Hi!
This question is super super easy.
<u><em>Explanation: Product is a you had to multiply by the number. And it gave us 40*600=24,000 is the right answer. Hope this helps you! And thank you for posting your question at here on Brainly. And have a great day. -Charlie</em></u>
(0, 4)
(-1, -3)
(2, -3)
For a 90 degrees clockwise rotation, the rule is (y, -x)
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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Answer: c) 14,871
Step-by-step explanation:
See photo attached - if my work doesn’t make sense I can explain it, just ask (:
Answer: 4 / 663
Step-by-step explanation:
There are 4 queens in a deck of 52 cards.
Probability = 4/52 = 1/13
There are 4 sevens
Probability = 4/51
Total probability = 1/13 x 4/51 = 4 / 663
