Answer:
a) d²y/dx² = ½ x + y − ½
b) Relative minimum
Step-by-step explanation:
a) Take the derivative with respect to x.
dy/dx = ½ x + y − 1
d²y/dx² = ½ + dy/dx
d²y/dx² = ½ + (½ x + y − 1)
d²y/dx² = ½ x + y − ½
b) At (0, 1), the first and second derivatives are:
dy/dx = ½ (0) + (1) − 1
dy/dx = 0
d²y/dx² = ½ (0) + (1) − ½
d²y/dx² = ½
The first derivative is 0, and the second derivative is positive (concave up). Therefore, the point is a relative minimum.
Answer: $122.50
Step-by-step explanation:
We know the difference between the time the employee clocked in and clocked out = 1200 - 0800 = 4 hours
The next clock in and out = 17:30 - 12:45 = 4 hours, 45 minutes.
These times combined = 8 hours, 45 minutes
minutes in an hour = 
of an hour.
The total time worked was 8 hours.
Multiply 8.75 × $14 = $122.50
I am not a professional, simply using prior knowledge.
Note- it would mean the world to me if you could mark me brainliest!
Answer:
That it satisfies x = 0
Step-by-step explanation:
The y-intercept is whatever the y-value is when the x-value is zero, therefore if the x-value is anything other than 0, you can't have the y-intercept value.
Answer:
y = 5/6x - 5.167
Or
y = 5/6x - 31/6
Step-by-step explanation:
The equation of a line
y = mx + c
Step 1: find the slope
m = y2 - y1 / x2 - x1
Given points
( 0 , -7) ( 5 , -1)
x1 = 0
y1 = -7
x2 = 5
y2 = -1
Insert the values into the equation
m = -1 - (-7) / 5 - 0
m = -1 + 7 / 5
m = 6/5
y = 6/5x + c
Step 2: sub any of the two points given into the equation
y = 5/6x + c
( 5 , -1)
x = 5
y = -1
-1 = 5/6(5) + c
-1 = 5*5/6 + c
-1 = 25/6 + c.
c = -1 - 25/6
LCM = 6
c = -6 - 25 / 6
c = -31/6
c = -5.167
Step 3: sub c into the equation
y = 5/6x + c
y = 5/6x - 31/6
Or
y = 5/6x - 5.167
The equation of the line is
y = 5/6x - 5.167
Answer:
y = 5x-1
Step-by-step explanation:
parallel lines have the same slope.
y intercept: -1
slope: 5
- 1 is the same as +-1
so, y = 5x-1
