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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}

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E

Step-by-step explanation:

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Can anyone help??? I’m stuck
sukhopar [10]

Answer:

C)

Step-by-step explanation:

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7 0
2 years ago
Your team wins 18 medals at a competition. The metals are gold, silver, and bronze in a ratio of 2:4:3. How many of each metal d
Anarel [89]

Answer

Find out the how many of each metal did your team win.

To prove

As given

Your team wins 18 medals at a competition.

The metals are gold, silver, and bronze in a ratio of 2:4:3.

Let us assume that x be the scalar multiple of the gold, silver and bronze medal.

Thus

Number of gold medal = 2x

Number of silver medal = 4x

Number of bronze medal = 3x

Than the equation becomes

2x + 4x + 3x = 18

9x = 18

x = \frac{18}{9}

x = 2

Number of gold medal = 2 × 2

                                      = 4

Number of silver medal = 4 × 2

                                       = 8

Number of bronze medal = 3 × 2

                                           = 6

Therefore the number of gold medal are 4, silver medal are 8, bronze medal are 6.

3 0
3 years ago
assuming the growth rate stays constant at 1.2%, how many doublings would take place in a 500- year period?
Juliette [100K]

9514 1404 393

Answer:

  8.6

Step-by-step explanation:

The growth factor per year is 1.012, so in 500 years is ...

  1.012^500

The number of doublings is the solution to ...

  2^n = 1.012^500

Taking logarithms, we have ...

  n·log(2) = 500·log(1.012)

  n = 500·log(1.012)/log(2) ≈ 8.6046

About 8.6 doublings will take place in 500 years.

3 0
2 years ago
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