Answer:
Step-by-step explanation:
V=4/3pie(7)^3
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

.
Answer:
Barbara's speed in clear weather is
and in the thunderstorm is
.
Step-by-step explanation:
Let
be the speed and
be the time Barbara drives in clear weather, and let
be the speed and
be the time she drives in the thunderstorm.
Barbara drives 22 mph lower in the thunderstorm than in the clear weather; therefore,
(1). 
Also,
(2).
(3).
,
and
(4). 
From equations (2) and (3) we get:


putting these in equation (4) we get:

and substituting for
from equation (1) we get:

This equation can be rewritten as

which has solutions


We take the first solution
because it gives a positive value for 


.
Thus, Barbara's speed in clear weather is
and in the thunderstorm is
.
Answer:
1 3/4 or 1.75
Step-by-step explanation:
An easy way to do this is to convert to decimals
1/4 = 0.25
2/4 = 0.5
3/4 = 0.75
Now, for the numbers for this problem.
2 3/4 would be equal to 2.75
3 1/2 would be equal to 3.5
Add those two numbers together and you get 6.25
Subtract that from 8 and you get 1.75 or 1 3/4