I have taught all levels of math from 7th grade to College Algebra. I taught for 37.5 years and retired 3 years ago, but because of need and my love of teaching, I have taught at least part of every semester since then. So what exactly does it mean to be retired?
Strontium- 90 has a half-life of 28 days.(a) A sample has a mass of 50 mg initially. Find a formula for the mass remaining after $ t $ days.(b) Find the mass remaining after 40 days.(c) How long does it take the sample to decay to a mass of 2 mg?(d) Sketch the graph of the mass function.
GEOMETRY A regulation NFL playing field (including the end zones) of length $ x $ and width $ y $ has a perimeter of $ 346\frac{2}{3} $ or $ \frac{1040}{3} $ yards.
(a) Draw a rectangle that gives a visual representation of the problem. Use the specified variables to label the sides of the rectangle.
(b) Show that the width of the rectangle is $ y = \frac{520}{3} - 3 $ and its area is $ A = x(\frac{530}{3} - x) $.
(c) Use a graphing utility to graph the area equation. Be sure to adjust your window settings.
(d) From the graph in part (c), estimate the dimensions of the rectangle that yield a maximum area.
(e) Use your school’s library, the Internet, or some other reference source to find the actual dimensions and area of a regulation NFL playing field and compare your findings with the results of part (d).
Evaluate the difference quotient for the given function. Simplify your answer.$f(x)=\frac{x+3}{x+1}, \quad \frac{f(x)-f(1)}{x-1}$
Finding Limits In Exercises $23-26,$ find the limits.
$f(x)=5-x, g(x)=x^{3}$$$(a) \lim _{x \rightarrow 1} f(x) \quad (b) \lim _{x \rightarrow 4} g(x) \quad(c) \lim _{x \rightarrow 1} g(f(x))$$
Sales Sales of a new model of compact disc player are approx- imated by the function $S(x)=1000-800 e^{-x},$ where $S(x)$ is in appropriate units and $x$ represents the number of years thedisc player has been on the market.(a) Find the sales during year 0.(b) In how many years will sales reach 500 units?(c) Will sales ever reach 1000 units?(d) Is there a limit on sales for this product? If so, whatis it?
Let $f(x)=x-3, \quad g(x)=\sqrt{x}, \quad h(x)=x^{3},$ and $j(x)=2 x .$ Express each of the functions in Exercises 11 and 12 as a composite involving one or more of $f, g, h,$ and $j$.a. $y=2 x-3 \quad$ b. $y=x^{3 / 2}$c. $y=x^{9} \quad$ d. $y=x-6$e. $y=2 \sqrt{x-3} \quad$ f. $y=\sqrt{x^{3}-3}$
f(x) = 3x^3 + 4x^2 - 9x - 10, the first part is to factor f(x) given that -1 is a zero.
6. Recall that in a standard deck of 52 cards, the cards aredivided into 4 suits, each with 13 ranks.a) What is the smallest number of cards we would need to takefrom the deck to guarantee that we will have a least 7 cards withthe same suit?b) what is the smallest number of cards we could need to takefrom the deck to guarantee that we will have at least 3 cards withthe same rank?c) what is the smallest number of cards we would need to takefrom the deck to guarantee that we will have at least 2 cards fromevery suit?
The function f(t) = 5(1.3)t determines the height of a sunflower (in inches) in terms of the number of weeks t since it was planted.Determine the average rate of change of the sunflower's height (in inches) with respect to the number of weeks since it was planted over the following time intervals.From t = 0 to t = 2 weeks.From t = 2 to t = 4 weeks.From t = 4 to t = 6 weeks.Based on your answers to part (a), which of the following are true? Select all that apply.The height of the sunflower is increasing at a decreasing rate on the interval 0 < t < 6.The graph of f is concave up on the interval 0 < t < 6.The height of the sunflower is increasing at an increasing rate on the interval 0 < t < 6.The graph of f is concave down on the interval 0 < t < 6.
If a certificate of deposit pays 15.2% simple interest, how muchwill $ 20,000 earn at the end of 26 weeks?
Find the coordinates of the holes for the graph of the givenfunction.R(x) = (x^2 - 3x) / (x^2 - 5x + 6) SHOW ALL WORKA) No holesB) (2, 0) and (3, 0) C) (3, 1)D) (0,0) and (3, 0)
Suppose Gwen wants to buy a car. The dealer offers a financingpackage consisting of a4.5%APR compounded monthly for a term of3years. Suppose Gwen wants her monthly payments to be at most$360.What is the maximum amount that she should finance?
