Answer: x = 23 and y = 13
Explanation:
let x and y be the two number.
Where:
(x + y)/2 = 18 => x + y = 18 x 2 = 36
and:
x - y = 10
Thus we get:
x + y = 36 (1)
x - y = 10 (2)
Add (1) and (2):
x + y + x - y = 36 + 10
2x = 46
x = 23
If x = 23
then x - y = 10
23 - y = 10
-y = -13
y = 13
In the slope intercept form equation, y =mx+b, m is the slope, or the coefficient of x.
Therefore, the slope, or m, in this situation is -2/3.
Hope this helps!
Answer:
No, it can't perform because C_p < 1
Step-by-step explanation:
We are told that a product with specifications of ± 0.07 inches has to be processed on that machine. This means that the product is centered on the machine.
Thus;
Specification Width = 2 × 0.07 = 0.14
Now, formula for capability index is;
C_p = specification width/(6 × standard deviation)
We are given standard deviation = 0.04. Thus;
C_p = 0.14/(6 × 0.04)
C_p = 0.5833
Now, for this process, C_p should not be less than 1. However in this case it is less than 1,thus it means that the machine will not be able to perform the job.
In slope intercept form it would be y=2/3x-2
I'm just going to take a dab at this. I haven't done calculus in years.
So you found the equation of the tangent line for your equation at the point (1,2) which is:
y = 5 - 3x
Which is correct and all, but the question seems to be asking for "another tangent", so we are looking for another tangent line that is parallel to:
y = 5 - 3x
So we know that the equation of this line must also have a slope of "-3".
So if it must have a slope of "-3", then it must follow that:
-3 = -3 + 24x - 24x²
I got the above from setting our derivative equation equal to -3.
So if we solve the above equation we get:
24x - 24x² = 0
24x(1 - x) = 0
So "x" must be equal to 0 or 1. (These are the two points that have a slope of -3)
And since we already know about the point x = 1, we are interested in the point x = 0. So from our original equation the point x = 0 has a y-value of 1, therefore we have the point (0,1). Finally, we just need to find the equation of the line that has a slope of -3 and contains the point (0,1).
I'm sure you can do this part on your own. The equation of that line is:
y = -3x +1
or
y = 1 - 3x (as you pointed out)
Whew, that was a nice refresher. :)
I hope that was easy to follow!