Prove or disprove: two consecutive rotations about two different axis are commutative. That is, is RuRv = RvRu? (Hint: For simplicity, you can assume that the axis u is the x-axis and v is the y-axis without loss of generality).

let p3x be the third order polynomiol interpolatign function f(x)=sin(x) at 0,1/3,2/3,1 show that for any x in [0,1] we have f(x)-p3(x), or equal to 1/54

Block copy, and paste, the argument into the window below, and do a proof to prove that the argument is valid.

1. (p   ⊃ z)   •   (q • ~z)
2. (~p • q)    ⊃   s
3. m   v ~s     : .    m

1. m •   (n • p)
2. (q   ⊃ ~t) • (~m v q)
3.   ~t ⊃ z     : .     z

show that if  f Darboux/Riemann integrable, then so is |f|. and given example show that the inverse is false.

1. As you are solving a related rates problem that is asking for the rate of change of an angle, you come up with the following equation that relates the given variables. Show on your paper (or enter using the equation editor in the space provided below) what the next step would be. That is, show the work for differentiating both sides with respect to the time variable,

sin\theta =(5)/(x)

2 .Determine the vertical and horizontal asymptotes for:

y=(x^(2)+5)/(3x^(2)-14x-5)

3. Two trucks start at the same point. Truck A drives south at 16 mi/hr and truck B drives west at 12 mi/h. At what rate is the distance between the trucks changing 2 hours later? (Hint: at one point, you will need to figure out how far each truck has traveled in 2 hours.) Make sure to show all the work on your paper.

Show that Thomae's function is Darboux/Riemann integrable and its integral is equal to 0.

A non-uniform b-spline curve knot vector is given as (-1, -1, -1, -1/2, 0, 0, 0, 1, 1, 1, 3/2, 2, 2, 3, 3, 3, 3). Show the equation diagrammatically and sketch the curve with their respective control polygons if the curve is cubic (degree 3, order 4).

For the function f(x)4tan(2x), find the following:

What is the period of f

T=

B. List all x-intercepts of f in the interval [-π,π]

c. List all the equations of the vertical asymptotes in the interval [-π,π]

d. What transformations on the graph of y=tan(x) are used to find the graph of f(x)

show a graph of f(x)

7. Construct a LOAN AMORTIZATION schedule for a 3 year 5% loan of $100, 000.

Please show your calculations clearly and include calculated answers in the table below.

(Please only do this question if you are certain how to do it)

1a) In a certain year, 89% of all Caucasians in the U.S., 75% of all African-Americans, 75% of all Hispanics, and 74% of residents not classified into one of these groups used the Internet for e-mail. At that time, the U.S. population was 64% Caucasian, 11% African-American, and 14% Hispanic. What percentage of U.S. residents who used the Internet for e-mail were Hispanic? (Round your answer to the nearest whole percent.)

_____%

1b)According to a study in a medical journal, 202 of a sample of 5,990 middle-aged men had developed diabetes. It also found that men who were very active (burning about 3,500 calories daily) were a fifth as likely to develop diabetes compared with men who were sedentary. Assume that one in 12 middle-aged men is very active, and the rest are classified as sedentary. What is the probability that a middle-aged man with diabetes is very active? (Round your answer to four decimal places.)

______

1. Darla purchased a new car during a special sales promotion by the manufacturer. She secured a loan from the manufacturer in the amount of $24,000 at a rate of 4.5%/year compounded monthly. Her bank is now charging 6.8%/year compounded monthly for new car loans. Assuming that each loan would be amortized by 36 equal monthly installments, determine the amount of interest she would have paid at the end of 3 years for each loan. How much less will she have paid in interest payments over the life of the loan by borrowing from the manufacturer instead of her bank? (Round your answers to the nearest cent.)

Interest paid to manufacturer=

Interest paid to bank =

savings =

2. Joe secured a loan of $10,000 two years ago from a bank for use toward his college expenses. The bank charges interest at the rate of 3%/year compounded monthly on his loan. Now that he has graduated from college, Joe wishes to repay the loan by amortizing it through monthly payments over 13 years at the same interest rate. Find the size of the monthly payments he will be required to make. (Round your answer to the nearest cent.)

Part 1A: Why is ρ=8cos(φ) a sphere? (greek symbols are rho and phi). What is its center and radius? Algebra and trig will be needed.  

Part 1B: Given a right circular cone of radius R and height H, set up a triple integral in spherical coordinates to determine its volume. (Answer should be 1/3πr^2h)

Please clearly outline steps used to solve this problem. I have been stuck for a long time. Thank you in advance!