Answer:
33) RQ
34) PQ
35) NO
36) MO
Step-by-step explanation:
I've attached a plot of one such cross-section (orange) over the region in the x-y plane (blue), including the bounding curves (red). (I've set

for this example.)
The length of each cross section (the side lying in the base) has length determined by the horizontal distance

between the y-axis

and the curve

. In terms of

, this distance is

. The height of each cross section is twice the value of

, so the area of each rectangular cross section should be

.
This means the volume would be given by the integral
X+y=11
22x+15y=228
y=11-x
22x+15y=228
22x+15(11-x)=228
22x+165-15x=228
7x+165=228
7x=63
x=9
9+y=11
y=2
The solution to the system of equations is (9,2)
Answer:
The answer is C.
Step-by-step explanation:
Hit 'em with the Law of Sines.
sin(A)/a = sin(B)/b.
Let's say x is equal to "A", thus 5 is "a".
sin(x)/5 = sin(B)/b.
We could go for the obvious choice for "B", which would be the 90 degrees shown. To solve for the hypotenuse which will be "b", let's use the Pythagorean Theorem:
a^2 + b^2 = c^2
5^2 + 20^2 = c^2
25 + 400 = 425
sqrt(425) = about 20.6, which we can now substitute "b" with.
sin(x)/5 = sin(90)/20.6
sin(x)/5 = 1/20.6
sin(x)/5 = 0.04854...
sin(x) = 0.2427...
You can plug in sin^-1(0.2427) into your calculator, and you should end up with something like 14.047... which equates to answer choice C.
Answer: 80 feet.
Step-by-step explanation:
1. As you can see in the figure, triangle ABC and the triangle DFG are similar.
2. The scale of factor of triangle ABC to triangle DFG is the following:

3. Therefore, the lenght of the side DG of the trinagle DFG is:

4. The perimeter of the triangle DFG is:

5. Therefore, she would need 80 feet of fence.