Answer:
There are 96 large tents and 60 small tents
Step-by-step explanation:
Here, we want to calculate the number of tents of each sizes there
Let the number of 6-boys tent be s and the number of 4-boys tent be f
6s + 4f = 816 ••••••(i)
Ratio of large to small ( ratio of s to f)
8:5 = s/f
8/5 = s/f
8f = 5s
f = 5s/8 ••••(ii)
Substitute ii into i
6s + 4(5s/8) = 816
6s + 5s/2 = 816
Multiply through by 2
12s + 5s = 1,632
17s = 1632
s = 1632/17
s = 96
f = 5s/8
f = (5 * 96)/8 = 60
The cylinder is a clue to use cylindrical coordinates. Taking
and
, we then are forced to use
. So the parameterization of the intersection of the plane and cylinder is
To get the surface, we can introduce a second parameter
that "contracts" the elliptical intersection to a point. The simplest way to do this is to use
with
and
.
There are 4 cups per 1 quart...
4/1 × 2/2 = 8/2
There are 8 cups in 2 quarts.