Algebra and Trigonometry: Structure and Method, Book 2
Algebra and Trigonometry: Structure and Method, Book 2
2000th Edition
ISBN: 9780395977255
Author: MCDOUGAL LITTEL
Publisher: McDougal Littell
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Chapter 5.4, Problem 21WE

a.

To determine

To find the domain of the given rational function.

a.

Expert Solution
Check Mark

Answer to Problem 21WE

Domain: (,0)(0,9)(9,)

Explanation of Solution

Given:

Rational function: f(t)=t29t29t

Concept used:

To find the domain of the rational function, the following steps are to be followed:

  1. Equate the denominator equal to zero.
  2. Solve and find the t values that make the denominator equal to zero.
  3. The domain is all the real numbers except for those t values equal to zero.

Calculation:

The given rational function is f(t)=t29t29t

The denominator of the given function is t29t.

Equating the denominator to zero,

  t29t=0t(t9)=0

  t=0 and t9=0

Therefore,

  t=0 and 

  t9=0

Adding 9 on both sides,

  t9+9=0+9t=9

Hence, the domain of the function is all real numbers except t=0 and t=9.

Conclusion:

Therefore, the domain of the function is a (,0)(0,9)(9,).

b.

To determine

To find the zeros of the function if any.

b.

Expert Solution
Check Mark

Answer to Problem 21WE

  t=3

Explanation of Solution

Given:

Rational function: f(t)=t29t29t

Concept used:

To find the zeros of the rational function,

  1. Equate f(t)=0.
  2. Simplify and find the values of t which are the zeros of the rational function.

Calculation:

Equate the rational function f(t) to zero.

  f(t)=0t29t29t=0

Cross multiplying,

  t29=(t29t)(0)t29=0

Adding9 on both sides,

  t29+9=0+9t2=9

Taking square root on both sides,

  t2=9t=3

Conclusion:

Therefore, the zeroes of the rational function are t=3 .

Chapter 5 Solutions

Algebra and Trigonometry: Structure and Method, Book 2

Ch. 5.1 - Prob. 11OECh. 5.1 - Prob. 12OECh. 5.1 - Prob. 1WECh. 5.1 - Prob. 2WECh. 5.1 - Prob. 3WECh. 5.1 - Prob. 4WECh. 5.1 - Prob. 5WECh. 5.1 - Prob. 6WECh. 5.1 - Prob. 7WECh. 5.1 - Prob. 8WECh. 5.1 - Prob. 9WECh. 5.1 - Prob. 10WECh. 5.1 - Prob. 11WECh. 5.1 - Prob. 12WECh. 5.1 - Prob. 13WECh. 5.1 - Prob. 14WECh. 5.1 - Prob. 15WECh. 5.1 - Prob. 16WECh. 5.1 - Prob. 17WECh. 5.1 - Prob. 18WECh. 5.1 - Prob. 19WECh. 5.1 - Prob. 20WECh. 5.1 - Prob. 21WECh. 5.1 - Prob. 22WECh. 5.1 - Prob. 23WECh. 5.1 - Prob. 24WECh. 5.1 - Prob. 25WECh. 5.1 - Prob. 26WECh. 5.1 - Prob. 27WECh. 5.1 - Prob. 28WECh. 5.1 - Prob. 29WECh. 5.1 - Prob. 30WECh. 5.1 - Prob. 31WECh. 5.1 - Prob. 32WECh. 5.1 - Prob. 33WECh. 5.1 - Prob. 34WECh. 5.1 - Prob. 35WECh. 5.1 - Prob. 36WECh. 5.1 - Prob. 1MRECh. 5.1 - Prob. 2MRECh. 5.1 - Prob. 3MRECh. 5.1 - Prob. 4MRECh. 5.1 - Prob. 5MRECh. 5.1 - Prob. 6MRECh. 5.1 - Prob. 7MRECh. 5.1 - Prob. 8MRECh. 5.1 - Prob. 9MRECh. 5.1 - Prob. 10MRECh. 5.1 - Prob. 11MRECh. 5.1 - Prob. 12MRECh. 5.1 - 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