solve for x. if anyone could explain how exactly I solve this question, it would be greatly appreciated!!! thank you
1 answer:
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Answer:
a)
Highest (-3,-3)
Lowest (2,2)
b)
Farthest (-3,-3)
Closest (2,2)
Step-by-step explanation:
To solve this problem we will be using Lagrange multipliers.
a)
Let us find out first the restriction, which is the projection of the intersection on the XY-plane.
From x+y+z=12 we get z=12-x-y and replace this in the equation of the paraboloid:
completing the squares:
and we want the maximum and minimum of the paraboloid when (x,y) varies on the circumference we just found. That is, we want the maximum and minimum of
subject to the constraint
Now we have
Let be the Lagrange multiplier.
The maximum and minimum must occur at points where
that is,
we can assume (x,y)≠ (-1/2, -1/2) since that point is not in the restriction, so
Replacing in the constraint
from this we get
<em>x=-1/2 + 5/2 = 2 or x = -1/2 - 5/2 = -3 </em>
<em> </em>
and the candidates for maximum and minimum are (2,2) and (-3,-3).
Replacing these values in f, we see that
f(-3,-3) = 9+9 = 18 is the maximum and
f(2,2) = 4+4 = 8 is the minimum
b)
Since the square of the distance from any given point (x,y) on the paraboloid to (0,0) is f(x,y) itself, the maximum and minimum of the distance are reached at the points we just found.
We have then,
(-3,-3) is the farthest from the origin
(2,2) is the closest to the origin.
Using proportions, it is found that the amount of the novel she would have read is:
D. 14/15.
<h3>What is a proportion?</h3>A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
She has finished 5/6 of the novel, and will have read more 1/10 in the next two days, hence the total amount read is given by:
Hence option D is correct.
More can be learned about proportions at brainly.com/question/24372153
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