MATH SOLVE

2 months ago

Q:
# I am confused about how to do this problem and I don't think it should be hard, but I just don't know how to approach it, so if anyone could help, I would appreciate it greatly. The biggest problem I have is on finding the hole.

Accepted Solution

A:

Answer:a) (0.555, 0) and (6, 0)b) r = -3 and r = 1.8c) (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 6In the denominator:r = 9/5, 7/8, or -3Zeros 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 = 1.8c) 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) = 0.676The 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) = 1.235The m(r)-intercept is (0, 1.235).