 64,8 1/3, 8.14, 15/2
    12·2 answers
  • What is 0.7 in word form
    13·2 answers
  • A(7, −3), B(9, 7) (a) Find the distance d(A, B) between A and B. (Round your answer to two decimal places.) d(A, B) =
    9·1 answer
  • 1. What would the polynomial x + 7 – 4x^3 be written as in standard form?
    10·1 answer
  • H e l p ; - ; <br><br>idk how to manipulate it ; - ; .
    6·1 answer
  • What formula should be used when factoring the expressionn x^3+27
    9·1 answer
  • The angle of elevation from ground level to the top of a water tower that is 280 feet away measures 27 degrees. What is the heig
    14·1 answer
  • Help me find <br> the y-intercept <br> The slope <br> The equation of the line<br> Please
    6·2 answers
  • the vertex of parabola is (-2,-3).when the y-value is -2 , the x-value is -5. what is the coefficient of the squared expression
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!