Answer: equation of the tangent plane is z = 1
Step-by-step explanation:
Given equation
z = e^(-x²-y²) at point (0,0,1)
now let z = f(x,y)
Δf(x,y) = [ fx, fy ]
= (-2xe^(-x²-y²)), (-2ye^(-x²-y²))
now
Δf (0,0) = [ 0, 0 ] = [ a, b ]
equation of the tangent plane therefore will be
z - z₀ = a(x-x₀) + b(y-y₀)
z - 1 = 0(x-0) + 0(y-0)
z - 1 = 0 + 0
z = 1
Therefore equation of the tangent plane is z = 1
Answer:
She will be able to cut approximately 2 yards off and still have 1 yard.
Step-by-step explanation:
Because 3-2=1 so there would be 1 yard left.
Answer:
25.13274125 in³
Step-by-step explanation:
The radius = 4 ± 0.1
height = 10
Volume of a cylinder = πr²h
Actual volume of the cylinder = π × 4² × 10
= 502.6548246
Maximum volume = π × 4.1² × 10
= 528.1017251
Minimum volume = π × 3.9² × 10
= 477.8362426
Average error = (528.1017251 - 477.8362426)/2
= 50.2654825/2
= 25.13274125 in³
The units are inches cubed.
Comment
There is no exact answer to this. It will have to shown in terms of the width. Also we need to use the Pythagorean Formula
Givens
L = 10 * W
W = W
Formula
L^2 + W^2 = C^2
Solution
(10W)^2 + (W^2) = C^2
C^2 = 100W^2 +W^2
C^2 = 101W^2 Now take the square root.
C = sqrt(101W^2)
C= W*sqrt(101) <<<<< Answer. I think this is what they mean
