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2 answers:
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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.
Answer:
k ∈ (-∞,)∪(1,∞)
Step-by-step explanation:
For quadratic equations you can find the solutions with the Bhaskara's Formula:
A quadratic equation usually has two solutions.
If you only want real solutions the condition is that the discriminant () has to be greater than zero, this means:
Then we have the expression:
Now to find two distinct real solutions to the original quadratic equation we have to calculate the discriminant:
We got another quadratic function.
we can simplify the expression dividing both sides in 8.
We can apply Bhaskara's Formula except that the condition in this case is that the solutions have to be greater than zero.
Then,
The answer is:
For all the real values of k who belongs to the interval:
(-∞,)∪(1,∞)
there are two distinct real solutions to the original quadratic equation