# Need help on study guide

• May 3rd 2011, 09:12 AM
conn337
Need help on study guide
Working on a study guide for a test, not sure how to work these problems out. Anyone mind showing me how to work them out?

Solve: 9+3/x = 2/x^2

The function F(X) = -x^2+46x-360 models the daily profit, F(X), in hundreds of dollars, for a company that manufactures x computers daily. How many computers should be manufactured to maximize profit? What is the maximum daily profit?

Find the domain of F(X)= x/x^2-16

Solve: 4^x+6=16

Solve: 3^2x+1=27

Solve: x^1/2-2x^1/4-15=0
• May 3rd 2011, 10:08 AM
masters
Quote:

Originally Posted by conn337
Working on a study guide for a test, not sure how to work these problems out. Anyone mind showing me how to work them out?

Solve: 9+3/x = 2/x^2

Hi conn337,

$\displaystyle 9 + \frac{3}{x} = \frac{2}{x^2}$

$\displaystyle \text{Assume }x \ne 0$

Multiply each term by $\displaystyle x^2$ and set equal to zero, arriving at

$\displaystyle 9x^2+3x-2=0$

Factor and solve for x.

Quote:

Originally Posted by conn337
The function F(X) = -x^2+46x-360 models the daily profit, F(X), in hundreds of dollars, for a company that manufactures x computers daily. How many computers should be manufactured to maximize profit? What is the maximum daily profit?

Find the x coordinate of the maximum point.

$\displaystyle x=\frac{-b}{2a}$

Quote:

Originally Posted by conn337
Find the domain of F(X)= x/x^2-16

$\displaystyle f(x)=\frac{x}{x^2-16}$

Factor the denominator to get:

$\displaystyle f(x)=\frac{x}{(x+4)(x-4)}$

The domain of the function is all real numbers except the two that cause the denominator to be zero.

Quote:

Originally Posted by conn337
Solve: 4^x+6=16

$\displaystyle 4^{x+6}=16$

$\displaystyle 4^{x+6}=4^2$

Use this rule: $\displaystyle \text{If }a^x=a^y \text{ , then }x=y$

Quote:

Originally Posted by conn337
Solve: 3^2x+1=27

Solve this one like the one before it.

Quote:

Originally Posted by conn337
Solve: x^1/2-2x^1/4-15=0

$\displaystyle x^{\frac{1}{2}}-2x^{\frac{1}{4}}-15=0$

$\displaystyle x^{(\frac{1}{4})^2}-2x^{\frac{1}{4}}-15=0$