Answer:
Perimeter = 24 + 8π /3 m.
Step-by-step explanation:
Arc length = rC where r = radius and C = angle in radians.
40 degrees = 40 π / 180
= 2π /9 radians.
Arc length = 12 * 2π /9
= 8π /3 m.
Perimeter of the sector = 2*12 + 8π /3
= 24 + 8π /3 m.
<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>
Answer:
40
Step-by-step explanation:
The answer is 40 because:
1) First, we need to know that:
negative x negative = positive
negative x positive = negative
positive x negative = negative
positive x positive = positive
2) Therefore, -8 x -5 equals to a positive 40
Hope this helps!
Answer:
<u>The correct answer is b = 6 √3 units</u>
Step-by-step explanation:
Let's recall that we can use the following ratio for the sides of a 90 - 60 - 30 triangle:
1 : √3 : 2, where 2 is the hypotenuse.
Upon saying that, we have that in our triangle:
Hypotenuse = 12 units
a = 6 units
b = 6 √3 units
<u>The correct answer is b = 6 √3 units</u>
