First,multiply the -2 by everything in the brackets
so that's, -6x-(b-4x)+(x+6b)
then combine like terms
that's -6x-(7b-3x) which is
-3x-7b I believe
Formula for the area of a circle: A = pi x r^2
Solve for the radius:
36pi = pi x r^2
r^2 = 36
r = 6 cm
Hope this helps! :)
Answer:
What are the choices?
Step-by-step explanation:
Answer:
A. The situation is discrete B. i. { x : 0 ≤ x ≤ 6; x ∈ Z} ii. { C = 5x : 0 ≤ C ≤ 30; C ∈ Z}
Step-by-step explanation:
A. The situation is discrete since we have integral values for the amount paid per mile walked. The amount per mile is $5 and is only paid if a complete mile is walked. So, it is a discrete situation.
B. i. Since 0 miles represents 0 distance and the student walks a maximum of 6 miles, let x represent the distance walked. So the domain is 0 ≤ x ≤ 6 where x ∈ Z where Z represent integers.
{ x : 0 ≤ x ≤ 6; x ∈ Z}
ii. Since at 0 miles the amount earned is 0 miles × $5 per mile = $ 0 and at the maximum distance of 6 miles, the amount earned is 6 miles × $5 per mile = $ 30, let C represent the amount donated in dollars. So the range is 0 ≤ C ≤ $ 30 where C = 5x.
{ C = 5x : 0 ≤ C ≤ 30; C ∈ Z}
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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