Step-by-step explanation:
the answer is in the image above
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Answer:
66%(technically 0.66 repeating)
Step-by-step explanation:
We need to figure out what percentage of 69 equates to 46. In other words, we need to figure out what percentage <u>times</u> 69 equals 46:
Now that we formed this equation, we can solve for the percentage as if it was x.
First lets simplfy:
Now we can solve for x just by getting x alone, which means we must remove the coefficent. We can do this by dividing both sides of the equation by 69:
=
Putting this into the form of percentage, we must multiply by 100. Since, the percentage form of a decimal is 100 times bigger(moved up 2 decimal places):
=
percentage = 66%
Hope this helps! :3
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