For starters, the probability of finding any of these colors is a 50/50 type of thing, or in this case, an equal quarter. So each would be 1/4, or 25%. Unless, of course, they're lying about having one or more colors of marbles in their possession. But I'm answering under the assumption that they're not.
Answer:
Remember to add "$" before the number.
The points on the intersection of the ellipsoid with the plane that are respectively closest and furthest from the origin are
(2–√,−2–√,2−22–√)
(−2–√,2–√,2+22–√)
Using Lagrange multipliers we attempt to find the extrema of f(x,y,z)=x2+y2+z2 given that g(x,y,z)=x−y+z−2=0 and that h(x,y,z)=x2+y2−4=0.
Given,
∇f=⟨2x,2y,2z⟩
∇g=⟨1,−1,1⟩
∇h=⟨2x,2y,0⟩
Extrema satisfy the condition that ∇f=μ∇g+λ∇h for some λ,μ∈R.
This is to say,
2x=2λx+μ
2y=2λy−μ
2z=μ
If λ=1 then μ=0 and so z=0, the g constraint tells us that x=y+2, and the h constraint tells us that y2+(y+2)2=4, meaning that either y=0 or y=2. This provides us with two crucial points in addition to the g constraint:
(2,0,0)
(0,−2,0)
Now assume λ≠1, and so
x=μ2−2λ
y=−μ2−2λ=−x
Since x=−y, we have that x=±2–√, y=∓2–√. Using the g constraint, our two critical points are
(2–√,−2–√,2−22–√)
(−2–√,2–√,2+22–√)
And then it's east to determine which is the max and which is the min out of these four critical points.
To learn more about Lagrange multiplier
brainly.com/question/4609414
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Area=lw
l=2w
aera=2l^2
72=area
72=2l^2
divide both sides by 2
36=l^2
sqrt both sides
6=l
length=6 units
Answer:
$8.25 y(cost) = 5.50(x pounds coffee) - 2.75
Step-by-step explanation:
5.50 × 2
11 - 2.75
$8.25
y=5.50x-2.75
