Question

Consider the rational function p=(5,125,000V2−449,000V+19307)/(125V2(1,000V−43)), What value of V is/are the vertical asymptote(s) of the function? (decimal up to third decimal figure)

Answer 1

"Solve for v:

5,125,000 v^2 - 449,000 v + 19307 / 125 v^2 (100 0v-43) = 0

5,125,000 v^2 - 449,000 v + 19307/ 125 v^2 (100 0v-43)  =   5,125,000 v^2 - 449,000 v +19307/ 125 v^2 (100 0v-43)

Multiply both sides by 125

5,125,000 v^2 - 449,000 v + 19307/ v^2 (100 0v-43)

Multiply both sides by  v^2 (100 0v-43)

5,125,000 v^2 - 449,000 v + 19307 = 0

Divide both sides by 5125000

V^2 - 449,000 v /5125000 + 19307/5125000

Subtract19307/5125000 from both sides

 V^2 449v / 5125 = - 19307/5125000        

Add 201601/ 105062500 to both sides:

V^2 – 449 v/5125 +20601/ 105062500 = - 77677/42025000

Write the left hand side as a square

(V – 449)^2/10250 – 77677/42025000

Take the square root of both sides:

V – 449/10250 = -i√77677/10/2050

Add 449/10250 to both sides:

Answer: V = 449/10250 + ( 0+i/2050) √77677/10

"