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
chubhunter [2.5K]
1 year ago
9

Find the area of the part of the plane 3x 2y z = 6 that lies in the first octant.

Mathematics
1 answer:
gavmur [86]1 year ago
5 0

The area of the part of the plane 3x 2y z = 6 that lies in the first octant  is  mathematically given as

A=3 √(4) units ^2

<h3>What is the area of the part of the plane 3x 2y z = 6 that lies in the first octant.?</h3>

Generally, the equation for is  mathematically given as

The Figure is the x-y plane triangle formed by the shading. The formula for the surface area of a z=f(x, y) surface is as follows:

A=\iint_{R_{x y}} \sqrt{f_{x}^{2}+f_{y}^{2}+1} d x d y(1)

The partial derivatives of a function are f x and f y.

\begin{aligned}&Z=f(x)=6-3 x-2 y \\&=\frac{\partial f(x)}{\partial x}=-3 \\&=\frac{\partial f(y)}{\partial y}=-2\end{aligned}

When these numbers are plugged into equation (1) and the integrals are given bounds, we get:

&=\int_{0}^{2} \int_{0}^{3-\frac{3}{2} x} \sqrt{(-3)^{2}+(-2)^2+1dxdy} \\\\&=\int_{0}^{2} \int_{0}^{3-\frac{3}{2} x} \sqrt{14} d x d y \\\\&=\sqrt{14} \int_{0}^{2}[y]_{0}^{3-\frac{3}{2} x} d x d y \\\\&=\sqrt{14} \int_{0}^{2}\left[3-\frac{3}{2} x\right] d x \\\\

&=\sqrt{14}\left[3 x-\frac{3}{2} \cdot \frac{1}{2} \cdot x^{2}\right]_{0}^{2} \\\\&=\sqrt{14}\left[3-\frac{3}{2} \cdot \frac{1}{2} \cdot x^{2}\right]_{0}^{2} \\\\&=\sqrt{14}\left[3.2-\frac{3}{2} \cdot \frac{1}{2} \cdot 3^{2}\right] \\\\&=3 \sqrt{14} \text { units }{ }^{2}

In conclusion,  the area is

A=3 √4 units ^2

Read more about the plane

brainly.com/question/1962726

#SPJ4

You might be interested in
The teacher asks Mel and Kate to use base 10 blocks to model the number that is ten times the value of 4 rods. Mel's modle uses
AveGali [126]
Kate's model is correct because 10 times the value of 4 rods, 10(4(10)), is 400. Mel's model represents 4(1)=4, which is incorrect. Kate's model represents 4*100=400, which is correct.
Hope I answered your question!
4 0
3 years ago
i have math questions that i need answers for please loook at the photos, please do them in order so i know please and thankssss
nikitadnepr [17]

The first picture about the rational numbers I am not sure the answer.

In the second picture the set that are all equivalent to the fraction is the second set.

In the third picture

the equivalent expression is the first one.

In the fourth picture the correct situation is the first one about buying popcorn.

Hope this helps a little, sorry I could not help more.

7 0
3 years ago
A block of cheese has a volume of 178 cm3 and a mass of 120 g.
Anna35 [415]

Answer:

375

Step-by-step explanation:

7 0
3 years ago
Solve the system of equations by finding the reduced row-echelon form of the augmented matrix for the system of equations.
ycow [4]

This  involves quite a lot of arithmetic to do manually.

The first thing you do is to make the first number in  row 2  = to 0.

This is done by R2 = -3/2 R1 + R2

so the matrix becomes

( 2        1          1)    ( -3 )

( 0    -13/2   3/2)   (1/2 )

(5       -1           2)  (-2)

Next step is to make  the 5 in row 5  = 0  

then  the -1  must become zero

You aim  for the form

( 1 0 0) (x)

(0 1 0) (y)

(0 0 1) ( z)

x , y and z will be the required solutions.


4 0
3 years ago
Read 2 more answers
Express the fraction 6/22 as a percent. Round the answer to the nearest whole percent.
faltersainse [42]

Answer:

27%

Step-by-step explanation:

6 divided by 22 times 100= 27%

5 0
3 years ago
Other questions:
  • A.y=x-1<br> B.y=x+1<br> What does the graph represent?
    8·1 answer
  • AC is the perpendicular bisector of ZB. What can you predict about AZ and AB
    8·2 answers
  • HELP I REALLY REALLY NEED THIS HELP MEE SUPER EZ 28 POINTS I REALLY NEED THIS I DONT REALLY CARE IF ITS WRONG AT LEAST YOU TRY ;
    7·1 answer
  • I NEED IT ASAP PWEASE A function, g(x), has an x-intercept of 5 and a slope of -3. Another function, f(x), is given by the graph
    11·2 answers
  • Hello<br><br><br><br><br>jdbshsvejdjduxyxbdbecenrlxndbdhdnfbbfbd​
    5·2 answers
  • Need help with the answer for both questions!!!!!!!!
    14·1 answer
  • The functions f(x) and g(x) are shown below:
    12·1 answer
  • PLS HELP! <br> which of the following shows an example of the identity property of 0?
    9·1 answer
  • Which graph represents the solutions to the inequality |2x − 6| &lt; 4? (5 points) number line with a closed circle on 1, shadin
    8·1 answer
  • Please help me im begging ANYONE​
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!