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
<1 = <2
vertical angles (congruent)
<3 = <2
corresponding angles (congruent)
so that: <1 = <2 = <3 = 112 degree
The sample space would be 6 . this is because when you roll the dice there are 6 different outcomes
With this information we can set up 2 equations:
x + y = 312 (# of tickets sold for adults + # of tickets sold to adults = 312)
12x + 5y = 2204 ( # of tickets sold for adults times $12 + # of tickets sold to adults times $5 = $2204)
Where x is how many tickets were sold to adults and y how many tickets were sold to children
Now we can solve this system of equations by substitution:
isolate y in the first equation to find its value and plug it in the second equation
x + y = 312
isolate y by subtracting x from both sides:
x - x + y = 312
y = 312 - x
Apply y = 312 - x to the second equation
12x + 5y = 2204
12x + 5( 312 - x) = 2204
12x + 1560 - 5x = 2204
7x + 1560 = 2204
Subtract 1560 from both sides to isolate x
7x + 1560 - 1560 = 2204 - 1560
7x = 644
Divide both sides by 7
7/7x = 644/7
x = 92
Now plugin 92 for x in the first equation to find the value of y
x + y = 312
92 + y = 312
subtract 92 from both sides
92 - 92 + y = 312 - 92
y = 220
x = 92, y = 220
92 tickets were sold to adults and 220 tickets were sold to children
Hope it helps :)
Branliest would be appreciated
Answer:
x=12
Step-by-step explanation:
90 = x + 42 + 3x
48 = x + 3x
48 = 4x
12 = x
