Answer:
40 cubic units
Step-by-step explanation:
An alternating series
converges if
is monotonic and
as
. Here
.
Let
. Then
, which is positive for all
, so
is monotonically increasing for
. This would mean
must be a monotonically decreasing sequence over the same interval, and so must
.
Because
is monotonically increasing, but will still always be positive, it follows that
as
.
So,
converges.
12) 2.3
13) 4/13
14) 8 7/11
7) .3434...
8) 3.166...
15) (2700-600)/2700 = 2100/2700 = 21/27 = 7/9
1) .4666666667
2) .4444...
3) -0.6666666667
4) -0.8571428571
5) 3.3409090909...
6) -2.227272727273
**bar notation is when you put a bar over the repeating part of a decimal because you can't right it all since it goes on forever
Plane #1 speed: x mph
Plane #2 speed: (x+30) mph
time = time becomes
170 mi 185 mi
---------- = --------------
x x+30
Solving for x, the speed of the slower plane, we get
170x + 5100 = 185 x
5100
Then 15x = 5100, and x = ---------- (mi/hr) = 340 mph
15
The slower plane flies at 340 mph, and the faster one at 370 mph.
