Answer:
A
Step-by-step explanation:
Calculate the distance using the distance formula
d = 
with (x₁, y₁ ) = (7, 4 ) and (x₂, y₂ ) = (- 1, - 4 )
d = 
= 
= 
= 
≈ 11.31 ( to 2 dec. places )
Answer: Dependent Variable sowwy if im wrong
Step-by-step explanation: Linear regression models are used to show or predict the relationship between two variables or factors. The factor that is being predicted (the factor that the equation solves for) is called the dependent variable.
Answer:
The area is π= 3.14 approx
Hope it helps!
Step-by-step explanation:
Area of circle = πr^2
Radius= r = 1 unit
So area,
= 3.14*(r)^2
= 3.14*(1)^2
= 3.14*1
= 3.14 or π if you want the specific answer
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
#SPJ4
Answer:
15.8
Step-by-step explanation:
15/360*(3.14*(11)^2)
0.04166666666*(3.14*(11)^2)
0.04166666666*(379.94)
= ~15.8
