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
Nesterboy [21]
3 years ago
14

Find the mass of the triangle with vertices (1; 0; 0), (0; 2; 0), (0; 1; 1) if the density function is given by (x; y; z)

Mathematics
1 answer:
Luda [366]3 years ago
3 0

Answer:

=\frac{17}{3}

Step-by-step explanation:

Density of a function is \rho(x,y)=x^{2} +y^{2}

I have drawn the right angle triangle for visualization

equation for the line passing through (1,0) and (0,4) is

\frac{y}{4} =\frac{x-1}{-1}

y=4-4x

=$$\int_{0}^1\int_{0}^{4-4x} (x^{2}+y^{2})dydx$$

=$\int_{0}^{1}(x^{2}+\frac{y^{3} }{3})dx$  

=$\int_{0}^{1}(x^{2}(4-4x)+\frac{1}{3}(4-4x)^{3} )dx$

=$\int_{0}^{1}(\frac{-76}{3}x^{3} +68x^{2}-64x^{}+\frac{64}{3}  )dx$

==(\frac{-76}{3} \frac{x^{4} }{4})+\frac{68}{3}x^{3}-32x^{2}+\frac{64}{3}x^{})  

=\frac{17}{3}

You might be interested in
Find the sum.
hichkok12 [17]

Answer:

C - 19/24

Step-by-step explanation:

Take the fractions and put the denominators into a common factor

\frac{1}{3}+ \frac{1}{3}+ \frac{1}{8}

\frac{8}{24}+ \frac{8}{24}+ \frac{3}{24}

Add Numerators Across

\frac{16}{24}+ \frac{3}{24}

\frac{19}{24}

8 0
3 years ago
Find the surface area of the figure.<br> PLEASE HELP!
olya-2409 [2.1K]

Answer:

The total surface area is: 468 in^2  which agrees with answer a)

Step-by-step explanation:

The three lateral faces of the prism are rectangles, and the sums of their areas give:

12 * 10 + 9 * 10 + 15 * 10 = 360 in^2

The area of each triangular base (notice it is a right triangle) is given by:

9 * 12 / 2 = 54 in^2, so we add TWO of these to the three rectangular faces:

Total surface = 360 in^2 + 2 * 54 in^2 = 468 in^2

6 0
3 years ago
A flagpole is at the top of a building. 300 feet from the base of the building, the angle of elevation of the top of the pole is
Grace [21]

Answer: We can use tangent here to find the length of the flagpole

First, find the length of the building + the flag pole

tan 32 = x/300

x=300tan32=187.460805573

(length of building + flagpole)

find length of building

tan 30 = x/300

x=173.205080757

subtract

187.460805573-173.205080757=14.255724816

round, length of flagpole = 14 feet

7 0
3 years ago
Find the surface area of the ball shown to the right <br><br> d=20
netineya [11]

Answer:

<h3>Surface Area = 1,256 cm</h3>

<u>Solution:</u>

formula: Surface Area of a Sphere: 4π · r²

Surface area = 4π · r²

SA = 4(3.14) (10)²

SA =  (12.56)(100)

SA = 1,256

7 0
3 years ago
What is the axis of symmetry equation from f(x)=-x^(2)-6x
Sergeeva-Olga [200]

Answer:

  • \lim_{n \to \infty} a_n13

Step-by-step explanation:

6 0
3 years ago
Other questions:
  • Jake ate 4/8 of a pizza. Millie ate 2/8 of a pizza. How much pizza was eaten by Jake and Millie? Write in the simplest form
    8·1 answer
  • 4m^2 + 4m + 1 = 0 quadratic formula
    10·1 answer
  • Find the value of the variable.
    11·1 answer
  • Work and answer for 24/40 equivalent
    15·2 answers
  • Integration of sin⁶ x​
    14·1 answer
  • Plz help and include an explanation, will mark brainliest
    6·2 answers
  • Equilateral, isosceles, and scalene are ways in which you can classify triangles by their ___.
    7·1 answer
  • i know this is a lot but can someone pls help me with these 3 questions. i would very much appreciate it. c:
    7·1 answer
  • HELPPPPP PLEASDEEEEEEEE!!!!!!!!!!!!!
    6·1 answer
  • _____ teaspoon is equivalent to 5 ml.
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!