Answer:
y = 1
Step-by-step explanation:
Answer:
The answer is D
Step-by-step explanation:
Answer:
a)
Lowell: 4 counselors
Fairview: 9 counselors
b)
2 new counselors
Step-by-step explanation:
How many counselors should be assigned to each school using Hamilton's method?
Number of students
Lowell: 3584
Fairview: 6816
Total number of students: 10400
Divisor D = (Total number of students)/(number of counselors)= 10400/13 = 800
<u>Temporal assignment</u>
3584/800 = 4 + 0.48 ==> 4 counselors for Lowell
6816/800 = 8 + 0.52 ==> 8 counselors for Fairview
There is one counselor left. According to Hamilton's method she should be assigned to the school with the largest remainder, that is Fairview.
<u>Final assignment</u>
Lowell: 4 counselors
Fairview: 9 counselors
The next year, a new school is opened, with 1824 students. Using the divisor from above, determine how many additional counselors should be hired for the new school
1824/800 = 2 + 0.28
<em>Two new counselors should be hired.</em>
<span>We want to optimize f(x,y,z)=x^2 y^2 z^2, subject to g(x,y,z) = x^2 + y^2 + z^2 = 289.
Then, ∇f = λ∇g ==> <2xy^2 z^2, 2x^2 yz^2, 2x^2 y^2 z> = λ<2x, 2y, 2z>.
Equating like entries:
xy^2 z^2 = λx
x^2 yz^2 = λy
x^2 y^2 z = λz.
Hence, x^2 y^2 z^2 = λx^2 = λy^2 = λz^2.
(i) If λ = 0, then at least one of x, y, z is 0, and thus f(x,y,z) = 0 <---Minimum
(Note that there are infinitely many such points.)
(f being a perfect square implies that this has to be the minimum.)
(ii) Otherwise, we have x^2 = y^2 = z^2.
Substituting this into g yields 3x^2 = 289 ==> x = ±17/√3.
This yields eight critical points (all signage possibilities)
(x, y, z) = (±17/√3, ±17/√3, ±17/√3), and
f(±17/√3, ±17/√3, ±17/√3) = (289/3)^3 <----Maximum
I hope this helps! </span><span>
</span>
I divided 18450 divide by 6 I got 3,075
