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
If you double 16 you get the answer to 8*4 (Which is 32)
Look the lesson up online. Sometimes there is an answer key
9514 1404 393
Answer:
5 miles
Step-by-step explanation:
It may get a bit messy, but we can solve for the desired value directly. Let d = the distance walked (in miles). Then 20-d is the distance traveled in the car. The relevant relation is ...
time = distance / speed
The total travel time is 9:00 -6:50 = 2:10 = 2 1/6 hours = 13/6 hours. Here is the equation for total travel time.
total time = time spent walking + time spent riding
13/6 = (d/3) + (20-d)/30
Multiplying by 30 gives ...
65 = 10d + 20 -d
45 = 9d . . . . . . . . . . subtract 20
5 = d . . . . . . . . . . . . divide by 9
The girl walked 5 miles.
_____
<em>Check</em>
Her walking time was (5 mi)/(3 mph) = 5/3 h = 1:40.
Her riding time was (15 mi)/(30 mph) = 1/2 h = 0:30.
Her total travel time was 1:40 +0:30 = 1:70 = 2:10, as required.
