Since $\rho=\dfrac mV$ (density = mass/volume), we can get the mass/weight of the liquid by integrating the density $\rho(x,y,z)$ over the interior of the tank. This is done with the integral

$\displaystyle\int_{-1}^1\int_{-\sqrt{1-x^2}}^{\sqrt{1-x^2}}\int_{x^2+y^2}^1(2-z^2)\,\mathrm dz\,\mathrm dy\,\mathrm dx$

which is more readily computed in cylindrical coordinates as

$\displaystyle\int_0^{2\pi}\int_0^1\int_{r^2}^1(2-z^2)r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta=\boxed{\frac{3\pi}4}$

7 0

3 years ago

Waf number us 20% of 40

NikAS [45]

Answer:. .

Answer:

20% of 40 is 8

6 0

3 years ago

The sum of two numbers is 12. The difference of the same two numbers is 24. what is the larger of the two numbers

Vsevolod [243]

ANSWER

The larger number is 18

<u>EXPLANATION</u>

Let x be the larger number and y be the smaller number.

Then,

$x+y=12--(1)$

$x-y=24--(2)$

Let us add equation (1) and (2).

$2x=36$

Divide through by 2

$x=18$

Put $x=18$ in to equation (1).

This implies that,

$18=y=12$

$y=12-18=-6$

4 0

3 years ago