Evaluate   (If you see an error in the formatting – you are evaluating the Fifth root of the complex number that matches the coordinate from the previous problem). Leave all of your answers in polar form. Please note that the answer to the previous question is helpful for this problem!

(2 points each)  Find all solutions for the equations below (write the general solutions for each).  No calculator! a) sec(x)=2 b) cot(x)=33

(10 pts) Pat was given

Write the augmented matrix representing the following system of equations.  Then, using a calculator, write the matrix in reduced row echelon form and write the solution to the system. Write everything with simplified, improper fractions.   2x+ 9y +10z+7w =11   x  -y +z+  w = -33 x + 2y -11z+2w = 1   x + 3y + 4z+4w = 0

Write the Matrix Equation (AX=B) for the following system of equations.  Then solve using inverse matrices.  You must show the inverse matrix that your calculator gives you. This question should look familiar. I apologize for the formatting issue with the brackets.   There are 4 equations with 4 variables below.  2x+ 9y+ 10z+7w =11   x   -y +   z+  w = -33 x + 2y-11z+2w = 1   x + 3y + 4z+4w = 0

(10 points )   A boat can travel 10mph in still water.   Two docks are located directly across a 1 mile wide river flowing 4mph.  At what angle must the boat point upstream in order to travel directly between the two docks?  How long will the trip take?  Please specify which angle you are referring to in your answer.    

a) 2 pts:  find f(-4) and f(3) b) 3pts: Find the domain of f(x) c) 3pts: Find the range of f(x) d) 3pts: On what interval(s) is f(x) increasing? e) 3pts: On what interval(s) is f(x) decreasing? f) (2pts): Where and what are the local maximums? g) 2pts: Where and what are the local minimums? h) Sketch a graph of  f(x+2) + 2  on your answer document.  i) Sketch a graph of -f(2x) j) Sketch a graph of 2f(x)

If you want to have $7,000 after 25 years – how much should you invest into an account earning 6% interest compounded continuously?    

Let be a point on the graph of

The Diabolical Doubler takes bacteria samples and creates an environment which allows them to follow the law of uninhibited growth until they double in size, after which the diabolical doubler lives up to its name and destroys the bacteria and laughs.  Yes, the machine laughs.  It is that diabolical.  A culture of bacteria that grows at a rate of 4.6% per hour.  How many hours will it take for the bacteria to double in size and allow the world to hear the diabolical doublers’ laugh?