Answer:
Step-by-step explanation:
A) 5/7
B) 12/8
c) 6/6
We have two unknowns and two equations so we can solve this question.
The two unknowns are C (speed of current) and B (speed of boat)
Our boat traveled 20 miles in 55 hours going upstream which means it traveled .36 miles in 1 hour; in other words .36mph . Our boat traveled 50 miles in 55 hours going downstream; in other words .909mph .
We can assume that because the boat managed to cover distance in the direction it was headed upstream it must have been going faster than the current so it moved at the speed of the boat minus the speed of the current and when it was going downstream it moved at the speed of the boat plus the speed of the current.
This gives us;
.36mph = B - C
.909mph= B + C
We solve for this system of equations and it simplifies to 1.27mph=2B
and B= .636mph
Plug this into one of the equations and we get that C= .2727mph
This means that the boat moved at .363mph and the current moved at .2727mph.
It is asking you to slice off 40% of the bounce height in each subsequent bounce.
So you start with full height 1, that's n = 0 bounces. Then after n = 1 bounce the new height is .6. After the second bounce, n = 2, the height becomes .6 X .6 = .36. And after n = 3, we have .6 X .6 X .6 = .216
So by induction we see that h(n = 5) = .6^n = .6^5 = 0.07776 = .078 of its original height or H = .078*200 = 15.6 ft. after five bounces. ANS. 16.0 if rounded to the nearest tenth
:)
W=-37/24, 1 13/24, or -1.5416
