Answer:
Step-by-step explanation:
The directional derivative of a function in a particular direction u is given as the dot product of the unit vector in the direction of u and the gradient of the function
g(x,y) = sin(π(x−5y)
∇g = [(∂/∂x)î + (∂/∂y)j + (∂/∂z)ķ] [sin(π(x−5y))
(∂/∂x) g = (∂/∂x) sin (πx−5πy) = π [cos(π(x−5y))]
(∂/∂y) g = (∂/∂y) sin (πx−5πy) = - 5π [cos (π(x−5y))]
∇g = π [cos(π(x−5y))] î - 5π [cos (π(x−5y))] j
∇g = π [cos (π(x−5y))] [î - 5j]
So, the question requires a direction vector and a point to fully evaluate this directional derivative now.
the answer 11
Step-by-step explanation:
6+16=22
22÷2=11
The slope-intercept form: y = mx + b
We have the slope m = 9, therefore: y = 9x + b.
Next. We have the table:
x | -5 | -2 | 1 | 3 | 4 |
y |-46|-19| 8 |26|35|
(1, 8) → x = 1, y = 8
substitute the values of x and y to the equation:
8 = 9(1) + b
8 = 9 + b |-9
b = -1
Answer: y = 9x - 1 → y-intercept is -1.
The average rate of change for the height of the plant measured in centimeters per day between day 0 and day 20 is 1.32 cm per day.
<h3>What is average height?</h3>
The average height is the ratio of change in height of the plant and the time taken taken for that change.
Given is the height of a plant in centimeters is modeled as a function of time, in days.
For day 0, the height is 18cm and the height for day 20 is 42 cm, then the average height change is
height per day = 42 - 18/ 20 -0
height per day = 1.2 cm/day
Thus, the average height of plant is 1.2 cm/day.
Learn more about average height.
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