<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>
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I believe the answer is 116.
23-8=15
8*15=120
sqrt2=4
the number 120-4=116
that’s what i got not sure if that is correct
<span>Normally when they tell you interest rate they say per annum meaning the percent interest rate for a year.
But in this problem they seem to say John pays 12% for a 146 day loan.
So interest = P * r / 100 = 8400 * 12/100 = $1,008.00
Maturity value = Principal + Interest = 8400 + 1008 = $9,408.00</span>
No answer possible as you didn’t supply the diagram
3 sq rt of 7 is a terminating decimal meaning it ends t therefore it's a rational number
