Evaluate each expression
1 answer:
You might be interested in
Lagrange multipliers:
(if 
)
(if )
(if 
)
In the first octant, we assume
, so we can ignore the caveats above. Now,
so that the only critical point in the region of interest is (1, 2, 2), for which we get a maximum value of
.
We also need to check the boundary of the region, i.e. the intersection of
with the three coordinate axes. But in each case, we would end up setting at least one of the variables to 0, which would force 
, so the point we found is the only extremum.
In the first octant, we assume
so that the only critical point in the region of interest is (1, 2, 2), for which we get a maximum value of
We also need to check the boundary of the region, i.e. the intersection of
For this case we have:
If after 2 hours the marathon runner has traveled 22 kilometers we have:
2h -----------> 22km
Applying a rule of three, we can know the time it takes to run 42km. So, we have:
2h -----------> 22km
x -------------> 42km
Where "x" is the time it takes to travel 42km. Resolving we have:
Thus, after 3.82 hours the marathon runner will travel 42km.
Answer:
3.82 hours
Answer:
Step-by-step explanation:
GIVEN: kayden paddled a canoe to an island. the island is miles from the shore. his trip to the island took two hours while paddling against the current. he paddles
mph with no current.
TO FIND: what was the speed of the current.
SOLUTION:
distance of island from the shore miles
total time taken by Kayden hours
speed of Kayden in still water
Let the speed of current be
Speed of Kayden against current
As,
Hence speed of current is