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2 years ago

6) 9x - 7y = -4 18x - 14 y = 10 A) (8, -1) C) (-8,-8) B) (-8,-1) D) No solution

Mathematics

1 answer:

Soloha48 [4]2 years ago

6 0

Answer:

D). No solution

Step-by-step explanation:

9x - 7y = -4

18x - 14 y = 10

9x - 7y = 5

9x - 7y = -4

9x - 7y = 5

__________--

0 = -9

No solution

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17 1/3 + (-50 1/3) -5 1/2

vovangra [49]

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3 years ago

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Every female chicken lays 4 eggs. What is the constant of proportionality for the ratio of eggs to female chickens? 4 3

satela [25.4K]

Since every female chicken lays 4 eggs, if you have one chicken you have 4 eggs, if you have two chicken you have 8 eggs, and so on.

We can even build a little table to show some values:

$\begin{array}{c|c}1&4\\2&8\\3&12\\4&16\\5&20\\\vdots & \vdots\\n& 4n\end{array}$

So, as you can see, the ratio between the number of eggs and the number of female chicken is 4.

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3 years ago

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:

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

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