Math Problem Statement

if h(s)=(3s+6)/(s-A);h(2)=-2, solve for A

Solution

Given the function h(s)=3s+6sAh(s) = \frac{3s + 6}{s - A}, and knowing that h(2)=2h(2) = -2, we need to solve for AA.

First, substitute s=2s = 2 into the function:

h(2)=3(2)+62A=2h(2) = \frac{3(2) + 6}{2 - A} = -2

Simplify the expression:

6+62A=2\frac{6 + 6}{2 - A} = -2 122A=2\frac{12}{2 - A} = -2

Now, solve for AA. First, multiply both sides by (2A)(2 - A) to eliminate the denominator:

12=2(2A)12 = -2(2 - A)

Expand the right side:

12=4+2A12 = -4 + 2A

Now, solve for AA:

12+4=2A12 + 4 = 2A 16=2A16 = 2A A=162=8A = \frac{16}{2} = 8

Thus, A=8A = 8.

Would you like further details or explanations?

Here are five related questions:

  1. What happens if A=0A = 0 in the function h(s)h(s)?
  2. How would the graph of h(s)h(s) change as AA increases?
  3. What is the domain of h(s)h(s) when A=8A = 8?
  4. Can you find ss if given h(s)=0h(s) = 0?
  5. What is the horizontal asymptote of h(s)h(s)?

Tip: When solving for constants, multiplying to eliminate fractions is an effective first step to simplify the equation.

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Math Problem Analysis

Mathematical Concepts

Functions
Equations
Algebra

Formulas

Function evaluation
Solving equations

Theorems

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Suitable Grade Level

Grades 9-12