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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

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Help pls I need homework done soon!
Cloud [144]

The resulting expression is -9.661

<h3>Solving by substitution</h3>

Given the expression below;

-a+(-b)

Given the following

a = 6.05

b = 3.611

Substitute the given parameters into the formula

-a+(-b) = -6.05 + (-3.611)

-a+(-b) = -6.05 - 3.611

-a+(-b) = -9.661

Hence the resulting expression is -9.661

Learn more on substitution method here; brainly.com/question/22340165

#SPJ1

8 0
2 years ago
Suppose a bag of marbles has 4 green, 2 red, 5 yellow, 1 brown, and 7 blue marbles. What is the probability of picking a green m
nata0808 [166]

The bag of marbles has 4 green, 2 red, 5 yellow, 1 brown, and 7 blue marbles.

Total number of marble=4+2+5+1+7=19

The probability P(E) is defined as P(E)=\frac{n(E)}{n(s)}

where n(E) is the total number of favourable events.

and n(s) is the total number of events

Hence for the given data we can write

P(E)=\frac{4}{19}

Because total number of green marbles = n(E)=4

Total number of Marbles =n(S)=19

Hence P(E)=4/19

4 0
3 years ago
Read 2 more answers
Help please! I don't understand these...
melisa1 [442]
Number 4 (as asked in comments)

57 degrees
21 legnth shadow
drwa diagram

remember
SOHCAHTOA
we need last one
tan of angle=oposite angle/ajacent
oposite angle=height=?
ajacent=21
angle=57
tan(57)=?/21
multiply both sides by 21
21tan(57)=?
use calculator
32.3372 m
h=32.3372m (round if nececary)


5 0
3 years ago
Solve for y 11(y-2)+3y=-7y+14
Greeley [361]
11y - 22 + 3y = -7y + 14
*combine like terms*
       14y - 22 = -7y + 14
                21y = 36
                     y = 36/21 = 12/7 or 1 5/7

hope this helps :)

6 0
3 years ago
HELP if you’re smart answer all 9 questions its easy<br><br> NO LINKS!!! pls be correct
Nesterboy [21]

Step-by-step explanation:

if it's easy why don't you do it. not trying to be rude are whatever

8 0
3 years ago
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