Answer:
Volume = 16 unit^3
Step-by-step explanation:
Given:
- Solid lies between planes x = 0 and x = 4.
- The diagonals rum from curves y = sqrt(x) to y = -sqrt(x)
Find:
Determine the Volume bounded.
Solution:
- First we will find the projected area of the solid on the x = 0 plane.
A(x) = 0.5*(diagonal)^2
- Since the diagonal run from y = sqrt(x) to y = -sqrt(x). We have,
A(x) = 0.5*(sqrt(x) + sqrt(x) )^2
A(x) = 0.5*(4x) = 2x
- Using the Area we will integrate int the direction of x from 0 to 4 too get the volume of the solid:
V = integral(A(x)).dx
V = integral(2*x).dx
V = x^2
- Evaluate limits 0 < x < 4:
V= 16 - 0 = 16 unit^3
The area of the ellipse
is given by

To use Green's theorem, which says

(
denotes the boundary of
), we want to find
and
such that

and then we would simply compute the line integral. As the hint suggests, we can pick

The line integral is then

We parameterize the boundary by

with
. Then the integral is


###
Notice that
kind of resembles the equation for a circle with radius 4,
. We can change coordinates to what you might call "pseudo-polar":

which gives

as needed. Then with
, we compute the area via Green's theorem using the same setup as before:






Answer:

Step-by-step explanation:
<em>Subtract the students who don't have protractors from the students who have mathematical instruments.</em>

Answer:
∠ZXY and ZX
XYZ is not found on the diagram, as there is no line going from Z to Y, and YX is not a line segement in the diagram, its a full line.
They could miss each other 30 different ways. I solved this by drawing it out six different stores and making Alice and Betsy go to each one may different times. Example photo included for how I got the first five. Then I did the same thing, but switch A and B, counted that towards the total and continued the is drawing until all the possibilities were found.