Answer:
a) (0.555, 0) and (6, 0)
b) r = -3 and r = 1.8
c) (0.875, 0.676)
d) (0, 1.235)
Step-by-step explanation:
Set each term in the numerator and denominator equal to 0 and find r.
In the numerator:
r = 7/8, 5/9, or 6
In the denominator:
r = 9/5, 7/8, or -3
Zeros in the numerator that aren't in the denominator are r-intercepts.
Zeros in the denominator that aren't in the numerator are vertical asymptotes.
Zeros in both the numerator and the denominator are holes.
a) (0.555, 0) and (6, 0)
b) r = -3 and r = 1.8
c) Evaluate m(r) at r = 7/8. To do that, first divide out the common term (-8r + 7) from the numerator and denominator.
m(r) = (-9r+5)² (r−6)² / ( (-5r+9)² (r+3)² )
m(⅞) = (-9×⅞+5)² (⅞−6)² / ( (-5×⅞+9)² (⅞+3)² )
m(⅞) = (-23/8)² (-41/8)² / ( (37/8)² (31/8)² )
m(⅞) = (-23)² (-41)² / ( (37)² (31)² )
m(⅞) = 0.676
The hole is at (0.875, 0.676).
d) Evaluate m(r) at r = 0.
m(0) = (-9×0+5)² (0−6)² / ( (-5×0+9)² (0+3)² )
m(0) = (5)² (-6)² / ( (9)² (3)² )
m(0) = 1.235
The m(r)-intercept is (0, 1.235).
Answer:
1/10
Step-by-step explanation:
2/5=4/10
4/10-3/10=1/10
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You work x hours. you get 20 dollars per hour. this is a random situation, because u didn't give us choices.
It is convenient to do part b first, then use that result to do part a.
b. For some pair of points (x1, y1) and (x2, y2), you want to find a point (a, b) such that (a, b) - (x1, y1) = (x2, y2) - (a, b). That is, the differences of coordinates from one end to the center are the same as the differences from the center to the other end.
Adding (a, b) to the above equation gives
2(a, b) - (x1, y1) = (x2, y2)
Adding (x1, y1) then gives
2(a, b) = (x1, y1) + (x2, y2)
Finally, dividing by 2 gives a formula for (a, b):
(a, b) = ((x1, y1) + (x2, y2))/2
The midpoint is the average of the end points.
a. Using the result from part b, the midpoint is
midpoint = ((2, 3) + (6, 7))/2 = (8, 10)/2
midpoint = (4, 5)
