Answer:
Time taken by the un powered raft to cover this distance is T = 192.12 hr
Step-by-step explanation:
Let speed of boat = u 
Speed of current = v 
Let distance between A & B = 100 km
Time taken in downstream = 32 hours


u + v = 3.125 ------ (1)
Time taken in upstream = 48 hours


u - v = 2.084 ------- (2)
By solving equation (1) & (2)
u = 2.6045 
v = 0.5205 
Now the time taken by the un powered raft to cover this distance

Because un powered raft travel with the speed of the current.

T = 192.12 hr
Therefore the time taken by the un powered raft to cover this distance is
T = 192.12 hr
Answer:

Step-by-step explanation:
Given : 
Solution:



Thus , 
Thus the solution is irrational since square root 7 does not have a perfect square and equal to 6+2square root of 14
Step-by-step explanation:
Clearly, there is a common difference between the monthly employment rates:
8.7% - 8.9% = -0.2%
8.5% - 8.7% = -0.2%
8.3% - 8.5% = -0.2%
a) So, for every month x, the percentage will go down 0.2%, starting at 8.9%. So, we can make this equation:
y = -0.2x + 9.1, where x = 1 would be October 2011.
January 2013 is 16 months after October 2011, so:
y = -0.2(16) + 9.1
y = 5.9%
b) To find when the unemployment rate will be zero, we set the equation equal to zero:
0 = -0.2x + 9.1
-0.2x = -9.1
x = 45.5 months
So, rounding up, the U.S. would reach a zero unemployment rate in 46 months or around September 2014? Not completely sure.
The vertex form is 
Step-by-step explanation:
The given equation
is a parabola. The vertex of the parabola is of the form
The parameters of the parabola are
and 
The vertex of the x-coordinate is given by 
Thus, substituting the values of a and b in
, we get,

Now, substituting
in
, we get,

Thus, the vertex is 
The equation of parabola to be in vertex form is 
where a is the coefficient of
, h is vertex of the x-coordinate and k is the vertex of the y-coordinate.
Hence,
and 
Thus, substituting the values in the equation of the vertex form,

Hence, the vertex form is 
Answer:
2 5/8 cups of flour
Step-by-step explanation:
Use a proportion.
1 3/4 cups of flour is to 2/3 of a batch as x cups of flour is to 1 batch.
1 3/4 : 2/3 = x : 1
2/3 x = 1 3/4 * 1
2/3 x = 1 3/4
2/3 x = 7/4
3/2 * 2/3 x = 3/2 * 7/4
x = 21/8
x = 2 5/8
Answer: 2 5/8 cups of flour