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
It would be 15 because the way you would set it up is equal to 180 because they are opposite and they have to add up to 180 in order for the whole shape to be 360. so 3x+9x=180 and then 12x=180 and divide 180 by 12 which is 15 and you can also plug in 15 to check
Answer:
He stepped back 59.71 feet.
Step-by-step explanation:
Start by making 2 triangles. One has 68 degrees as the acute angle at the base of the triangle and the other has 41 degrees as the acute angle at the base of the triangle. The side opposite of said angle on both triangles will be 80, the height of the tree. You're solving for the bottom (horizontal) side for both triangles.
For the triangle with an acute base angle of 68, the formula to solve for the horizontal side is tan(68) = 80/x.
Get x by itself to get 80/tan(68) = x
x = 32.32.
For the next triangle, the equation is the same but the angle is changed to 41.
tan(41) = 80/x
80/tan(41) = x
x = 92.03
Finally, subtract the smaller distance from the larger:
92.03 - 32.32 = 59.71 steps.
