Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y2 = 2x, x = 2y;
about the y-axis
b) Sketch the region
c) Sketch the solid, and a typical disk or washer.

V = 34,13*π   cubic units

Step-by-step explanation: See Annex

We find the common points of the two curves, solving the system of equations:

y²  = 2*x                           x = 2*y  ⇒  y = x/2

(x/2)² = 2*x

x²/4 = 2*x

x  =  2*4         x  = 8      and   y = 8/2       y = 4

Then point  P ( 8 ;  4 )

The other point Q is  Q ( 0; 0)

From these  two points, we get the integration limits for dy ( 0 , 4 )are the integration limits.

Now with the help of geogebra we have: In the annex segment ABCD is dy then

V = π *∫₀⁴ (R² - r² ) *dy   =  π *∫₀⁴ (2*y)² - (y²/2)² dy =  π * ∫₀⁴ [(4y²) - y⁴/4 ] dy

V = π * [(4/3)y³ - (1/20)y⁵] |₀⁴

V =  π * [ (4/3)*4³ - 0 - 1/20)*1024 + 0 )

V = π * [256/3  - 51,20]

V = 34,13*π   cubic units

the answer   is 200

step-by-step explanation:

this is a problem about poisson probabilities.   i don't know if you've

already studied poisson distributions, or if you have a place to look

to read more about the subject.  

here's how you can see a poisson distribution coming.   when there are

a lot of events that may happen at any time (or any place), and when

you're counting how many of them happen at a particular time (or a

particular place), and each event is independent of the others, then

the result is a poisson distribution.   this is roughly true for the

chocolate chips; one chip being in a cookie has only a small effect on

the probability that another chip will be in the cookie.

once you know you have a poisson distribution, you know a lot.   there

is only one parameter to a poisson distribution, so if you know the

mean, you know everything.   the form of the distribution is

  probability of n chips = {[e^(-x)]*(x^n)} / (n! )

they will manufacture 8496 cars