Exam 12: Mathematical Problem Set

Solve the equation log (x-4)+log (x+5)=1 . List any extraneous roots and explain.

A computer randomly generates a password that is 8 entries long. The password is 4 letters followed by 4 numbers with repetitions of numbers and/or letters permitted. What is the probability that the computer will generate a password for Jonathan that has the same four letters followed by the same four numbers, such as KKKK5555?

Find the equation that describes the set of all points (x, y, z) that are 5 units from the point (2,-1,6).

For the function y=2 ln (x+3) , what is the inverse function, $f^{-1}$ ?

Eliminate the parameter and identify the graph of the parametric curve given by x=t-3 , $y=\frac{2}{t} .$

Find the average rate of change of $f(x)=e^{x}$ over the interval [-1,1] .

Determine the sum, if it exists, of the infinite geometric series $6-3+\frac{3}{2}-\frac{3}{4}+\ldots$

Solve the equation graphically. $|4 x-3|=5 \sqrt{x+4}$