Long’s Coffee Shop sells a refill mug for $8.95. Each refill costs $1.50. Last month,
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<u>Answer:</u>
The equation of a line, in point slope form that passes through (-2, -6) and has a slope of 1/3 is
<u>Solution:</u>
Given that line passes through (-2, -6) and has slope of 1/3
We have to find the equation of the line
The point slope form is given as
where m is the slope of the line and a, b are the x, y coordinates of the given point through which the line passes.
Here in this question, m = 1/3 and a = -2 and b = -6
By substituting in point slope form we get,
Hence the equation of a line, in point slope form that passes through (-2, -6) and has a slope of 1/3 is
Remark
If you don't start exactly the right way, you can get into all kinds of trouble. This is just one of those cases. I think the best way to start is to divide both terms by x^(1/2)
Step One
Divide both terms in the numerator by x^(1/2)
y= 6x^(1/2) + 3x^(5/2 - 1/2)
y =6x^(1/2) + 3x^(4/2)
y = 6x^(1/2) + 3x^2 Now differentiate that. It should be much easier.
Step Two
Differentiate the y in the last step.
y' = 6(1/2) x^(- 1/2) + 3*2 x^(2 - 1)
y' = 3x^(-1/2) + 6x I wonder if there's anything else you can do to this. If there is, I don't see it.
I suppose this is possible.
y' = 3/x^(1/2) + 6x
y' =
Frankly I like the first answer better, but you have a choice of both.
If you don't start exactly the right way, you can get into all kinds of trouble. This is just one of those cases. I think the best way to start is to divide both terms by x^(1/2)
Step One
Divide both terms in the numerator by x^(1/2)
y= 6x^(1/2) + 3x^(5/2 - 1/2)
y =6x^(1/2) + 3x^(4/2)
y = 6x^(1/2) + 3x^2 Now differentiate that. It should be much easier.
Step Two
Differentiate the y in the last step.
y' = 6(1/2) x^(- 1/2) + 3*2 x^(2 - 1)
y' = 3x^(-1/2) + 6x I wonder if there's anything else you can do to this. If there is, I don't see it.
I suppose this is possible.
y' = 3/x^(1/2) + 6x
y' =
Frankly I like the first answer better, but you have a choice of both.
Option B: 5 is the value of f(3)
Explanation:
The equation of the piecewise function is given by
We need to find the value of
The value of the function f can be determined when by identifying in which interval does the value of
lie in the piecewise function.
Thus, lies in the interval
, the function f is given by
Substituting in the function
, we get,
Thus, the value of is 5.
Therefore, Option B is the correct answer.