Write a vector equation of the line that passes through p(–1 6) and is parallel to a = (3, -1).
2 answers:
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Answer:
3x-2y=6
Step-by-step explanation:
Subtract 3x from both sides of the equation
Divide each term by −2 and simplify.
y=-3+
Rewrite in slope-intercept form
y=
Use the slope-intercept form to find the slope and y-intercept.
Find the values of m and b using the form y=mx+b
The slope of the line is the value of m, and the y-intercept is the value of b.
Slope:
y-intercept: -3
Any line can be graphed using two points. Select two x values, and plug them into the equation to find the corresponding y values.
Choose 0 to substitute in for x to find the ordered pair.
(0,−3)
Choose 1 to substitute in for x to find the ordered pair.
Graph the line using the slope and the y-intercept, or the points.
slope:
y-intercept:-3
a) You are told the function is quadratic, so you can write cost (c) in terms of speed (s) as
... c = k·s² + m·s + n
Filling in the given values gives three equations in k, m, and n.
Subtracting each equation from the one after gives
Subtracting the first of these equations from the second gives
Using the next previous equation, we can find m.
Then from the first equation
[tex]28=100\cdot 0.01+10\cdot (-1)+n\\\\n=37[tex]
There are a variety of other ways the equation can be found or the system of equations solved. Any way you do it, you should end with
... c = 0.01s² - s + 37
b) At 150 kph, the cost is predicted to be
... c = 0.01·150² -150 +37 = 112 . . . cents/km
c) The graph shows you need to maintain speed between 40 and 60 kph to keep cost at or below 13 cents/km.
d) The graph has a minimum at 12 cents per km. This model predicts it is not possible to spend only 10 cents per km.
