Answer:
- a) (fx, fy, fz) = (54, 9, 12)
- b) (fx, fy, fz) = (16, 30, 9)
Step-by-step explanation:
a) The partial derivatives of f(x, y, z) = x³yz² are ...
- fx = 3x²yz²
- fy = x³z²
- fz = 2x³yz
At the given point, these are ...
- fx(1, 2, 3) = 3(1²)(2)(3²) = 54
- fy(1, 2, 3) = (1³)(3²) = 9
- fz(1, 2, 3) = 2(1³)(2)(3) = 12
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b) The partial derivatives of f(x, y, z) = x² -2xy +3xyz² are ...
- fx = 2x -2y +3yz²
- fy = -2x +3xz²
- fz = 3xy
At the given point, these are ...
- fx(3, 1, -2) = 2(3) -2(1) +3(1)(-2)² = 16
- fy(3, 1, -2) = -2(3) +3(3)(-2)² = 30
- fz(3, 1, -2) = 3(3)(1) = 9
Answer:
0.9783 = 97.83% probability that a can that gets shipped for use will be of perfect shape
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is

In which
P(B|A) is the probability of event B happening, given that A happened.
is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Shipped for use
Event B: Perfect shape
Probability of being shipped for use:
Perfect shape(0.9 probability) or unnoticeable dent(0.02 probability). So

Being shipped for use and being in perfect shape.
0.9 probability, so 
What is the probability that a can that gets shipped for use will be of perfect shape?

0.9783 = 97.83% probability that a can that gets shipped for use will be of perfect shape
I believe that it would be 3. 14
— minus. —- i
41. 41
Simplified I think it would be -11/41 i
Divide 30 ft by 5280 ft and you get 0.00568182 then round that number
Answer:
0
Step-by-step explanation:
Given:
(-3, 2)
(4, 2)
Required:
Slope that passes through the two points given.
Solution:
Slope = 
Let,


Plug in the values into the formula
Slope = 

