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Ugo [173]
3 years ago
9

Help! i just need the answers. maybe some explanations would be good too :)

Mathematics
1 answer:
Dennis_Churaev [7]3 years ago
5 0

For Number one: -xy + 2x = 20, x = 5

To solve this, all we need to do is plugin 5 for every place we have x. So...

- (5)y + 2(5) = 20

-5y + 10 = 20

-5y = 10

y = -2

For number two: 4x - 3y - 10 = 1, x = -1

To solve this, we need to plugin -1 for all of the x variables. So...

4 (-1) - 3y - 10 = 1

-4 - 3y - 10 = 1

-14 - 3y = 1

-3y = 15

y = -5

For number three: 5x + 7y = -1, x = 4

We need to plugin -4 for all of the x variables. So...

5 (4) + 7y = -1

20 + 7y = -1

7y = -21

y = -3

For number four: x = 6 + xy, x = -3

Same as the other ones, just plugin -3 for all of the x variables. So...

-3 = 6 + (-3)y

-3 = 6 - 3y

-9 = -3y

3 = y

I hope this helps :)

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3 years ago
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4 0
2 years ago
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Find the mass of the solid paraboloid Dequals=​{(r,thetaθ​,z): 0less than or equals≤zless than or equals≤8181minus−r2​, 0less th
Lubov Fominskaja [6]

Answer:

M = 5742π  

Step-by-step explanation:

Given:-

- Find the mass of a solid with the density ( ρ ):

                             ρ ( r, θ , z ) = 1 + z / 81

- The solid is bounded by the planes:

                             0 ≤ z ≤ 81 - r^2

                             0 ≤ r ≤ 9

Find:-

Find the mass of the solid paraboloid

Solution:-

- The mass (M) of any solid body is given by the following triple integral formulation:

                           M = \int \int \int {p ( r ,theta, z)} \, dV\\\\

- We can write the above expression in cylindrical coordinates:

                           M = \int\limits\int\limits_r\int\limits_z {r*p(r,theta,z)} \, dz.dr.dtheta \\\\M = \int\limits\int\limits_r\int\limits_z {r*[ 1 + \frac{z}{81}] } \, dz.dr.dtheta\\\\

- Perform integration:

                           M = \int\limits\int\limits_r{r*[ z + \frac{z^2}{162}] } \,|_0^8^1^-^r^2 dr.dtheta\\\\M = \int\limits\int\limits_r{r*[ 81-r^2 + \frac{(81-r^2)^2}{162}] } \, dr.dtheta\\\\M = \int\limits\int\limits_r{r*[ 81-r^2 + \frac{6561 -162r + r^2}{162}] } \, dr.dtheta\\\\M = \int\limits\int\limits_r{r*[ 81-r^2 + 40.5 -r +\frac{r^2}{162} ] } \, dr.dtheta\\\\M = \int\limits\int\limits_r{[ 121.5r-r^2 -\frac{161r^3}{162} ] } \, dr.dtheta\\\\

                           M = 2*\int\limits_0^\pi {[ 121.5r^2-r^3 -\frac{161r^4}{162} ] } |_0^6 \, dtheta\\\\M = 2*\int\limits_0^\pi {[ 121.5(6)^2-(6)^3 -\frac{161(6)^4}{162} ] }  \, dtheta\\\\M = 2*\int\limits_0^\pi {[ 4375-216 -1288] }  \, dtheta\\\\M = 2*\int\limits_0^\pi {[ 2871] }  \, dtheta\\\\M = 5742\pi  kg              

- The mass evaluated is M = 5742π                      

8 0
3 years ago
Solve the system by graphing <br> y = -3/4x + 6 <br> y = 2x - 5
jonny [76]

Answer:

X= 4. Y = 3.

Step-by-step explanation:

If you have a graphing calculator, put the first equation into Y1. And second equation into Y2. Then, find the intersection of the two equations. That's how you find your answer.

4 0
3 years ago
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denis23 [38]

Answer:

Please refer to the attachment

8 0
3 years ago
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