Answer:
131.7%
Step-by-step explanation:
I used <em>https://www.omnicalculator.com/math/percentage-change</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>
9514 1404 393
Answer:
(b) Congruent Figures
Step-by-step explanation:
Reflections, rotations, and translations are called "rigid transformations" because they do not change the size or shape of the figure. The image is always congruent to the original.
On the other hand, dilations change the size of the figure, so the image is <em>not congruent</em> with the original.
Rigid transformations result in congruent figures.
To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.
x-intercept: (9/4,0)
y-intercept: (0,−9)
Answer:
8.3776 this is the circumference
Step-by-step explanation:
