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

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,

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

$\text{Assume }x \ne 0$

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

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

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.

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

Quote:

Originally Posted by conn337

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

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

Factor the denominator to get:

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

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

$4^{x+6}=16$

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

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

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

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

Use quadratic techniques to solve.

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

thanks!!