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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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Anna11 [10]

Answer:

y/x

Step-by-step explanation:

If x is proportional to y, then:

y = kx, where k is a constant

This can be rearranged to give:

k = y/x

As mentioned, k is a constant, therefore, the answer is y/x

7 0
2 years ago
Nanu borrowed a certain sum at the rate of 10 % p.a. If she paid compound interest Rs. 1,290 at the end of two years compounded
Leokris [45]

Answer:

whats your answer please give

5 0
2 years ago
Help I need to know I only have 15 min <br> What does x equal in x/2=-5
SSSSS [86.1K]

Answer:

x= -10

Step-by-step explanation:

Brainliest please? :)

3 0
3 years ago
The area of a square is 49 square meters. How long is each side?
Artemon [7]

A square has 4 equal sides, which means when you need to work out the area, you're doing length × width, but the length and width are exactly the same, because it's a square (look at the picture if you don't understand this).

That means you just have to pick any side (let's call this side x), and multiply it by another side of the square. Now, because all of the sides are equal, you're doing x multiplied by x, which is the same as x².

Therefore, if the area is equal to x², and in this question, it's also equal to 49 (as stated in the question), we can equate them to each other:

x² = 49

Now to get the x by itself, we need to do the opposite of squaring, which is square rooting. Therefore, we square root both sides of the equation:

√x² = √49

The √ and the ² cancel out, so you're just left with x:

x = √49

The square root of 49 is just 7, so we can replace √49 with 7, and we get:

x = 7

Now remember, earlier, I called x the value of one side. Therefore, by remembering that, you know that the value of one side is equal to 7. And because all the sides are the same as each other, each side is equal to 7 metres.

Therefore, your final answer is 7 metres :)

3 0
3 years ago
To paint a sunset, you make a shade of orange paint using 55 drops of red paint for every 88 drops of yellow paint. If you use 1
alexandr402 [8]
Since the ratio of red drops to yellow drops is 55:88 and you have 1515 red drops, the yellow drops needed is given as
If 55=1515
   88=?
88/55*1515=2424
therefore 2424 drops of yellow will be needed to make a shade of orange
8 0
3 years ago
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