<span>An arithmetic sequence is a sequence with the difference between two consecutive terms constant. The difference is called the common difference.<span>A geometric sequence is a sequence with the ratio between two consecutive terms constant.</span></span>
Answer:
The answer to your question is 1/8
Step-by-step explanation:
Data
Total volume = 1 gallon
Water drank by the hiker = 1/2
Water drank by each of his friends = ?
Process
1.- Calculate the water that he gave to his friends
Water gave to his friends = 1 - 1/2
= 1/2
2.- Calculate the amount of water each friend received.
1/2 ÷ 4 = 1/8
3.- Conclusion
Each of the friends received 1/8 of the gallon.
I assume there are some plus signs that aren't rendering for some reason, so that the plane should be
.
You're minimizing
subject to the constraint
. Note that
and
attain their extrema at the same values of
, so we'll be working with the squared distance to avoid working out some slightly more complicated partial derivatives later.
The Lagrangian is
Take your partial derivatives and set them equal to 0:
Adding the first three equations together yields
and plugging this into the first three equations, you find a critical point at
.
The squared distance is then
, which means the shortest distance must be
.
Answer: the speed of the current is 0.6 mph
Step-by-step explanation:
Let x represent the speed of the current.
James is kayaking. He can row 3 mph in still water. If he can travel 6 miles downstream. Assuming he went with the current, it means that his total speed while travelling downstream is (3 + x)
Time = distance/speed
Time taken to travel downstream is
6/(3 + x)
In the same amount of time, he can travel 4 miles upstream. Assuming he went against the current, it means that his total speed while travelling downstream is (3 - x). Time taken to travel upstream is
4/(3 - x)
Since the time is the same, then
6/(3 + x) = 4/(3 - x)
Cross multiplying, it becomes
6(3 - x) = 4(3 + x)
18 - 6x = 12 + 4x
4x + 6x = 18 - 12
10x = 6
x = 6/10
x = 0.6 mph
